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href="#Enlightenment"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Enlightenment</span> </div> </a> <ul id="toc-Enlightenment-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Caloric_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Caloric_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Caloric theory</span> </div> </a> <ul id="toc-Caloric_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electromagnetic_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electromagnetic_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Electromagnetic theory</span> </div> </a> <ul id="toc-Electromagnetic_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantum_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Quantum theory</span> </div> </a> <ul id="toc-Quantum_theory-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Characteristics" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Characteristics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Characteristics</span> </div> </a> <button aria-controls="toc-Characteristics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Characteristics subsection</span> </button> <ul id="toc-Characteristics-sublist" class="vector-toc-list"> <li id="toc-Frequency" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Frequency"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Frequency</span> </div> </a> <ul id="toc-Frequency-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relationship_to_temperature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relationship_to_temperature"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Relationship to temperature</span> </div> </a> <ul id="toc-Relationship_to_temperature-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Appearance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Appearance"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Appearance</span> </div> </a> <ul id="toc-Appearance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reciprocity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reciprocity"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Reciprocity</span> </div> </a> <ul id="toc-Reciprocity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Fundamental_principles" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Fundamental_principles"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Fundamental principles</span> </div> </a> <button aria-controls="toc-Fundamental_principles-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Fundamental principles subsection</span> </button> <ul id="toc-Fundamental_principles-sublist" class="vector-toc-list"> <li id="toc-Electromagnetic_waves" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electromagnetic_waves"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Electromagnetic waves</span> </div> </a> <ul id="toc-Electromagnetic_waves-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Irradiation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Irradiation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Irradiation</span> </div> </a> <ul id="toc-Irradiation-sublist" class="vector-toc-list"> <li id="toc-Absorptivity_and_emissivity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Absorptivity_and_emissivity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Absorptivity and emissivity</span> </div> </a> <ul id="toc-Absorptivity_and_emissivity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reflectivity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Reflectivity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.2</span> <span>Reflectivity</span> </div> </a> <ul id="toc-Reflectivity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Transmissivity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Transmissivity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.3</span> <span>Transmissivity</span> </div> </a> <ul id="toc-Transmissivity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Radiation_intensity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Radiation_intensity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Radiation intensity</span> </div> </a> <ul id="toc-Radiation_intensity-sublist" class="vector-toc-list"> <li id="toc-Emissive_power" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Emissive_power"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.1</span> <span>Emissive power</span> </div> </a> <ul id="toc-Emissive_power-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Blackbody_radiation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Blackbody_radiation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Blackbody radiation</span> </div> </a> <ul id="toc-Blackbody_radiation-sublist" class="vector-toc-list"> <li id="toc-The_Planck_distribution" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#The_Planck_distribution"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.1</span> <span>The Planck distribution</span> </div> </a> <ul id="toc-The_Planck_distribution-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stefan-Boltzmann_law" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Stefan-Boltzmann_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.2</span> <span>Stefan-Boltzmann law</span> </div> </a> <ul id="toc-Stefan-Boltzmann_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wien's_displacement_law" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Wien's_displacement_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.3</span> <span>Wien's displacement law</span> </div> </a> <ul id="toc-Wien's_displacement_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Constants" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Constants"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.4</span> <span>Constants</span> </div> </a> <ul id="toc-Constants-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Variables" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Variables"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4.5</span> <span>Variables</span> </div> </a> <ul id="toc-Variables-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Emission_from_non-black_surfaces" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Emission_from_non-black_surfaces"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Emission from non-black surfaces</span> </div> </a> <ul id="toc-Emission_from_non-black_surfaces-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Heat_transfer_between_surfaces" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Heat_transfer_between_surfaces"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Heat transfer between surfaces</span> </div> </a> <ul id="toc-Heat_transfer_between_surfaces-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Solar_energy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Solar_energy"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Solar energy</span> </div> </a> <ul id="toc-Solar_energy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Incandescent_light_bulbs" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Incandescent_light_bulbs"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Incandescent light bulbs</span> </div> </a> <ul id="toc-Incandescent_light_bulbs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Thermal_comfort" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Thermal_comfort"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Thermal comfort</span> </div> </a> <ul id="toc-Thermal_comfort-sublist" class="vector-toc-list"> <li id="toc-Personal_heating" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Personal_heating"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3.1</span> <span>Personal heating</span> </div> </a> <ul id="toc-Personal_heating-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Personal_cooling" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Personal_cooling"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3.2</span> <span>Personal cooling</span> </div> </a> <ul id="toc-Personal_cooling-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Windows" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Windows"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Windows</span> </div> </a> <ul id="toc-Windows-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spacecraft" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spacecraft"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Spacecraft</span> </div> </a> <ul id="toc-Spacecraft-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nanostructures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nanostructures"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6</span> <span>Nanostructures</span> </div> </a> <ul id="toc-Nanostructures-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Health_and_safety" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Health_and_safety"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Health and safety</span> </div> </a> <button aria-controls="toc-Health_and_safety-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Health and safety subsection</span> </button> <ul id="toc-Health_and_safety-sublist" class="vector-toc-list"> <li id="toc-Metabolic_temperature_regulation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Metabolic_temperature_regulation"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Metabolic temperature regulation</span> </div> </a> <ul id="toc-Metabolic_temperature_regulation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Burns" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Burns"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Burns</span> </div> </a> <ul id="toc-Burns-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Near-field_radiative_heat_transfer" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Near-field_radiative_heat_transfer"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Near-field radiative heat transfer</span> </div> </a> <ul id="toc-Near-field_radiative_heat_transfer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc 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Available in 60 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-60" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">60 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Termiese_straling" title="Termiese straling – Afrikaans" lang="af" hreflang="af" data-title="Termiese straling" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D8%B4%D8%B9%D8%A7%D8%B9_%D8%AD%D8%B1%D8%A7%D8%B1%D9%8A" title="إشعاع حراري – Arabic" lang="ar" hreflang="ar" data-title="إشعاع حراري" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C4%B0stilik_%C5%9F%C3%BCalanmas%C4%B1" title="İstilik şüalanması – Azerbaijani" lang="az" hreflang="az" data-title="İstilik şüalanması" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A6%D0%B5%D0%BF%D0%BB%D0%B0%D0%B2%D0%BE%D0%B5_%D0%B2%D1%8B%D0%BF%D1%80%D0%B0%D0%BC%D0%B5%D0%BD%D1%8C%D0%B2%D0%B0%D0%BD%D0%BD%D0%B5" title="Цеплавое выпраменьванне – Belarusian" lang="be" hreflang="be" data-title="Цеплавое выпраменьванне" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BF%D0%BB%D0%B8%D0%BD%D0%BD%D0%BE_%D0%B8%D0%B7%D0%BB%D1%8A%D1%87%D0%B2%D0%B0%D0%BD%D0%B5" title="Топлинно излъчване – Bulgarian" lang="bg" hreflang="bg" data-title="Топлинно излъчване" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Radiaci%C3%B3_t%C3%A8rmica" title="Radiació tèrmica – Catalan" lang="ca" hreflang="ca" data-title="Radiació tèrmica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%C4%82%D1%88%C4%83%D0%BB%D0%BB%D0%B0_%D0%BF%D0%B0%D0%B9%C4%83%D1%80%D0%BA%D0%B0%D0%BB%D0%B0%D0%B2" title="Ăшăлла пайăркалав – Chuvash" lang="cv" hreflang="cv" data-title="Ăшăлла пайăркалав" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/S%C3%A1l%C3%A1n%C3%AD" title="Sálání – Czech" lang="cs" hreflang="cs" data-title="Sálání" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Varmestr%C3%A5ling" title="Varmestråling – Danish" lang="da" hreflang="da" data-title="Varmestråling" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/W%C3%A4rmestrahlung" title="Wärmestrahlung – German" lang="de" hreflang="de" data-title="Wärmestrahlung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Soojuskiirgus" title="Soojuskiirgus – Estonian" lang="et" hreflang="et" data-title="Soojuskiirgus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%98%CE%B5%CF%81%CE%BC%CE%B9%CE%BA%CE%AE_%CE%B1%CE%BA%CF%84%CE%B9%CE%BD%CE%BF%CE%B2%CE%BF%CE%BB%CE%AF%CE%B1" title="Θερμική ακτινοβολία – Greek" lang="el" hreflang="el" data-title="Θερμική ακτινοβολία" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Radiaci%C3%B3n_t%C3%A9rmica" title="Radiación térmica – Spanish" lang="es" hreflang="es" data-title="Radiación térmica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Varmoradiado" title="Varmoradiado – Esperanto" lang="eo" hreflang="eo" data-title="Varmoradiado" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Erradiazio_termiko" title="Erradiazio termiko – Basque" lang="eu" hreflang="eu" data-title="Erradiazio termiko" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A7%D8%A8%D8%B4_%DA%AF%D8%B1%D9%85%D8%A7%DB%8C%DB%8C" title="تابش گرمایی – Persian" lang="fa" hreflang="fa" data-title="تابش گرمایی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Rayonnement_thermique" title="Rayonnement thermique – French" lang="fr" hreflang="fr" data-title="Rayonnement thermique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%B4%EB%B3%B5%EC%82%AC" title="열복사 – Korean" lang="ko" hreflang="ko" data-title="열복사" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8B%D5%A5%D6%80%D5%B4%D5%A1%D5%B5%D5%AB%D5%B6_%D5%B3%D5%A1%D5%BC%D5%A1%D5%A3%D5%A1%D5%B5%D5%A9%D5%B8%D6%82%D5%B4" title="Ջերմային ճառագայթում – Armenian" lang="hy" hreflang="hy" data-title="Ջերմային ճառագայթում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%8A%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE_%E0%A4%B5%E0%A4%BF%E0%A4%95%E0%A4%BF%E0%A4%B0%E0%A4%A3" title="ऊष्मा विकिरण – Hindi" lang="hi" hreflang="hi" data-title="ऊष्मा विकिरण" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Toplinsko_zra%C4%8Denje" title="Toplinsko zračenje – Croatian" lang="hr" hreflang="hr" data-title="Toplinsko zračenje" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Radiasi_termal" title="Radiasi termal – Indonesian" lang="id" hreflang="id" data-title="Radiasi termal" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Radiazione_termica" title="Radiazione termica – Italian" lang="it" hreflang="it" data-title="Radiazione termica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A8%D7%99%D7%A0%D7%94_%D7%AA%D7%A8%D7%9E%D7%99%D7%AA" title="קרינה תרמית – Hebrew" lang="he" hreflang="he" data-title="קרינה תרמית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D1%8B%D0%BB%D1%83%D0%BB%D1%8B%D2%9B_%D1%81%D3%99%D1%83%D0%BB%D0%B5%D0%BB%D0%B5%D0%BD%D1%83" title="Жылулық сәулелену – Kazakh" lang="kk" hreflang="kk" data-title="Жылулық сәулелену" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/%C5%A0iluminis_spinduliavimas" title="Šiluminis spinduliavimas – Lithuanian" lang="lt" hreflang="lt" data-title="Šiluminis spinduliavimas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Irradiazion" title="Irradiazion – Lombard" lang="lmo" hreflang="lmo" data-title="Irradiazion" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/H%C5%91m%C3%A9rs%C3%A9kleti_sug%C3%A1rz%C3%A1s" title="Hőmérsékleti sugárzás – Hungarian" lang="hu" hreflang="hu" data-title="Hőmérsékleti sugárzás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BF%D0%BB%D0%B8%D0%BD%D1%81%D0%BA%D0%BE_%D0%B7%D1%80%D0%B0%D1%87%D0%B5%D1%9A%D0%B5" title="Топлинско зрачење – Macedonian" lang="mk" hreflang="mk" data-title="Топлинско зрачење" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%89%E0%A4%B7%E0%A5%8D%E0%A4%A3%E0%A4%A4%E0%A4%BE_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B0%E0%A4%A3" title="उष्णता प्रारण – Marathi" lang="mr" hreflang="mr" data-title="उष्णता प्रारण" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sinaran_terma" title="Sinaran terma – Malay" lang="ms" hreflang="ms" data-title="Sinaran terma" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%94%D1%83%D0%BB%D0%B0%D0%B0%D0%BD%D1%8B_%D1%86%D0%B0%D1%86%D1%80%D0%B0%D0%B3" title="Дулааны цацраг – Mongolian" lang="mn" hreflang="mn" data-title="Дулааны цацраг" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%95%E1%80%B0%E1%80%96%E1%80%BC%E1%80%AC%E1%80%80%E1%80%B0%E1%80%B8%E1%80%81%E1%80%BC%E1%80%84%E1%80%BA%E1%80%B8" title="အပူဖြာကူးခြင်း – Burmese" lang="my" hreflang="my" data-title="အပူဖြာကူးခြင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Warmtestraling" title="Warmtestraling – Dutch" lang="nl" hreflang="nl" data-title="Warmtestraling" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%86%B1%E6%94%BE%E5%B0%84" title="熱放射 – Japanese" lang="ja" hreflang="ja" data-title="熱放射" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Varmestr%C3%A5ling" title="Varmestråling – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Varmestråling" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Varmestr%C3%A5ling" title="Varmestråling – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Varmestråling" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Issiqlik_nurlanish" title="Issiqlik nurlanish – Uzbek" lang="uz" hreflang="uz" data-title="Issiqlik nurlanish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Anrajament" title="Anrajament – Piedmontese" lang="pms" hreflang="pms" data-title="Anrajament" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Promieniowanie_cieplne" title="Promieniowanie cieplne – Polish" lang="pl" hreflang="pl" data-title="Promieniowanie cieplne" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Irradia%C3%A7%C3%A3o_t%C3%A9rmica" title="Irradiação térmica – Portuguese" lang="pt" hreflang="pt" data-title="Irradiação térmica" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Radia%C8%9Bie_termic%C4%83" title="Radiație termică – Romanian" lang="ro" hreflang="ro" data-title="Radiație termică" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BF%D0%BB%D0%BE%D0%B2%D0%BE%D0%B5_%D0%B8%D0%B7%D0%BB%D1%83%D1%87%D0%B5%D0%BD%D0%B8%D0%B5" title="Тепловое излучение – Russian" lang="ru" hreflang="ru" data-title="Тепловое излучение" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AD%E0%B7%8F%E0%B6%B4_%E0%B7%80%E0%B7%92%E0%B6%9A%E0%B7%92%E0%B6%BB%E0%B6%AB%E0%B6%BA" title="තාප විකිරණය – Sinhala" lang="si" hreflang="si" data-title="තාප විකිරණය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Thermal_radiation" title="Thermal radiation – Simple English" lang="en-simple" hreflang="en-simple" data-title="Thermal radiation" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/S%C3%A1lanie" title="Sálanie – Slovak" lang="sk" hreflang="sk" data-title="Sálanie" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Toplotno_sevanje" title="Toplotno sevanje – Slovenian" lang="sl" hreflang="sl" data-title="Toplotno sevanje" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BF%D0%BB%D0%BE%D1%82%D0%BD%D0%BE_%D0%B7%D1%80%D0%B0%D1%87%D0%B5%D1%9A%D0%B5" title="Топлотно зрачење – Serbian" lang="sr" hreflang="sr" data-title="Топлотно зрачење" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Zra%C4%8Denje_toplote" title="Zračenje toplote – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Zračenje toplote" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/L%C3%A4mp%C3%B6s%C3%A4teily" title="Lämpösäteily – Finnish" lang="fi" hreflang="fi" data-title="Lämpösäteily" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/V%C3%A4rmestr%C3%A5lning" title="Värmestrålning – Swedish" lang="sv" hreflang="sv" data-title="Värmestrålning" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AF%86%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AF%8D%E0%AE%B5%E0%AF%80%E0%AE%9A%E0%AE%B2%E0%AF%8D" title="வெப்பக் கதிர்வீசல் – Tamil" lang="ta" hreflang="ta" data-title="வெப்பக் கதிர்வீசல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%81%E0%B8%9C%E0%B9%88%E0%B8%A3%E0%B8%B1%E0%B8%87%E0%B8%AA%E0%B8%B5%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%A3%E0%B9%89%E0%B8%AD%E0%B8%99" title="การแผ่รังสีความร้อน – Thai" lang="th" hreflang="th" data-title="การแผ่รังสีความร้อน" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A2%D0%BE%D0%B1%D0%B8%D1%88%D0%B8_%D0%B3%D0%B0%D1%80%D0%BC%D0%BE%D3%A3" title="Тобиши гармоӣ – Tajik" lang="tg" hreflang="tg" data-title="Тобиши гармоӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Is%C4%B1_radyasyonu" title="Isı radyasyonu – Turkish" lang="tr" hreflang="tr" data-title="Isı radyasyonu" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BF%D0%BB%D0%BE%D0%B2%D0%B5_%D0%B2%D0%B8%D0%BF%D1%80%D0%BE%D0%BC%D1%96%D0%BD%D1%8E%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F" title="Теплове випромінювання – Ukrainian" lang="uk" hreflang="uk" data-title="Теплове випромінювання" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/B%E1%BB%A9c_x%E1%BA%A1_nhi%E1%BB%87t" title="Bức xạ nhiệt – Vietnamese" lang="vi" hreflang="vi" data-title="Bức xạ nhiệt" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%83%AD%E8%BE%90%E5%B0%84" title="热辐射 – Wu" lang="wuu" hreflang="wuu" data-title="热辐射" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%86%B1%E8%BC%BB%E5%B0%84" title="熱輻射 – Cantonese" lang="yue" hreflang="yue" data-title="熱輻射" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%86%B1%E8%BC%BB%E5%B0%84" title="熱輻射 – Chinese" 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Electromagnetic radiation generated by the thermal motion of particles</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Heat radiation" redirects here. Not to be confused with <a href="/wiki/Heat-Ray_(disambiguation)" class="mw-disambig" title="Heat-Ray (disambiguation)">Heat-Ray (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Hot_metalwork.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Hot_metalwork.jpg/220px-Hot_metalwork.jpg" decoding="async" width="220" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Hot_metalwork.jpg/330px-Hot_metalwork.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Hot_metalwork.jpg/440px-Hot_metalwork.jpg 2x" data-file-width="1600" data-file-height="1163" /></a><figcaption>Thermal radiation in visible light can be seen on this hot metalwork. Its emission in the <a href="/wiki/Infrared" title="Infrared">infrared</a> is invisible to the human eye. <a href="/wiki/Thermographic_camera" class="mw-redirect" title="Thermographic camera">Infrared cameras</a> are capable of capturing this infrared emission (see <i><a href="/wiki/Thermography" title="Thermography">Thermography</a></i>).</figcaption></figure> <p><b>Thermal radiation</b> is <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> emitted by the <a href="/wiki/Thermal_motion" class="mw-redirect" title="Thermal motion">thermal motion</a> of particles in <a href="/wiki/Matter" title="Matter">matter</a>. All matter with a <a href="/wiki/Temperature" title="Temperature">temperature</a> greater than <a href="/wiki/Absolute_zero" title="Absolute zero">absolute zero</a> emits thermal radiation. The emission of energy arises from a combination of electronic, molecular, and lattice oscillations in a material.<sup id="cite_ref-:9_1-0" class="reference"><a href="#cite_note-:9-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Kinetic_energy" title="Kinetic energy">Kinetic energy</a> is converted to <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> due to <a href="/wiki/Larmor_formula" title="Larmor formula">charge-acceleration</a> or <a href="/wiki/Dipole" title="Dipole">dipole</a> oscillation. At <a href="/wiki/Room_temperature" title="Room temperature">room temperature</a>, most of the emission is in the <a href="/wiki/Infrared" title="Infrared">infrared</a> (IR) spectrum,<sup id="cite_ref-:1_2-0" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 73–86">: 73–86 </span></sup> though above around 525 °C (977 °F) enough of it becomes <a href="/wiki/Visible_spectrum" title="Visible spectrum">visible</a> for the matter to visibly glow. This visible glow is called <b>incandescence</b>. Thermal radiation is one of the fundamental mechanisms of <a href="/wiki/Heat_transfer" title="Heat transfer">heat transfer</a>, along with <a href="/wiki/Thermal_conduction" title="Thermal conduction">conduction</a> and <a href="/wiki/Convection_(heat_transfer)" title="Convection (heat transfer)">convection</a>. </p><p>The primary method by which the <a href="/wiki/Sun" title="Sun">Sun</a> transfers heat to the <a href="/wiki/Earth" title="Earth">Earth</a> is thermal radiation. This energy is partially absorbed and scattered in the <a href="/wiki/Atmosphere" title="Atmosphere">atmosphere</a>, the latter process being the reason why the sky is visibly blue.<sup id="cite_ref-:3_3-0" class="reference"><a href="#cite_note-:3-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Much of the Sun's radiation transmits through the atmosphere to the surface where it is either absorbed or reflected. </p><p>Thermal radiation can be used to detect objects or phenomena normally invisible to the human eye. <a href="/wiki/Infrared_camera" class="mw-redirect" title="Infrared camera">Thermographic cameras</a> create an image by sensing infrared radiation. These images can represent the temperature gradient of a scene and are commonly used to locate objects at a higher temperature than their surroundings. In a dark environment where visible light is at low levels, infrared images can be used to locate animals or people due to their body temperature. <a href="/wiki/Cosmic_microwave_background_radiation" class="mw-redirect" title="Cosmic microwave background radiation">Cosmic microwave background radiation</a> is another example of thermal radiation. </p><p><a href="/wiki/Black-body_radiation" title="Black-body radiation">Blackbody radiation</a> is a concept used to analyze thermal radiation in idealized systems. This model applies if a radiation object meets the physical characteristics of a <a href="/wiki/Black_body" title="Black body">black body</a> in <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>.<sup id="cite_ref-:8_4-0" class="reference"><a href="#cite_note-:8-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 278">: 278 </span></sup> <a href="/wiki/Planck%27s_law" title="Planck's law">Planck's law</a> describes the spectrum of blackbody radiation, and relates the radiative heat flux from a body to its temperature. <a href="/wiki/Wien%27s_displacement_law" title="Wien's displacement law">Wien's displacement law</a> determines the most likely frequency of the emitted radiation, and the <a href="/wiki/Stefan%E2%80%93Boltzmann_law" title="Stefan–Boltzmann law">Stefan–Boltzmann law</a> gives the radiant intensity.<sup id="cite_ref-:8_4-1" class="reference"><a href="#cite_note-:8-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 280">: 280 </span></sup> Where blackbody radiation is not an accurate approximation, emission and absorption can be modeled using <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a> (QED).<sup id="cite_ref-:9_1-1" class="reference"><a href="#cite_note-:9-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermal radiation is the emission of <a href="/wiki/Electromagnetic_waves" class="mw-redirect" title="Electromagnetic waves">electromagnetic waves</a> from all matter that has a <a href="/wiki/Temperature" title="Temperature">temperature</a> greater than <a href="/wiki/Absolute_zero" title="Absolute zero">absolute zero</a>.<sup id="cite_ref-blundell_5-0" class="reference"><a href="#cite_note-blundell-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_2-1" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Thermal radiation reflects the conversion of <a href="/wiki/Thermal_energy" title="Thermal energy">thermal energy</a> into <a href="/wiki/Electromagnetic_energy" class="mw-redirect" title="Electromagnetic energy">electromagnetic energy</a>. Thermal energy is the kinetic energy of random movements of <a href="/wiki/Atom" title="Atom">atoms</a> and <a href="/wiki/Molecule" title="Molecule">molecules</a> in matter. It is present in all matter of nonzero temperature. These atoms and molecules are composed of charged particles, i.e., <a href="/wiki/Proton" title="Proton">protons</a> and <a href="/wiki/Electron" title="Electron">electrons</a>. The kinetic interactions among matter particles result in charge acceleration and <a href="/wiki/Dipole" title="Dipole">dipole</a> oscillation. This results in the electrodynamic generation of coupled electric and magnetic fields, resulting in the emission of <a href="/wiki/Photon" title="Photon">photons</a>, radiating energy away from the body. Electromagnetic radiation, including visible light, will propagate indefinitely in <a href="/wiki/Vacuum" title="Vacuum">vacuum</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Emissivity_differences_on_Chopfab_beer_can.png" class="mw-file-description"><img alt="Beer can thermal imaging" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Emissivity_differences_on_Chopfab_beer_can.png/220px-Emissivity_differences_on_Chopfab_beer_can.png" decoding="async" width="220" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Emissivity_differences_on_Chopfab_beer_can.png/330px-Emissivity_differences_on_Chopfab_beer_can.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Emissivity_differences_on_Chopfab_beer_can.png/440px-Emissivity_differences_on_Chopfab_beer_can.png 2x" data-file-width="640" data-file-height="960" /></a><figcaption>Beer can being imaged by a FLIR thermal camera to demonstrate temperature differences caused by emissivity</figcaption></figure> <p>The characteristics of thermal radiation depend on various properties of the surface from which it is emanating, including its temperature and its spectral <a href="/wiki/Emissivity" title="Emissivity">emissivity</a>, as expressed by <a href="/wiki/Kirchhoff%27s_law_of_thermal_radiation" title="Kirchhoff's law of thermal radiation">Kirchhoff's law</a>.<sup id="cite_ref-blundell_5-1" class="reference"><a href="#cite_note-blundell-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The radiation is not monochromatic, i.e., it does not consist of only a single frequency, but comprises a continuous spectrum of photon energies, its characteristic spectrum. If the radiating body and its surface are in <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a> and the surface has perfect absorptivity at all wavelengths, it is characterized as a <a href="/wiki/Black_body" title="Black body">black body</a>. A black body is also a perfect emitter. The radiation of such perfect emitters is called <a href="/wiki/Black-body_radiation" title="Black-body radiation">black-body radiation</a>. The ratio of any body's emission relative to that of a black body is the body's <a href="/wiki/Emissivity" title="Emissivity">emissivity</a>, so a black body has an emissivity of one. </p><p>Absorptivity, <a href="/wiki/Reflectivity" class="mw-redirect" title="Reflectivity">reflectivity</a>, and emissivity of all bodies are dependent on the wavelength of the radiation. Due to <a href="/wiki/Reciprocity_(electromagnetism)" title="Reciprocity (electromagnetism)">reciprocity</a>, absorptivity and emissivity for any particular wavelength are equal at equilibrium – a good absorber is necessarily a good emitter, and a poor absorber is a poor emitter. The temperature determines the wavelength distribution of the electromagnetic radiation. </p><p>The distribution of power that a black body emits with varying frequency is described by <a href="/wiki/Planck%27s_law" title="Planck's law">Planck's law</a>. At any given temperature, there is a frequency <i>f</i><sub>max</sub> at which the power emitted is a maximum. Wien's displacement law, and the fact that the frequency is inversely proportional to the wavelength, indicates that the peak frequency <i>f</i><sub>max</sub> is proportional to the absolute temperature <i>T</i> of the black body. The photosphere of the sun, at a temperature of approximately 6000 K, emits radiation principally in the (human-)visible portion of the electromagnetic spectrum. Earth's atmosphere is partly transparent to visible light, and the light reaching the surface is absorbed or reflected. Earth's surface emits the absorbed radiation, approximating the behavior of a black body at 300 K with spectral peak at <i>f</i><sub>max</sub>. At these lower frequencies, the atmosphere is largely opaque and radiation from Earth's surface is absorbed or scattered by the atmosphere. Though about 10% of this radiation escapes into space, most is absorbed and then re-emitted by atmospheric gases. It is this spectral selectivity of the atmosphere that is responsible for the planetary <a href="/wiki/Greenhouse_effect" title="Greenhouse effect">greenhouse effect</a>, contributing to <a href="/wiki/Global_warming" class="mw-redirect" title="Global warming">global warming</a> and <a href="/wiki/Climate_change_(general_concept)" class="mw-redirect" title="Climate change (general concept)">climate change in general</a> (but also critically contributing to climate stability when the composition and properties of the atmosphere are not changing). </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ancient_Greece">Ancient Greece</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=3" title="Edit section: Ancient Greece"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Burning_glass" title="Burning glass">Burning glasses</a> are known to date back to about 700 BC. One of the first accurate mentions of burning glasses appears in <a href="/wiki/Aristophanes" title="Aristophanes">Aristophanes</a>'s comedy, <i><a href="/wiki/The_Clouds" title="The Clouds">The Clouds</a></i>, written in 423 BC.<sup id="cite_ref-:4_6-0" class="reference"><a href="#cite_note-:4-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> According to the <a href="/wiki/Archimedes%27_heat_ray" title="Archimedes' heat ray">Archimedes' heat ray</a> anecdote, <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> is purported to have developed mirrors to concentrate heat rays in order to burn attacking <a href="/wiki/Roman_navy" title="Roman navy">Roman ships</a> during the <a href="/wiki/Siege_of_Syracuse_(213%E2%80%93212_BC)" title="Siege of Syracuse (213–212 BC)">Siege of Syracuse</a> (<abbr>c.</abbr> 213–212 BC), but no sources from the time have been confirmed.<sup id="cite_ref-:4_6-1" class="reference"><a href="#cite_note-:4-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <i>Catoptrics</i> is a book attributed to <a href="/wiki/Euclid" title="Euclid">Euclid</a> on how to focus light in order to produce heat, but the book might have been written in 300 AD.<sup id="cite_ref-:4_6-2" class="reference"><a href="#cite_note-:4-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Renaissance">Renaissance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=4" title="Edit section: Renaissance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>During the Renaissance, <a href="/wiki/Santorio_Santorio" title="Santorio Santorio">Santorio Santorio</a> came up with one of the earliest <a href="/wiki/Thermoscope" title="Thermoscope">thermoscopes</a>. In 1612 he published his results on the heating effects from the Sun, and his attempts to measure heat from the Moon.<sup id="cite_ref-:4_6-3" class="reference"><a href="#cite_note-:4-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Earlier, in 1589, <a href="/wiki/Giambattista_della_Porta" title="Giambattista della Porta">Giambattista della Porta</a> reported on the heat felt on his face, emitted by a remote candle and facilitated by a concave metallic mirror. He also reported the cooling felt from a solid ice block.<sup id="cite_ref-:4_6-4" class="reference"><a href="#cite_note-:4-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Della Porta's experiment would be replicated many times with increasing accuracy. It was replicated by astronomers <a href="/wiki/Giovanni_Antonio_Magini" title="Giovanni Antonio Magini">Giovanni Antonio Magini</a> and <a href="/wiki/Christopher_Heydon" title="Christopher Heydon">Christopher Heydon</a> in 1603, and supplied instructions for <a href="/wiki/Rudolf_II,_Holy_Roman_Emperor" title="Rudolf II, Holy Roman Emperor">Rudolf II, Holy Roman Emperor</a> who performed it in 1611. In 1660, della Porta's experiment was updated by the <a href="/wiki/Accademia_del_Cimento" title="Accademia del Cimento">Accademia del Cimento</a> using a thermometer invented by <a href="/wiki/Ferdinand_II,_Grand_Duke_of_Tuscany" class="mw-redirect" title="Ferdinand II, Grand Duke of Tuscany">Ferdinand II, Grand Duke of Tuscany</a>.<sup id="cite_ref-:4_6-5" class="reference"><a href="#cite_note-:4-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Enlightenment">Enlightenment</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=5" title="Edit section: Enlightenment"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1761, <a href="/wiki/Benjamin_Franklin" title="Benjamin Franklin">Benjamin Franklin</a> wrote a letter describing his experiments on the relationship between color and heat absorption.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> He found that darker color clothes got hotter when exposed to sunlight than lighter color clothes. One experiment he performed consisted of placing square pieces of cloth of various colors out in the snow on a sunny day. He waited some time and then measured that the black pieces sank furthest into the snow of all the colors, indicating that they got the hottest and melted the most snow. </p> <div class="mw-heading mw-heading3"><h3 id="Caloric_theory">Caloric theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=6" title="Edit section: Caloric theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Caloric_theory" title="Caloric theory">Caloric theory</a></div> <p><a href="/wiki/Antoine_Lavoisier" title="Antoine Lavoisier">Antoine Lavoisier</a> considered that radiation of heat was concerned with the condition of the surface of a physical body rather than the material of which it was composed.<sup id="cite_ref-:22_8-0" class="reference"><a href="#cite_note-:22-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Lavoisier described a poor radiator to be a substance with a polished or smooth surface as it possessed its molecules lying in a plane closely bound together thus creating a surface layer of caloric fluid which insulated the release of the rest within.<sup id="cite_ref-:22_8-1" class="reference"><a href="#cite_note-:22-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> He described a good radiator to be a substance with a rough surface as only a small proportion of molecules held caloric in within a given plane, allowing for greater escape from within.<sup id="cite_ref-:22_8-2" class="reference"><a href="#cite_note-:22-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Benjamin_Thompson" title="Benjamin Thompson">Count Rumford</a> would later cite this explanation of caloric movement as insufficient to explain the radiation of cold, which became a point of contention for the theory as a whole.<sup id="cite_ref-:22_8-3" class="reference"><a href="#cite_note-:22-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>In his first memoir, <a href="/wiki/Augustin-Jean_Fresnel" title="Augustin-Jean Fresnel">Augustin-Jean Fresnel</a> responded to a view he extracted from a French translation of <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>'s <i><a href="/wiki/Optics" title="Optics">Optics</a></i>. He says that Newton imagined particles of light traversing space uninhibited by the caloric medium filling it, and refutes this view (never actually held by Newton) by saying that a body under illumination would increase indefinitely in heat.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Marc-Auguste_Pictet" title="Marc-Auguste Pictet">Marc-Auguste Pictet</a>'s famous <a href="/wiki/Pictet%27s_experiment" title="Pictet's experiment">experiment of 1790</a>, it was reported that a thermometer detected a lower temperature when a set of mirrors were used to focus "frigorific rays" from a cold object.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>In 1791, <a href="/wiki/Pierre_Prevost_(physicist)" title="Pierre Prevost (physicist)">Pierre Prevost</a> a colleague of Pictet, introduced the concept of <a href="/wiki/Radiative_equilibrium" title="Radiative equilibrium">radiative equilibrium</a>, wherein all objects both radiate and absorb heat.<sup id="cite_ref-:5_11-0" class="reference"><a href="#cite_note-:5-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> When an object is cooler than its surroundings, it absorbs more heat than it emits, causing its temperature to increase until it reaches equilibrium. Even at equilibrium, it continues to radiate heat, balancing absorption and emission.<sup id="cite_ref-:5_11-1" class="reference"><a href="#cite_note-:5-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>The discovery of infrared radiation is ascribed to astronomer <a href="/wiki/William_Herschel" title="William Herschel">William Herschel</a>. Herschel published his results in 1800 before the <a href="/wiki/Royal_Society_of_London" class="mw-redirect" title="Royal Society of London">Royal Society of London</a>. Herschel used a <a href="/wiki/Triangular_prism_(optics)" class="mw-redirect" title="Triangular prism (optics)">prism</a> to <a href="/wiki/Refract" class="mw-redirect" title="Refract">refract</a> light from the <a href="/wiki/Sun" title="Sun">sun</a> and detected the calorific rays, beyond the <a href="/wiki/Red" title="Red">red</a> part of the spectrum, by an increase in the temperature recorded on a <a href="/wiki/Thermometer" title="Thermometer">thermometer</a> in that region.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Electromagnetic_theory">Electromagnetic theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=7" title="Edit section: Electromagnetic theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At the end of the 19th century it was shown that the transmission of light or of <a href="/wiki/Radiant_heat" class="mw-redirect" title="Radiant heat">radiant heat</a> was allowed by the propagation of <a href="/wiki/Electromagnetic_waves" class="mw-redirect" title="Electromagnetic waves">electromagnetic waves</a>.<sup id="cite_ref-hsu_14-0" class="reference"><a href="#cite_note-hsu-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Television" title="Television">Television</a> and <a href="/wiki/Radio" title="Radio">radio</a> broadcasting waves are types of electromagnetic waves with specific <a href="/wiki/Wavelengths" class="mw-redirect" title="Wavelengths">wavelengths</a>.<sup id="cite_ref-becker_15-0" class="reference"><a href="#cite_note-becker-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> All <a href="/wiki/Electromagnetic_waves" class="mw-redirect" title="Electromagnetic waves">electromagnetic waves</a> travel at the same speed; therefore, shorter <a href="/wiki/Wavelengths" class="mw-redirect" title="Wavelengths">wavelengths</a> are associated with high frequencies. All bodies generate and receive electromagnetic waves at the expense of heat exchange.<sup id="cite_ref-becker_15-1" class="reference"><a href="#cite_note-becker-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>In 1860, <a href="/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff">Gustav Kirchhoff</a> published a mathematical description of <a href="/wiki/Thermal_equilibrium" title="Thermal equilibrium">thermal equilibrium</a> (i.e. <a href="/wiki/Kirchhoff%27s_law_of_thermal_radiation" title="Kirchhoff's law of thermal radiation">Kirchhoff's law of thermal radiation</a>).<sup id="cite_ref-:7_16-0" class="reference"><a href="#cite_note-:7-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 275–301">: 275–301 </span></sup> By 1884 the emissive power of a perfect blackbody was inferred by <a href="/wiki/Josef_Stefan" title="Josef Stefan">Josef Stefan</a> using <a href="/wiki/John_Tyndall" title="John Tyndall">John Tyndall</a>'s experimental measurements, and derived by <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Ludwig Boltzmann</a> from fundamental statistical principles.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> This relation is known as <a href="/wiki/Stefan%E2%80%93Boltzmann_law" title="Stefan–Boltzmann law">Stefan–Boltzmann law</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Quantum_theory">Quantum theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=8" title="Edit section: Quantum theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Old_quantum_theory" title="Old quantum theory">Old quantum theory</a></div><figure typeof="mw:File/Thumb"><a href="/wiki/File:Max_Planck_1901.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Max_Planck_1901.GIF/140px-Max_Planck_1901.GIF" decoding="async" width="140" height="214" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Max_Planck_1901.GIF/209px-Max_Planck_1901.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Max_Planck_1901.GIF/279px-Max_Planck_1901.GIF 2x" data-file-width="301" data-file-height="461" /></a><figcaption>Max Planck in 1901</figcaption></figure><p>The microscopic theory of radiation is best known as the <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum theory</a> and was first offered by <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> in 1900.<sup id="cite_ref-hsu_14-1" class="reference"><a href="#cite_note-hsu-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> According to this theory, energy emitted by a radiator is not continuous but is in the form of quanta. Planck noted that energy was emitted in quantas of frequency of vibration similarly to the wave theory.<sup id="cite_ref-:6_18-0" class="reference"><a href="#cite_note-:6-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> The energy <i>E</i> an electromagnetic wave in vacuum is found by the expression <i>E</i> = <i>hf</i>, where <i>h</i> is the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a> and <i>f</i> is its frequency. </p><p>Bodies at higher temperatures emit radiation at higher frequencies with an increasing energy per quantum. While the propagation of electromagnetic waves of all wavelengths is often referred as "radiation", thermal radiation is often constrained to the visible and infrared regions. For engineering purposes, it may be stated that thermal radiation is a form of electromagnetic radiation which varies on the nature of a surface and its temperature.<sup id="cite_ref-hsu_14-2" class="reference"><a href="#cite_note-hsu-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Radiation waves may travel in unusual patterns compared to conduction <a href="/wiki/Heat_flow" class="mw-redirect" title="Heat flow">heat flow</a>. Radiation allows waves to travel from a heated body through a cold non-absorbing or partially absorbing medium and reach a warmer body again.<sup id="cite_ref-hsu_14-3" class="reference"><a href="#cite_note-hsu-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> An example is the case of the radiation waves that travel from the Sun to the Earth. </p> <div class="mw-heading mw-heading2"><h2 id="Characteristics">Characteristics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=9" title="Edit section: Characteristics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Frequency">Frequency</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=10" title="Edit section: Frequency"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:204px;max-width:204px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Human-Infrared.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Human-Infrared.jpg/200px-Human-Infrared.jpg" decoding="async" width="200" height="121" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Human-Infrared.jpg/300px-Human-Infrared.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/4/44/Human-Infrared.jpg 2x" data-file-width="355" data-file-height="214" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:162px;max-width:162px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Human-Visible.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Human-Visible.jpg/160px-Human-Visible.jpg" decoding="async" width="160" height="117" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Human-Visible.jpg/240px-Human-Visible.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/9/9b/Human-Visible.jpg 2x" data-file-width="289" data-file-height="211" /></a></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">A comparison of a thermal image (top) and an ordinary photograph (bottom). The plastic bag is mostly transparent to long-wavelength infrared, but the man's glasses are opaque.</div></div></div></div> <p>Thermal radiation emitted by a body at any temperature consists of a wide range of frequencies. The frequency distribution is given by <a href="/wiki/Planck%27s_law_of_black-body_radiation" class="mw-redirect" title="Planck's law of black-body radiation">Planck's law of black-body radiation</a> for an idealized emitter as shown in the diagram at top. </p><p>The dominant frequency (or color) range of the emitted radiation shifts to higher frequencies as the temperature of the emitter increases. For example, a <i>red hot</i> object radiates mainly in the long wavelengths (red and orange) of the visible band. If it is heated further, it also begins to emit discernible amounts of green and blue light, and the spread of frequencies in the entire visible range cause it to appear white to the human eye; it is <i>white hot</i>. Even at a white-hot temperature of 2000 K, 99% of the energy of the radiation is still in the infrared. This is determined by <a href="/wiki/Wien%27s_displacement_law" title="Wien's displacement law">Wien's displacement law</a>. In the diagram the peak value for each curve moves to the left as the temperature increases. </p> <table class="wikitable"> <caption>Subjective color to the eye of a black body thermal radiator </caption> <tbody><tr> <th>°C (°F) </th> <th>Subjective color<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </th></tr> <tr> <td>480 °C (896 °F)</td> <td>faint red glow </td></tr> <tr> <td>580 °C (1,076 °F)</td> <td>dark red </td></tr> <tr> <td>730 °C (1,350 °F)</td> <td>bright red, slightly orange </td></tr> <tr> <td>930 °C (1,710 °F)</td> <td>bright orange </td></tr> <tr> <td>1,100 °C (2,010 °F)</td> <td>pale yellowish orange </td></tr> <tr> <td>1,300 °C (2,370 °F)</td> <td>yellowish white </td></tr> <tr> <td>> 1,400 °C (2,550 °F)</td> <td>white (yellowish if seen from a distance through atmosphere) </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Relationship_to_temperature">Relationship to temperature</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=11" title="Edit section: Relationship to temperature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The total radiation intensity of a black body rises as the fourth power of the absolute temperature, as expressed by the <a href="/wiki/Stefan%E2%80%93Boltzmann_law" title="Stefan–Boltzmann law">Stefan–Boltzmann law</a>. A kitchen oven, at a temperature about double room temperature on the absolute temperature scale (600 K vs. 300 K) radiates 16 times as much power per unit area. An object at the temperature of the filament in an <a href="/wiki/Incandescent_light_bulb" title="Incandescent light bulb">incandescent light bulb</a>—roughly 3000 K, or 10 times room temperature—radiates 10,000 times as much energy per unit area. </p><p>As for <a href="/wiki/Photon_statistics" title="Photon statistics">photon statistics</a>, thermal light obeys <a href="/wiki/Photon_statistics#Super-Poissonian_light" title="Photon statistics">Super-Poissonian statistics</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Appearance">Appearance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=12" title="Edit section: Appearance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When the temperature of a body is high enough, its thermal radiation spectrum becomes strong enough in the <a href="/wiki/Visible_range" class="mw-redirect" title="Visible range">visible range</a> to visibly glow. The visible component of thermal radiation is sometimes called <i>incandescence</i>,<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> though this term can also refer to thermal radiation in general. The term derive from the Latin verb <span title="Latin-language text"><i lang="la">incandescere</i></span>, 'to glow white'.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>In practice, virtually all solid or liquid substances start to glow around 798 K (525 °C; 977 °F), with a mildly dull red color, whether or not a chemical reaction takes place that produces light as a result of an exothermic process. This limit is called the <a href="/wiki/Draper_point" title="Draper point">Draper point</a>. The incandescence does not vanish below that temperature, but it is too weak in the visible spectrum to be perceptible. </p> <div class="mw-heading mw-heading3"><h3 id="Reciprocity">Reciprocity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=13" title="Edit section: Reciprocity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The rate of electromagnetic radiation emitted by a body at a given frequency is proportional to the rate that the body absorbs radiation at that frequency, a property known as <a href="/wiki/Reciprocity_(electromagnetism)" title="Reciprocity (electromagnetism)">reciprocity</a>. Thus, a surface that absorbs more red light thermally radiates more red light. This principle applies to all properties of the wave, including <a href="/wiki/Wavelength" title="Wavelength">wavelength</a> (color), direction, <a href="/wiki/Polarization_(waves)" title="Polarization (waves)">polarization</a>, and even <a href="/wiki/Coherence_(physics)" title="Coherence (physics)">coherence</a>. It is therefore possible to have thermal radiation which is polarized, coherent, and directional; though polarized and coherent sources are fairly rare in nature. </p> <div class="mw-heading mw-heading2"><h2 id="Fundamental_principles">Fundamental principles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=14" title="Edit section: Fundamental principles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermal radiation is one of the three principal mechanisms of <a href="/wiki/Heat_transfer" title="Heat transfer">heat transfer</a>. It entails the emission of a spectrum of electromagnetic radiation due to an object's temperature. Other mechanisms are <a href="/wiki/Convection" title="Convection">convection</a> and <a href="/wiki/Heat_conduction" class="mw-redirect" title="Heat conduction">conduction</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Electromagnetic_waves">Electromagnetic waves</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=15" title="Edit section: Electromagnetic waves"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Electromagnetic_wave_EN.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Electromagnetic_wave_EN.svg/220px-Electromagnetic_wave_EN.svg.png" decoding="async" width="220" height="116" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Electromagnetic_wave_EN.svg/330px-Electromagnetic_wave_EN.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Electromagnetic_wave_EN.svg/440px-Electromagnetic_wave_EN.svg.png 2x" data-file-width="599" data-file-height="317" /></a><figcaption>Electromagnetic wave with perpendicular electric and magnetic components</figcaption></figure> <p>Thermal radiation is characteristically different from conduction and convection in that it does not require a medium and, in fact it reaches maximum <a href="/wiki/Efficiency" title="Efficiency">efficiency</a> in a <a href="/wiki/Vacuum" title="Vacuum">vacuum</a>. Thermal radiation is a type of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> which is often modeled by the propagation of waves. These waves have the standard wave properties of frequency, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> and <a href="/wiki/Wavelengths" class="mw-redirect" title="Wavelengths">wavelength</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> which are related by the equation<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda ={\frac {c}{\nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mi>ν</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ={\frac {c}{\nu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91436039f817d629f3a8e50c18476d0d0f991e34" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.522ex; height:4.676ex;" alt="{\displaystyle \lambda ={\frac {c}{\nu }}}"></span>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> is the speed of light in the medium.<sup id="cite_ref-:2_22-0" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 769">: 769 </span></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Irradiation">Irradiation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=16" title="Edit section: Irradiation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Irradiation" title="Irradiation">Irradiation</a></div> <p><i>Thermal irradiation</i> is the rate at which radiation is incident upon a surface per unit area.<sup id="cite_ref-:2_22-1" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 771">: 771 </span></sup> It is measured in <a href="/wiki/Watt" title="Watt">watts</a> per square meter. Irradiation can either be <i>reflected</i>, <i>absorbed</i>, or <i>transmitted</i>. The components of irradiation can then be characterized by the equation </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha +\rho +\tau =1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>+</mo> <mi>ρ</mi> <mo>+</mo> <mi>τ</mi> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha +\rho +\tau =1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce1bdd9fcff6840177329a8d0e03672a59e413a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.22ex; height:2.676ex;" alt="{\displaystyle \alpha +\rho +\tau =1\,}"></span></dd></dl> <p>where, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/652e1fd9c3a2ca00e1a517783cdbb0e18e4181f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.875ex; height:1.676ex;" alt="{\displaystyle \alpha \,}"></span> represents the <a href="/wiki/Absorption_(electromagnetic_radiation)" title="Absorption (electromagnetic radiation)">absorptivity</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1d651c28959a0f15127c097ff4488b123d9e708" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.589ex; height:2.176ex;" alt="{\displaystyle \rho \,}"></span> <a href="/wiki/Reflectance#Reflectivity" title="Reflectance">reflectivity</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8661cd2a09f95bb46a58ad86eebc9c7d81a31bea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.589ex; height:1.676ex;" alt="{\displaystyle \tau \,}"></span> <a href="/wiki/Transmittance" title="Transmittance">transmissivity</a>.<sup id="cite_ref-:2_22-2" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 772">: 772 </span></sup> These components are a function of the wavelength of the electromagnetic wave as well as the material properties of the medium. </p> <div class="mw-heading mw-heading4"><h4 id="Absorptivity_and_emissivity">Absorptivity and emissivity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=17" title="Edit section: Absorptivity and emissivity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The spectral absorption is equal to the <a href="/wiki/Emissivity" title="Emissivity">emissivity</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϵ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3837cad72483d97bcdde49c85d3b7b859fb3fd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.944ex; height:1.676ex;" alt="{\displaystyle \epsilon }"></span>; this relation is known as <a href="/wiki/Kirchhoff%27s_law_of_thermal_radiation" title="Kirchhoff's law of thermal radiation">Kirchhoff's law of thermal radiation</a>. An object is called a <a href="/wiki/Black_body" title="Black body">black body</a> if this holds for all frequencies, and the following formula applies: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =\epsilon =1.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mi>ϵ</mi> <mo>=</mo> <mn>1.</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha =\epsilon =1.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8d0ee88b060a992903ca46e50c4d325778fe5e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.825ex; height:2.176ex;" alt="{\displaystyle \alpha =\epsilon =1.\,}"></span></dd></dl> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:ThermalPaint.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/ThermalPaint.png/330px-ThermalPaint.png" decoding="async" width="330" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/ThermalPaint.png/495px-ThermalPaint.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/ThermalPaint.png/660px-ThermalPaint.png 2x" data-file-width="981" data-file-height="605" /></a><figcaption>Spectral response of two paints and a mirrored surface, in the visible and the infrared. From NASA.</figcaption></figure><p>If objects appear white (reflective in the <a href="/wiki/Visual_spectrum" class="mw-redirect" title="Visual spectrum">visual spectrum</a>), they are not necessarily equally reflective (and thus non-emissive) in the thermal infrared – see the diagram at the left. Most household radiators are painted white, which is sensible given that they are not hot enough to radiate any significant amount of heat, and are not designed as thermal radiators at all – instead, they are actually <a href="/wiki/Convection_heater" title="Convection heater">convectors</a>, and painting them matt black would make little difference to their efficacy. Acrylic and urethane based white paints have 93% blackbody radiation efficiency at room temperature<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> (meaning the term "black body" does not always correspond to the visually perceived color of an object). These materials that do not follow the "black color = high emissivity/absorptivity" caveat will most likely have functional spectral emissivity/absorptivity dependence. </p><p>Only truly <i>gray</i> systems (relative equivalent emissivity/absorptivity and no directional transmissivity dependence in <i>all</i> control volume bodies considered) can achieve reasonable steady-state heat flux estimates through the Stefan-Boltzmann law. Encountering this "ideally calculable" situation is almost impossible (although common engineering procedures surrender the dependency of these unknown variables and "assume" this to be the case). Optimistically, these "gray" approximations will get close to real solutions, as most divergence from Stefan-Boltzmann solutions is very small (especially in most <a href="/wiki/Standard_temperature_and_pressure" title="Standard temperature and pressure">standard temperature and pressure</a> lab controlled environments). </p> <div class="mw-heading mw-heading4"><h4 id="Reflectivity">Reflectivity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=18" title="Edit section: Reflectivity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Reflectivity" class="mw-redirect" title="Reflectivity">Reflectivity</a> deviates from the other properties in that it is bidirectional in nature. In other words, this property depends on the direction of the incident of radiation as well as the direction of the reflection. Therefore, the reflected rays of a radiation spectrum incident on a real surface in a specified direction forms an irregular shape that is not easily predictable. In practice, surfaces are often assumed to reflect either in a perfectly specular or a diffuse manner. In a <a href="/wiki/Specular_reflection" title="Specular reflection">specular reflection</a>, the angles of reflection and incidence are equal. In <a href="/wiki/Diffuse_reflection" title="Diffuse reflection">diffuse reflection</a>, radiation is reflected equally in all directions. Reflection from smooth and polished surfaces can be assumed to be specular reflection, whereas reflection from rough surfaces approximates diffuse reflection.<sup id="cite_ref-hsu_14-4" class="reference"><a href="#cite_note-hsu-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Radiation" title="Radiation">radiation</a> <a href="/wiki/Analysis" title="Analysis">analysis</a> a surface is defined as smooth if the height of the surface roughness is much smaller relative to the wavelength of the incident radiation. </p> <div class="mw-heading mw-heading4"><h4 id="Transmissivity">Transmissivity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=19" title="Edit section: Transmissivity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A medium that experiences no transmission (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4422051052da869dc5b1f0e1cfb06a045ee0c36a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.463ex; height:2.176ex;" alt="{\displaystyle \tau =0}"></span>) is <i>opaque,</i> in which case absorptivity and reflectivity sum to unity:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho +\alpha =1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>+</mo> <mi>α</mi> <mo>=</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho +\alpha =1.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce2013d60676ace9b7b7bba7656ce9d5ec0a2a97" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.438ex; height:2.676ex;" alt="{\displaystyle \rho +\alpha =1.}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Radiation_intensity">Radiation intensity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=20" title="Edit section: Radiation intensity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Radiant_intensity" title="Radiant intensity">Radiant intensity</a></div> <p>Radiation emitted from a surface can propagate in any direction from the surface.<sup id="cite_ref-:2_22-3" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 773">: 773 </span></sup> Irradiation can also be incident upon a surface from any direction. The amount of irradiation on a surface is therefore dependent on the relative orientation of both the emitter and the receiver. The parameter <i>radiation intensity,</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> is used to quantify how much radiation makes it from one surface to another. </p><p>Radiation intensity is often modeled using a <a href="/wiki/Spherical_coordinate_system" title="Spherical coordinate system">spherical coordinate system</a>.<sup id="cite_ref-:2_22-4" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 773">: 773 </span></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Emissive_power">Emissive power</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=21" title="Edit section: Emissive power"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Radiant_exitance" title="Radiant exitance">Radiant exitance</a></div> <p><i>Emissive power</i> is the rate at which radiation is emitted per unit area.<sup id="cite_ref-:2_22-5" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 776">: 776 </span></sup> It is a measure of <a href="/wiki/Heat_flux" title="Heat flux">heat flux</a>. The total emissive power from a surface is denoted as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> and can be determined by,<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=\pi I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>π</mi> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\pi I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4929035f3da81b95e87490d82b3e95bdae1448a4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.378ex; height:2.176ex;" alt="{\displaystyle E=\pi I}"></span>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> is in units of <a href="/wiki/Steradian" title="Steradian">steradians</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> is the total intensity. </p><p>The total emissive power can also be found by integrating the <i>spectral emissive power</i> over all possible wavelengths.<sup id="cite_ref-:2_22-6" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 776">: 776 </span></sup> This is calculated as,<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=\int _{0}^{\infty }E_{\lambda }(\lambda )d\lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\int _{0}^{\infty }E_{\lambda }(\lambda )d\lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b12f95bd3a6a98d9209b76eee74ce9b7c990922" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.242ex; height:5.843ex;" alt="{\displaystyle E=\int _{0}^{\infty }E_{\lambda }(\lambda )d\lambda }"></span>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> represents wavelength. </p><p>The spectral emissive power can also be determined from the spectral intensity, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\lambda }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\lambda }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62191ee151a9bf9cb12490516bbdfabb43ddf032" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.214ex; height:2.509ex;" alt="{\displaystyle I_{\lambda }}"></span>as follows, </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\lambda }(\lambda )=\pi I_{\lambda }(\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>π</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\lambda }(\lambda )=\pi I_{\lambda }(\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41339e32f9e56b0684a6792538b4cb67392cf050" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.879ex; height:2.843ex;" alt="{\displaystyle E_{\lambda }(\lambda )=\pi I_{\lambda }(\lambda )}"></span>where both spectral emissive power and emissive intensity are functions of wavelength.<sup id="cite_ref-:2_22-7" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 776">: 776 </span></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Blackbody_radiation">Blackbody radiation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=22" title="Edit section: Blackbody radiation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Black-body_radiation" title="Black-body radiation">Black-body radiation</a></div> <p>A "black body" is a body which has the property of allowing all incident rays to enter without surface reflection and not allowing them to leave again.<sup id="cite_ref-:7_16-1" class="reference"><a href="#cite_note-:7-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Blackbodies are idealized surfaces that act as the perfect absorber and emitter.<sup id="cite_ref-:2_22-8" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 782–783">: 782–783 </span></sup> They serve as the standard against which real surfaces are compared when characterizing thermal radiation. A blackbody is defined by three characteristics: </p> <ol><li><i>A blackbody absorbs all incident radiation, regardless of wavelength and direction.</i></li> <li><i>No surface can emit more energy than a blackbody for a given temperature and wavelength.</i></li> <li><i>A blackbody is a diffuse emitter.</i></li></ol> <div class="mw-heading mw-heading4"><h4 id="The_Planck_distribution">The Planck distribution</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=23" title="Edit section: The Planck distribution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Planck%27s_law" title="Planck's law">Planck's law</a></div> <p>The spectral intensity of a blackbody, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\lambda ,b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> <mo>,</mo> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\lambda ,b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/811e12eaa6d4e68674d3863584876f5c659a7c45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.376ex; height:2.843ex;" alt="{\displaystyle I_{\lambda ,b}}"></span> was first determined by Max Planck.<sup id="cite_ref-:3_3-1" class="reference"><a href="#cite_note-:3-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> It is given by <a href="/wiki/Planck%27s_law" title="Planck's law">Planck's law</a> per unit wavelength as:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\lambda ,b}(\lambda ,T)={\frac {2hc^{2}}{\lambda ^{5}}}\cdot {\frac {1}{e^{hc/k_{\rm {B}}T\lambda }-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> <mo>,</mo> <mi>b</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>h</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mi>T</mi> <mi>λ</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\lambda ,b}(\lambda ,T)={\frac {2hc^{2}}{\lambda ^{5}}}\cdot {\frac {1}{e^{hc/k_{\rm {B}}T\lambda }-1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/695f199c14fa23b86973b09e39bc746df05f43e0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.103ex; height:6.176ex;" alt="{\displaystyle I_{\lambda ,b}(\lambda ,T)={\frac {2hc^{2}}{\lambda ^{5}}}\cdot {\frac {1}{e^{hc/k_{\rm {B}}T\lambda }-1}}}"></span>This formula mathematically follows from calculation of spectral distribution of energy in <a href="/wiki/Quantization_(physics)" title="Quantization (physics)">quantized</a> electromagnetic field which is in complete <a href="/wiki/Thermal_equilibrium" title="Thermal equilibrium">thermal equilibrium</a> with the radiating object. Planck's law shows that radiative energy increases with temperature, and explains why the peak of an emission spectrum shifts to shorter wavelengths at higher temperatures. It can also be found that energy emitted at shorter wavelengths increases more rapidly with temperature relative to longer wavelengths.<sup id="cite_ref-rtps_24-0" class="reference"><a href="#cite_note-rtps-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>The equation is derived as an infinite sum over all possible frequencies in a semi-sphere region. The energy, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=h\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>h</mi> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=h\nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6c0386dc6d9530519404f95570fcc8548ed2326" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.445ex; height:2.176ex;" alt="{\displaystyle E=h\nu }"></span>, of each photon is multiplied by the number of states available at that frequency, and the probability that each of those states will be occupied. </p> <div class="mw-heading mw-heading4"><h4 id="Stefan-Boltzmann_law">Stefan-Boltzmann law</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=24" title="Edit section: Stefan-Boltzmann law"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Stefan%E2%80%93Boltzmann_law" title="Stefan–Boltzmann law">Stefan–Boltzmann law</a></div><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Emissive_Power.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Emissive_Power.svg/310px-Emissive_Power.svg.png" decoding="async" width="310" height="217" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Emissive_Power.svg/465px-Emissive_Power.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Emissive_Power.svg/620px-Emissive_Power.svg.png 2x" data-file-width="676" data-file-height="474" /></a><figcaption>Power emitted by a black body plotted against the temperature according to the Stefan–Boltzmann law.</figcaption></figure><p>The Planck distribution can be used to find the spectral emissive power of a blackbody, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\lambda ,b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> <mo>,</mo> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\lambda ,b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b32e3ba34417cabd55bc32e5f3ad5f10469f665" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.069ex; height:2.843ex;" alt="{\displaystyle E_{\lambda ,b}}"></span> as follows,<sup id="cite_ref-:2_22-9" class="reference"><a href="#cite_note-:2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 784–785">: 784–785 </span></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\lambda ,b}=\pi I_{\lambda ,b}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> <mo>,</mo> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mi>π</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> <mo>,</mo> <mi>b</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\lambda ,b}=\pi I_{\lambda ,b}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56a0c17888f88abfd9bd843a0ace3cfd7b0a58b0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.522ex; height:2.843ex;" alt="{\displaystyle E_{\lambda ,b}=\pi I_{\lambda ,b}.}"></span> </p><p>The total emissive power of a blackbody is then calculated as,<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{b}=\int _{0}^{\infty }\pi I_{\lambda ,b}d\lambda .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mi>π</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> <mo>,</mo> <mi>b</mi> </mrow> </msub> <mi>d</mi> <mi>λ</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{b}=\int _{0}^{\infty }\pi I_{\lambda ,b}d\lambda .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8353eb4b6e127f21612d1ec34afb2d1b141b4cc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.404ex; height:5.843ex;" alt="{\displaystyle E_{b}=\int _{0}^{\infty }\pi I_{\lambda ,b}d\lambda .}"></span>The solution of the above integral yields a remarkably elegant equation for the total emissive power of a blackbody, the <i>Stefan-Boltzmann law</i>, which is given as,<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{b}=\sigma T^{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mi>σ</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{b}=\sigma T^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5ce5a53779c77876e4eead5be989c3a390bc179" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.855ex; height:3.009ex;" alt="{\displaystyle E_{b}=\sigma T^{4}}"></span>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span> is the <i>Steffan-Boltzmann constant</i>. </p> <div class="mw-heading mw-heading4"><h4 id="Wien's_displacement_law"><span id="Wien.27s_displacement_law"></span>Wien's displacement law</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=25" title="Edit section: Wien's displacement law"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wiens_law.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Wiens_law.svg/330px-Wiens_law.svg.png" decoding="async" width="330" height="275" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Wiens_law.svg/495px-Wiens_law.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Wiens_law.svg/660px-Wiens_law.svg.png 2x" data-file-width="720" data-file-height="600" /></a><figcaption>The peak wavelength and total-s radiated amount vary with temperature according to <a href="/wiki/Wien%27s_displacement_law" title="Wien's displacement law">Wien's displacement law</a>. Although this shows relatively high temperatures, the same relationships hold true for any temperature down to absolute zero.</figcaption></figure><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Wien%27s_displacement_law" title="Wien's displacement law">Wien's displacement law</a></div> <p>The wavelength <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/988b7b8a22b11081bc97378c30391f573535c21c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.742ex; height:2.176ex;" alt="{\displaystyle \lambda \,}"></span> for which the emission intensity is highest is given by Wien's displacement law as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{\text{max}}={\frac {b}{T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>b</mi> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda _{\text{max}}={\frac {b}{T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf5c9c4bae9e811fd33cdcc49fc06a464d47f4d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.217ex; height:5.343ex;" alt="{\displaystyle \lambda _{\text{max}}={\frac {b}{T}}}"></span></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Constants">Constants</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=26" title="Edit section: Constants"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Definitions of constants used in the above equations: </p> <table class="wikitable"> <tbody><tr> <th>Symbol </th> <th>Constant name </th> <th>Value in SI units </th></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cecd947e6666832fcc39909b00dbde70caa9cf8c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.726ex; height:2.176ex;" alt="{\displaystyle h\,}"></span> </td> <td><a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a> </td> <td>6.626 069 3(11)×10<sup>−34</sup> J·s </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b1bcf19f4ec75b1d2cc0be001e58a314fb0a940" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.385ex; height:2.176ex;" alt="{\displaystyle b\,}"></span> </td> <td><a href="/wiki/Wien%27s_displacement_law" title="Wien's displacement law">Wien's displacement constant</a> </td> <td>2.897 768 5(51)×10<sup>−3</sup> m·K </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{\rm {B}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\rm {B}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f888f2a538c75aa814c617658f6d6cd35a7dea72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.994ex; height:2.509ex;" alt="{\displaystyle k_{\rm {B}}\,}"></span> </td> <td><a href="/wiki/Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a> </td> <td>1.380 650 5(24)×10<sup>−23</sup> J·K<sup>−1</sup> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df7f4b8e7c7fc824dd8c82008b7cceac27f60bcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.717ex; height:1.676ex;" alt="{\displaystyle \sigma \,}"></span> </td> <td><a href="/wiki/Stefan%E2%80%93Boltzmann_constant" class="mw-redirect" title="Stefan–Boltzmann constant">Stefan–Boltzmann constant</a> </td> <td>5.670 373 (21)×10<sup>−8</sup> W·m<sup>−2</sup>·K<sup>−4</sup> </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8573e7d95140b0d4068258d8162e189563baee6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,}"></span> </td> <td><a href="/wiki/Speed_of_light" title="Speed of light">Speed of light</a> </td> <td>299 792 458 m·s<sup>−1</sup> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Variables">Variables</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=27" title="Edit section: Variables"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Definitions of variables, with example values: </p> <table class="wikitable"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> </td> <td>Absolute <a href="/wiki/Temperature" title="Temperature">temperature</a> </td> <td>For units used above, must be in <a href="/wiki/Kelvin" title="Kelvin">kelvins</a> (e.g. average surface temperature on Earth = 288 K) </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> </td> <td>Surface <a href="/wiki/Area" title="Area">area</a> </td> <td><i>A</i><sub>cuboid</sub> = 2<i>ab</i> + 2<i>bc</i> + 2<i>ac</i>;<br /> <i>A</i><sub>cylinder</sub> = 2<i>π·r</i>(<i>h</i> + <i>r</i>);<br /> <i>A</i><sub>sphere</sub> = 4<i>π·r</i><sup>2</sup> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Emission_from_non-black_surfaces">Emission from non-black surfaces</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=28" title="Edit section: Emission from non-black surfaces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For surfaces which are not black bodies, one has to consider the (generally frequency dependent) emissivity factor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon (\nu )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϵ</mi> <mo stretchy="false">(</mo> <mi>ν</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon (\nu )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20a01b9dad7a79e1c5438527ae3df2a1fe395a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.986ex; height:2.843ex;" alt="{\displaystyle \epsilon (\nu )}"></span>. This factor has to be multiplied with the radiation spectrum formula before integration. If it is taken as a constant, the resulting formula for the power output can be written in a way that contains <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϵ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3837cad72483d97bcdde49c85d3b7b859fb3fd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.944ex; height:1.676ex;" alt="{\displaystyle \epsilon }"></span> as a factor: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P=\epsilon \sigma AT^{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mi>ϵ</mi> <mi>σ</mi> <mi>A</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=\epsilon \sigma AT^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/975a012ddddb6871f97568d368530551b303b91a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.635ex; height:2.676ex;" alt="{\displaystyle P=\epsilon \sigma AT^{4}}"></span></dd></dl> <p>This type of theoretical model, with frequency-independent emissivity lower than that of a perfect black body, is often known as a <i>grey body</i>. For frequency-dependent emissivity, the solution for the integrated power depends on the functional form of the dependence, though in general there is no simple expression for it. Practically speaking, if the emissivity of the body is roughly constant around the peak emission wavelength, the gray body model tends to work fairly well since the weight of the curve around the peak emission tends to dominate the integral. </p> <div class="mw-heading mw-heading2"><h2 id="Heat_transfer_between_surfaces">Heat transfer between surfaces</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=29" title="Edit section: Heat transfer between surfaces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Calculation of radiative heat transfer between groups of objects, including a 'cavity' or 'surroundings' requires solution of a set of <a href="/wiki/Simultaneous_equations" class="mw-redirect" title="Simultaneous equations">simultaneous equations</a> using the <a href="/wiki/Radiosity_(heat_transfer)" class="mw-redirect" title="Radiosity (heat transfer)">radiosity</a> method. In these calculations, the geometrical configuration of the problem is distilled to a set of numbers called <a href="/wiki/View_factor" title="View factor">view factors</a>, which give the proportion of radiation leaving any given surface that hits another specific surface. These calculations are important in the fields of <a href="/wiki/Solar_thermal_energy" title="Solar thermal energy">solar thermal energy</a>, <a href="/wiki/Boiler" title="Boiler">boiler</a> and <a href="/wiki/Furnace_(house_heating)" class="mw-redirect" title="Furnace (house heating)">furnace</a> design and <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">raytraced computer graphics</a>. </p><p> The <i>net</i> radiative heat transfer from one surface to another is the radiation leaving the first surface for the other minus that arriving from the second surface.</p><div><ul><li>For black bodies, the rate of energy transfer from surface 1 to surface 2 is: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {Q}}_{1\rightarrow 2}=A_{1}E_{b1}F_{1\rightarrow 2}-A_{2}E_{b2}F_{2\rightarrow 1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo stretchy="false">→</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo stretchy="false">→</mo> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo stretchy="false">→</mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {Q}}_{1\rightarrow 2}=A_{1}E_{b1}F_{1\rightarrow 2}-A_{2}E_{b2}F_{2\rightarrow 1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/273a16259f32e1da306719e1222c169fd9a2c730" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.869ex; height:3.343ex;" alt="{\displaystyle {\dot {Q}}_{1\rightarrow 2}=A_{1}E_{b1}F_{1\rightarrow 2}-A_{2}E_{b2}F_{2\rightarrow 1}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> is surface area, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69d2e3ccd9bce33b1ae1562c2e7e831eb8f55bf3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.653ex; height:2.509ex;" alt="{\displaystyle E_{b}}"></span> is <a href="/wiki/Energy_flux" title="Energy flux">energy flux</a> (the rate of emission per unit surface area) and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{1\rightarrow 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo stretchy="false">→</mo> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{1\rightarrow 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ef6c5d8cbda8359fdff44afcad899480f5285f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.014ex; height:2.509ex;" alt="{\displaystyle F_{1\rightarrow 2}}"></span> is the <a href="/wiki/View_factor" title="View factor">view factor</a> from surface 1 to surface 2. Applying both the <a href="/wiki/View_factor#Reciprocity" title="View factor">reciprocity rule</a> for view factors, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{1}F_{1\rightarrow 2}=A_{2}F_{2\rightarrow 1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo stretchy="false">→</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo stretchy="false">→</mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}F_{1\rightarrow 2}=A_{2}F_{2\rightarrow 1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f101c105fd6ae94565900cc4d53a0eda3c9887a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.721ex; height:2.509ex;" alt="{\displaystyle A_{1}F_{1\rightarrow 2}=A_{2}F_{2\rightarrow 1}}"></span>, and the <a href="/wiki/Stefan%E2%80%93Boltzmann_law" title="Stefan–Boltzmann law">Stefan–Boltzmann law</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{b}=\sigma T^{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mi>σ</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{b}=\sigma T^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5ce5a53779c77876e4eead5be989c3a390bc179" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.855ex; height:3.009ex;" alt="{\displaystyle E_{b}=\sigma T^{4}}"></span>, yields: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {Q}}_{1\rightarrow 2}=\sigma A_{1}F_{1\rightarrow 2}\left(T_{1}^{4}-T_{2}^{4}\right)\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo stretchy="false">→</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mi>σ</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo stretchy="false">→</mo> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {Q}}_{1\rightarrow 2}=\sigma A_{1}F_{1\rightarrow 2}\left(T_{1}^{4}-T_{2}^{4}\right)\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69982eab7eb6e4198a50611b72c937db2a7bf38f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.032ex; width:28.148ex; height:3.509ex;" alt="{\displaystyle {\dot {Q}}_{1\rightarrow 2}=\sigma A_{1}F_{1\rightarrow 2}\left(T_{1}^{4}-T_{2}^{4}\right)\!}"></span></dd></dl> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span> is the <a href="/wiki/Stefan%E2%80%93Boltzmann_constant" class="mw-redirect" title="Stefan–Boltzmann constant">Stefan–Boltzmann constant</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> is temperature.<sup id="cite_ref-:6_18-1" class="reference"><a href="#cite_note-:6-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> A negative value for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {Q}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Q</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {Q}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14ef647ca15bb236a9473fcbe17f16fe87c95ab4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:3.176ex;" alt="{\displaystyle {\dot {Q}}}"></span> indicates that net radiation heat transfer is from surface 2 to surface 1.</li><li>For two grey-body surfaces forming an enclosure, the heat transfer rate is: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {Q}}={\frac {\sigma \left(T_{1}^{4}-T_{2}^{4}\right)}{\displaystyle {\frac {1-\epsilon _{1}}{A_{1}\epsilon _{1}}}+{\frac {1}{A_{1}F_{1\rightarrow 2}}}+{\frac {1-\epsilon _{2}}{A_{2}\epsilon _{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>σ</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo stretchy="false">→</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {Q}}={\frac {\sigma \left(T_{1}^{4}-T_{2}^{4}\right)}{\displaystyle {\frac {1-\epsilon _{1}}{A_{1}\epsilon _{1}}}+{\frac {1}{A_{1}F_{1\rightarrow 2}}}+{\frac {1-\epsilon _{2}}{A_{2}\epsilon _{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6b663185cba7ea0ddf93c6d0ac1c3c225ee4f36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.505ex; width:33.776ex; height:9.676ex;" alt="{\displaystyle {\dot {Q}}={\frac {\sigma \left(T_{1}^{4}-T_{2}^{4}\right)}{\displaystyle {\frac {1-\epsilon _{1}}{A_{1}\epsilon _{1}}}+{\frac {1}{A_{1}F_{1\rightarrow 2}}}+{\frac {1-\epsilon _{2}}{A_{2}\epsilon _{2}}}}}}"></span></dd></dl> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7fcacdbda3738e37cc1f739c4c5739b3482732e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.998ex; height:2.009ex;" alt="{\displaystyle \epsilon _{1}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c7ce0a2b401d02627ae392bfb876b6e765fec7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.998ex; height:2.009ex;" alt="{\displaystyle \epsilon _{2}}"></span> are the emissivities of the surfaces.<sup id="cite_ref-:6_18-2" class="reference"><a href="#cite_note-:6-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li></ul></div> <p>Formulas for radiative heat transfer can be derived for more particular or more elaborate physical arrangements, such as between parallel plates, concentric spheres and the internal surfaces of a cylinder.<sup id="cite_ref-:6_18-3" class="reference"><a href="#cite_note-:6-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=30" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermal radiation is an important factor of many engineering applications, especially for those dealing with high temperatures. </p> <div class="mw-heading mw-heading3"><h3 id="Solar_energy">Solar energy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=31" title="Edit section: Solar energy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Solar_energy" title="Solar energy">Solar energy</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:0D1L_Radiation_Balance_Model.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/0D1L_Radiation_Balance_Model.svg/400px-0D1L_Radiation_Balance_Model.svg.png" decoding="async" width="400" height="317" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/0D1L_Radiation_Balance_Model.svg/600px-0D1L_Radiation_Balance_Model.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/0D1L_Radiation_Balance_Model.svg/800px-0D1L_Radiation_Balance_Model.svg.png 2x" data-file-width="694" data-file-height="550" /></a><figcaption>Diagram of a solar radiation balance model</figcaption></figure> <p>Sunlight is the incandescence of the "white hot" surface of the Sun. Electromagnetic radiation from the sun has a peak wavelength of about 550 nm,<sup id="cite_ref-:9_1-2" class="reference"><a href="#cite_note-:9-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and can be harvested to generate heat or electricity. </p><p>Thermal radiation can be concentrated on a tiny spot via reflecting mirrors, which <a href="/wiki/Concentrating_solar_power" class="mw-redirect" title="Concentrating solar power">concentrating solar power</a> takes advantage of. Instead of mirrors, <a href="/wiki/Fresnel_lens" title="Fresnel lens">Fresnel lenses</a> can also be used to concentrate <a href="/wiki/Radiant_energy" title="Radiant energy">radiant energy</a>. Either method can be used to quickly vaporize water into steam using sunlight. For example, the sunlight reflected from mirrors heats the <a href="/wiki/PS10_Solar_Power_Plant" class="mw-redirect" title="PS10 Solar Power Plant">PS10 Solar Power Plant</a>, and during the day it can heat water to 285 °C (558 K; 545 °F). </p><p>A <a href="/wiki/Selective_surface" title="Selective surface">selective surface</a> can be used when energy is being extracted from the sun. Selective surfaces are surfaces tuned to maximize the amount of energy they absorb from the sun's radiation while minimizing the amount of energy they lose to their own thermal radiation. Selective surfaces can also be used on solar collectors. </p> <div class="mw-heading mw-heading3"><h3 id="Incandescent_light_bulbs">Incandescent light bulbs</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=32" title="Edit section: Incandescent light bulbs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Incandescent_light_bulb" title="Incandescent light bulb">Incandescent light bulb</a></div> <p>The <a href="/wiki/Incandescent_light_bulb" title="Incandescent light bulb">incandescent light bulb</a> creates light by heating a filament to a temperature at which it emits significant visible thermal radiation. For a tungsten filament at a typical temperature of 3000 K, only a small fraction of the emitted radiation is visible, and the majority is infrared light. This infrared light does not help a person see, but still transfers heat to the environment, making incandescent lights relatively inefficient as a light source.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> If the filament could be made hotter, efficiency would increase; however, there are currently no materials able to withstand such temperatures which would be appropriate for use in lamps. </p><p>More efficient light sources, such as <a href="/wiki/Fluorescent_lamp" title="Fluorescent lamp">fluorescent lamps</a> and <a href="/wiki/LED" class="mw-redirect" title="LED">LEDs</a>, do not function by incandescence.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Thermal_comfort">Thermal comfort</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=33" title="Edit section: Thermal comfort"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Thermal_comfort" title="Thermal comfort">Thermal comfort</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Radiant_heat_panel_nrc_ottawa.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Radiant_heat_panel_nrc_ottawa.jpg/170px-Radiant_heat_panel_nrc_ottawa.jpg" decoding="async" width="170" height="259" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Radiant_heat_panel_nrc_ottawa.jpg/255px-Radiant_heat_panel_nrc_ottawa.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Radiant_heat_panel_nrc_ottawa.jpg/340px-Radiant_heat_panel_nrc_ottawa.jpg 2x" data-file-width="2323" data-file-height="3544" /></a><figcaption>Radiant heat panel for testing precisely quantified energy exposures at <a href="/wiki/National_Research_Council_(Canada)" class="mw-redirect" title="National Research Council (Canada)">National Research Council</a>, near <a href="/wiki/Ottawa" title="Ottawa">Ottawa</a>, <a href="/wiki/Ontario" title="Ontario">Ontario</a>, Canada</figcaption></figure><p>Thermal radiation plays a crucial role in human comfort, <a href="/wiki/Effect_of_radiation_on_perceived_temperature" title="Effect of radiation on perceived temperature">influencing perceived temperature sensation</a>. Various technologies have been developed to enhance thermal comfort, including personal heating and cooling devices. </p><p>The <a href="/wiki/Mean_radiant_temperature" title="Mean radiant temperature">mean radiant temperature</a> is a metric used to quantify the exchange of radiant heat between a human and their surrounding environment. </p> <div class="mw-heading mw-heading4"><h4 id="Personal_heating">Personal heating</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=34" title="Edit section: Personal heating"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Radiant_heating_and_cooling" title="Radiant heating and cooling">Radiant personal heaters</a> are devices that convert energy into infrared radiation that are designed to increase a user's perceived temperature. They typically are either gas-powered or electric. In domestic and commercial applications, gas-powered radiant heaters can produce a higher heat flux than electric heaters which are limited by the amount of current that can be drawn through a circuit breaker. </p> <div class="mw-heading mw-heading4"><h4 id="Personal_cooling">Personal cooling</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=35" title="Edit section: Personal cooling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Personalized cooling technology is an example of an application where optical spectral selectivity can be beneficial. Conventional personal cooling is typically achieved through heat conduction and convection. However, the human body is a very efficient emitter of infrared radiation, which provides an additional cooling mechanism. Most conventional fabrics are opaque to infrared radiation and block thermal emission from the body to the environment. Fabrics for personalized cooling applications have been proposed that enable infrared transmission to directly pass through clothing, while being opaque at visible wavelengths, allowing the wearer to remain cooler. </p> <div class="mw-heading mw-heading3"><h3 id="Windows">Windows</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=36" title="Edit section: Windows"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Low-emissivity" class="mw-redirect" title="Low-emissivity">Low-emissivity</a> windows in houses are a more complicated technology, since they must have low emissivity at thermal wavelengths while remaining transparent to visible light. To reduce the heat transfer from a surface, such as a glass window, a clear reflective film with a low emissivity coating can be placed on the interior of the surface. "Low-emittance (low-E) coatings are microscopically thin, virtually invisible, metal or metallic oxide layers deposited on a window or skylight glazing surface primarily to reduce the U-factor by suppressing radiative heat flow".<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> By adding this coating we are limiting the amount of radiation that leaves the window thus increasing the amount of heat that is retained inside the window. </p> <div class="mw-heading mw-heading3"><h3 id="Spacecraft">Spacecraft</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=37" title="Edit section: Spacecraft"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Shiny metal surfaces, have low emissivities both in the visible wavelengths and in the far infrared. Such surfaces can be used to reduce heat transfer in both directions; an example of this is the <a href="/wiki/Multi-layer_insulation" title="Multi-layer insulation">multi-layer insulation</a> used to insulate spacecraft. </p><p>Since any electromagnetic radiation, including thermal radiation, conveys momentum as well as energy, thermal radiation also induces very small forces on the radiating or absorbing objects. Normally these forces are negligible, but they must be taken into account when considering spacecraft navigation. The <a href="/wiki/Pioneer_anomaly" title="Pioneer anomaly">Pioneer anomaly</a>, where the motion of the craft slightly deviated from that expected from gravity alone, was eventually tracked down to asymmetric thermal radiation from the spacecraft. Similarly, the orbits of asteroids are perturbed since the asteroid absorbs solar radiation on the side facing the Sun, but then re-emits the energy at a different angle as the rotation of the asteroid carries the warm surface out of the Sun's view (the <a href="/wiki/Yarkovsky%E2%80%93O%27Keefe%E2%80%93Radzievskii%E2%80%93Paddack_effect" class="mw-redirect" title="Yarkovsky–O'Keefe–Radzievskii–Paddack effect">YORP effect</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Nanostructures">Nanostructures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=38" title="Edit section: Nanostructures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nanostructures with spectrally selective thermal emittance properties offer numerous technological applications for energy generation and efficiency,<sup id="cite_ref-:0_28-0" class="reference"><a href="#cite_note-:0-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> e.g., for <a href="/wiki/Daytime_radiative_cooling" class="mw-redirect" title="Daytime radiative cooling">daytime radiative cooling</a> of photovoltaic cells and buildings. These applications require high emittance in the frequency range corresponding to the atmospheric transparency window in 8 to 13 micron wavelength range. A selective emitter radiating strongly in this range is thus exposed to the clear sky, enabling the use of the outer space as a very low temperature heat sink.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Health_and_safety">Health and safety</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=39" title="Edit section: Health and safety"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Metabolic_temperature_regulation">Metabolic temperature regulation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=40" title="Edit section: Metabolic temperature regulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a practical, room-temperature setting, humans lose considerable energy due to infrared thermal radiation in addition to that lost by conduction to air (aided by concurrent convection, or other air movement like drafts). The heat energy lost is partially regained by absorbing heat radiation from walls or other surroundings. Human skin has an emissivity of very close to 1.0.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> A human, having roughly 2<span class="nowrap"> </span>m<sup>2</sup> in surface area, and a temperature of about 307 <a href="/wiki/Kelvin" title="Kelvin">K</a>, continuously radiates approximately 1000 W. If people are indoors, surrounded by surfaces at 296 K, they receive back about 900 W from the wall, ceiling, and other surroundings, resulting in a net loss of 100 W. These estimates are highly dependent on extrinsic variables, such as wearing clothes. </p><p>Lighter colors and also whites and metallic substances absorb less of the illuminating light, and as a result heat up less. However, color makes little difference in the heat transfer between an object at everyday temperatures and its surroundings. This is because the dominant emitted wavelengths are not in the visible spectrum, but rather infrared. Emissivities at those wavelengths are largely unrelated to visual emissivities (visible colors); in the far infra-red, most objects have high emissivities. Thus, except in sunlight, the color of clothing makes little difference as regards warmth; likewise, paint color of houses makes little difference to warmth except when the painted part is sunlit. </p> <div class="mw-heading mw-heading3"><h3 id="Burns">Burns</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=41" title="Edit section: Burns"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermal radiation is a phenomenon that can burn skin and ignite flammable materials. The time to a damage from exposure to thermal radiation is a function of the rate of delivery of the heat. Radiative heat flux and effects are given as follows:<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <th>kW/m<sup>2</sup></th> <th>Effect </th></tr> <tr> <td>170</td> <td>Maximum flux measured in a post-<a href="/wiki/Flashover" title="Flashover">flashover</a> compartment </td></tr> <tr> <td><span class="nowrap"> </span>80</td> <td>Thermal Protective Performance test for <a href="/wiki/Personal_protective_equipment" title="Personal protective equipment">personal protective equipment</a> </td></tr> <tr> <td><span class="nowrap"> </span>52</td> <td><a href="/wiki/Fiberboard" title="Fiberboard">Fiberboard</a> ignites at five seconds </td></tr> <tr> <td><span class="nowrap"> </span>29</td> <td><a href="/wiki/Wood" title="Wood">Wood</a> ignites, given time </td></tr> <tr> <td><span class="nowrap"> </span>20</td> <td>Typical beginning of <a href="/wiki/Flashover" title="Flashover">flashover</a> at floor level of a residential room </td></tr> <tr> <td><span class="nowrap"> </span>16</td> <td><a href="/wiki/Human_skin" title="Human skin">Human skin</a>: sudden pain and second-degree <a href="/wiki/Burn" title="Burn">burn</a> <a href="/wiki/Blister" title="Blister">blisters</a> after 5 seconds </td></tr> <tr> <td><span class="nowrap"> </span>12.5</td> <td><a href="/wiki/Wood" title="Wood">Wood</a> produces ignitable volatiles by <a href="/wiki/Pyrolysis" title="Pyrolysis">pyrolysis</a> </td></tr> <tr> <td><span class="nowrap"> </span>10.4</td> <td>Human skin: Pain after 3 seconds, second-degree burn blisters after 9 seconds </td></tr> <tr> <td><span class="nowrap">  </span>6.4</td> <td>Human skin: second-degree burn blisters after 18 seconds </td></tr> <tr> <td><span class="nowrap">  </span>4.5</td> <td>Human skin: second-degree burn blisters after 30 seconds </td></tr> <tr> <td><span class="nowrap">  </span>2.5</td> <td>Human skin: burns after prolonged exposure, radiant flux exposure typically encountered during <a href="/wiki/Firefighting" title="Firefighting">firefighting</a> </td></tr> <tr> <td><span class="nowrap">  </span>1.4</td> <td><a href="/wiki/Sunlight" title="Sunlight">Sunlight</a>, <a href="/wiki/Sunburn" title="Sunburn">sunburns</a> potentially within 30 minutes. Sunburn is NOT a thermal burn. It is caused by cellular damage due to ultraviolet radiation. </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Near-field_radiative_heat_transfer">Near-field radiative heat transfer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=42" title="Edit section: Near-field radiative heat transfer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Near-field_radiative_heat_transfer" title="Near-field radiative heat transfer">Near-field radiative heat transfer</a></div> <p>At distances on the scale of the wavelength of a radiated electromangetic wave or smaller, Planck's law is not accurate. For objects this small and close together, the <a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">quantum tunneling</a> of EM waves has a significant impact on the rate of radiation.<sup id="cite_ref-:9_1-3" class="reference"><a href="#cite_note-:9-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>A more sophisticated framework involving electromagnetic theory must be used for smaller distances from the thermal source or surface. For example, although <a href="/wiki/Near_and_far_field" title="Near and far field">far-field</a> thermal radiation at distances from surfaces of more than one wavelength is generally not coherent to any extent, near-field thermal radiation (i.e., radiation at distances of a fraction of various radiation wavelengths) may exhibit a degree of both temporal and spatial coherence.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>Planck's law of thermal radiation has been challenged in recent decades by predictions and successful demonstrations of the radiative heat transfer between objects separated by nanoscale gaps that deviate significantly from the law predictions. This deviation is especially strong (up to several orders in magnitude) when the emitter and absorber support surface polariton modes that can couple through the gap separating cold and hot objects. However, to take advantage of the surface-polariton-mediated near-field radiative heat transfer, the two objects need to be separated by ultra-narrow gaps on the order of microns or even nanometers. This limitation significantly complicates practical device designs. </p><p>Another way to modify the object thermal emission spectrum is by reducing the dimensionality of the emitter itself.<sup id="cite_ref-:0_28-1" class="reference"><a href="#cite_note-:0-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> This approach builds upon the concept of confining electrons in quantum wells, wires and dots, and tailors thermal emission by engineering confined photon states in two- and three-dimensional potential traps, including wells, wires, and dots. Such spatial confinement concentrates photon states and enhances thermal emission at select frequencies.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> To achieve the required level of photon confinement, the dimensions of the radiating objects should be on the order of or below the thermal wavelength predicted by Planck's law. Most importantly, the emission spectrum of thermal wells, wires and dots deviates from Planck's law predictions not only in the near field, but also in the far field, which significantly expands the range of their applications. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=43" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Incandescence" class="mw-redirect" title="Incandescence">Incandescence</a></li> <li><a href="/wiki/Infrared_photography" title="Infrared photography">Infrared photography</a></li> <li><a href="/wiki/Interior_radiation_control_coating" title="Interior radiation control coating">Interior radiation control coating</a></li> <li><a href="/wiki/Heat_transfer" title="Heat transfer">Heat transfer</a></li> <li><a href="/wiki/Microwave#Heating_and_power_application" title="Microwave">Microwave Radiation</a></li> <li><a href="/wiki/Planck_radiation" class="mw-redirect" title="Planck radiation">Planck radiation</a></li> <li><a href="/wiki/Radiant_cooling" class="mw-redirect" title="Radiant cooling">Radiant cooling</a></li> <li><a href="/wiki/Sakuma%E2%80%93Hattori_equation" title="Sakuma–Hattori equation">Sakuma–Hattori equation</a></li> <li><a href="/wiki/Thermal_dose_unit" title="Thermal dose unit">Thermal dose unit</a></li> <li><a href="/wiki/View_factor" title="View factor">View factor</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=44" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-:9-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:9_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:9_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:9_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:9_1-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFHowellMengüçSiegel2016" class="citation book cs1">Howell, John R.; Mengüç, M. Pinar; Siegel, Robert (2016). <i>Thermal radiation heat transfer</i> (Sixth ed.). Boca Raton, Fla. London New York: CRC Press, Taylor & Francis Group. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4665-9326-8" title="Special:BookSources/978-1-4665-9326-8"><bdi>978-1-4665-9326-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermal+radiation+heat+transfer&rft.place=Boca+Raton%2C+Fla.+London+New+York&rft.edition=Sixth&rft.pub=CRC+Press%2C+Taylor+%26+Francis+Group&rft.date=2016&rft.isbn=978-1-4665-9326-8&rft.aulast=Howell&rft.aufirst=John+R.&rft.au=Meng%C3%BC%C3%A7%2C+M.+Pinar&rft.au=Siegel%2C+Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-:1-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMeseguer2012" class="citation book cs1">Meseguer, José. (2012). <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/903167592"><i>Spacecraft thermal control</i></a>. Isabel Pérez-Grande, Angel Sanz-Andrés. Cambridge: Woodhead Pub. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-85709-608-1" title="Special:BookSources/978-0-85709-608-1"><bdi>978-0-85709-608-1</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/903167592">903167592</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20241006084643/https://search.worldcat.org/title/903167592">Archived</a> from the original on 6 October 2024<span class="reference-accessdate">. Retrieved <span class="nowrap">12 May</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Spacecraft+thermal+control&rft.place=Cambridge&rft.pub=Woodhead+Pub&rft.date=2012&rft_id=info%3Aoclcnum%2F903167592&rft.isbn=978-0-85709-608-1&rft.aulast=Meseguer&rft.aufirst=Jos%C3%A9.&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F903167592&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-:3-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Planck, M., <a rel="nofollow" class="external text" href="https://books.google.com/books?id=2PR_AAAAMAAJ&dq=Planck,+M.,+The+Theory+of+Heat+Radiation,+Dover+Publications,+New+York,+1959.&pg=PR13">The Theory of Heat Radiation</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20241006084644/https://books.google.com/books?id=2PR_AAAAMAAJ&dq=Planck,+M.,+The+Theory+of+Heat+Radiation,+Dover+Publications,+New+York,+1959.&pg=PR13#v=onepage&q&f=false">Archived</a> 6 October 2024 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, P Blakiston's Son & Co., New York, 1914.</span> </li> <li id="cite_note-:8-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:8_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:8_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuang1987" class="citation book cs1">Huang, Kerson (1987). <i>Statistical mechanics</i> (2nd ed.). New York: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-81518-1" title="Special:BookSources/978-0-471-81518-1"><bdi>978-0-471-81518-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+mechanics&rft.place=New+York&rft.edition=2nd&rft.pub=Wiley&rft.date=1987&rft.isbn=978-0-471-81518-1&rft.aulast=Huang&rft.aufirst=Kerson&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-blundell-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-blundell_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-blundell_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFS._Blundell,_K._Blundell2006" class="citation book cs1">S. Blundell, K. Blundell (2006). <i>Concepts in Thermal Physics</i>. Oxford University Press. p. 247. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-856769-1" title="Special:BookSources/978-0-19-856769-1"><bdi>978-0-19-856769-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Concepts+in+Thermal+Physics&rft.pages=247&rft.pub=Oxford+University+Press&rft.date=2006&rft.isbn=978-0-19-856769-1&rft.au=S.+Blundell%2C+K.+Blundell&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-:4-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-:4_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:4_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:4_6-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:4_6-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:4_6-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:4_6-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPutley1982" class="citation journal cs1">Putley, E.H. (1982). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/0020089182900306">"History of infrared detection—part I. The first detectors of thermal radiation"</a>. <i>Infrared Physics</i>. <b>22</b> (3): 125–131. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1982InfPh..22..125P">1982InfPh..22..125P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0020-0891%2882%2990030-6">10.1016/0020-0891(82)90030-6</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20241006084644/https://www.sciencedirect.com/unsupported_browser">Archived</a> from the original on 6 October 2024<span class="reference-accessdate">. Retrieved <span class="nowrap">29 February</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Infrared+Physics&rft.atitle=History+of+infrared+detection%E2%80%94part+I.+The+first+detectors+of+thermal+radiation&rft.volume=22&rft.issue=3&rft.pages=125-131&rft.date=1982&rft_id=info%3Adoi%2F10.1016%2F0020-0891%2882%2990030-6&rft_id=info%3Abibcode%2F1982InfPh..22..125P&rft.aulast=Putley&rft.aufirst=E.H.&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2F0020089182900306&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Cohen, I. B. (1943). <a rel="nofollow" class="external text" href="http://www.jstor.org/stable/225739">Franklin’s Experiments on Heat Absorption as a Function of Color</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240925182208/https://www.jstor.org/stable/225739">Archived</a> 25 September 2024 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. <i>Isis</i>, <i>34</i>(5), 404–407.</span> </li> <li id="cite_note-:22-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-:22_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:22_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:22_8-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:22_8-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrown1967" class="citation cs2">Brown, Sanborn C. (1967), <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1016/b978-0-08-012179-6.50008-3">"The Caloric Theory"</a>, <i>Men of Physics: Benjamin Thompson – Count Rumford</i>, Elsevier, pp. 16–24, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fb978-0-08-012179-6.50008-3">10.1016/b978-0-08-012179-6.50008-3</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780080121796" title="Special:BookSources/9780080121796"><bdi>9780080121796</bdi></a>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20241006084656/https://www.sciencedirect.com/unsupported_browser">archived</a> from the original on 6 October 2024<span class="reference-accessdate">, retrieved <span class="nowrap">3 December</span> 2021</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Men+of+Physics%3A+Benjamin+Thompson+%E2%80%93+Count+Rumford&rft.atitle=The+Caloric+Theory&rft.pages=16-24&rft.date=1967&rft_id=info%3Adoi%2F10.1016%2Fb978-0-08-012179-6.50008-3&rft.isbn=9780080121796&rft.aulast=Brown&rft.aufirst=Sanborn+C.&rft_id=http%3A%2F%2Fdx.doi.org%2F10.1016%2Fb978-0-08-012179-6.50008-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGillispie1960" class="citation book cs1"><a href="/wiki/Charles_Coulston_Gillispie" title="Charles Coulston Gillispie">Gillispie, Charles Coulston</a> (1960). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/edgeofobjectivit00char/page/408"><i>The Edge of Objectivity: An Essay in the History of Scientific Ideas</i></a></span>. Princeton University Press. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/edgeofobjectivit00char/page/408">408–9</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-02350-6" title="Special:BookSources/0-691-02350-6"><bdi>0-691-02350-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Edge+of+Objectivity%3A+An+Essay+in+the+History+of+Scientific+Ideas&rft.pages=408-9&rft.pub=Princeton+University+Press&rft.date=1960&rft.isbn=0-691-02350-6&rft.aulast=Gillispie&rft.aufirst=Charles+Coulston&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fedgeofobjectivit00char%2Fpage%2F408&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLemonsShanahanBuchholtz2022" class="citation book cs1">Lemons, Don S.; Shanahan, William R.; Buchholtz, Louis J. (20 September 2022). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=fUpTEAAAQBAJ"><i>On the Trail of Blackbody Radiation: Max Planck and the Physics of his Era</i></a>. MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-04704-3" title="Special:BookSources/978-0-262-04704-3"><bdi>978-0-262-04704-3</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20241006084643/https://books.google.com/books?id=fUpTEAAAQBAJ">Archived</a> from the original on 6 October 2024<span class="reference-accessdate">. Retrieved <span class="nowrap">29 February</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=On+the+Trail+of+Blackbody+Radiation%3A+Max+Planck+and+the+Physics+of+his+Era&rft.pub=MIT+Press&rft.date=2022-09-20&rft.isbn=978-0-262-04704-3&rft.aulast=Lemons&rft.aufirst=Don+S.&rft.au=Shanahan%2C+William+R.&rft.au=Buchholtz%2C+Louis+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DfUpTEAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-:5-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-:5_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:5_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100344451">"Pierre Prévost"</a>. <i>Oxford Reference</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20241006084644/https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100344451">Archived</a> from the original on 6 October 2024<span class="reference-accessdate">. Retrieved <span class="nowrap">29 February</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Oxford+Reference&rft.atitle=Pierre+Pr%C3%A9vost&rft_id=https%3A%2F%2Fwww.oxfordreference.com%2Fdisplay%2F10.1093%2Foi%2Fauthority.20110803100344451&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHerschel1800" class="citation journal cs1">Herschel, William (1800). <a rel="nofollow" class="external text" href="https://babel.hathitrust.org/cgi/pt?id=pst.000054592520;view=1up;seq=358">"Experiments on the refrangibility of the invisible rays of the Sun"</a>. <i>Philosophical Transactions of the Royal Society of London</i>. <b>90</b>: 284–292. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1800.0015">10.1098/rstl.1800.0015</a></span>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/107057">107057</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210204133019/https://babel.hathitrust.org/cgi/pt?id=pst.000054592520;view=1up;seq=358">Archived</a> from the original on 4 February 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">1 March</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+of+London&rft.atitle=Experiments+on+the+refrangibility+of+the+invisible+rays+of+the+Sun&rft.volume=90&rft.pages=284-292&rft.date=1800&rft_id=info%3Adoi%2F10.1098%2Frstl.1800.0015&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F107057%23id-name%3DJSTOR&rft.aulast=Herschel&rft.aufirst=William&rft_id=https%3A%2F%2Fbabel.hathitrust.org%2Fcgi%2Fpt%3Fid%3Dpst.000054592520%3Bview%3D1up%3Bseq%3D358&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120225094516/http://coolcosmos.ipac.caltech.edu/cosmic_classroom/classroom_activities/herschel_bio.html">"Herschel Discovers Infrared Light"</a>. <i>Coolcosmos.ipac.caltech.edu</i>. 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Van Nostrand Company, Inc.,1962.</span> </li> <li id="cite_note-becker-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-becker_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-becker_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Becker, Martin. <i>Heat Transfer a Modern Approach</i> New York: Plenum Publishing Corporation, 1986.</span> </li> <li id="cite_note-:7-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-:7_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:7_16-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKirchhoff1860" class="citation journal cs1">Kirchhoff, G. (July 1860). <a rel="nofollow" class="external text" href="https://www.tandfonline.com/doi/full/10.1080/14786446008642901">"I. On the relation between the radiating and absorbing powers of different bodies for light and heat"</a>. <i>The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science</i>. <b>20</b> (130): 1–21. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F14786446008642901">10.1080/14786446008642901</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1941-5982">1941-5982</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+London%2C+Edinburgh%2C+and+Dublin+Philosophical+Magazine+and+Journal+of+Science&rft.atitle=I.+On+the+relation+between+the+radiating+and+absorbing+powers+of+different+bodies+for+light+and+heat&rft.volume=20&rft.issue=130&rft.pages=1-21&rft.date=1860-07&rft_id=info%3Adoi%2F10.1080%2F14786446008642901&rft.issn=1941-5982&rft.aulast=Kirchhoff&rft.aufirst=G.&rft_id=https%3A%2F%2Fwww.tandfonline.com%2Fdoi%2Ffull%2F10.1080%2F14786446008642901&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoltzmann1884" class="citation journal cs1 cs1-prop-foreign-lang-source">Boltzmann, Ludwig (1884). <a rel="nofollow" class="external text" href="https://babel.hathitrust.org/cgi/pt?id=uc1.a0002763670;view=1up;seq=305">"Ableitung des Stefan'schen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der electromagnetischen Lichttheorie"</a> [Derivation of Stefan's law, concerning the dependency of heat radiation on temperature, from the electromagnetic theory of light]. <i>Annalen der Physik und Chemie</i> (in German). <b>258</b> (6): 291–294. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1884AnP...258..291B">1884AnP...258..291B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18842580616">10.1002/andp.18842580616</a></span>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200729024251/https://babel.hathitrust.org/cgi/pt?id=uc1.a0002763670">Archived</a> from the original on 29 July 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">25 March</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik+und+Chemie&rft.atitle=Ableitung+des+Stefan%27schen+Gesetzes%2C+betreffend+die+Abh%C3%A4ngigkeit+der+W%C3%A4rmestrahlung+von+der+Temperatur+aus+der+electromagnetischen+Lichttheorie&rft.volume=258&rft.issue=6&rft.pages=291-294&rft.date=1884&rft_id=info%3Adoi%2F10.1002%2Fandp.18842580616&rft_id=info%3Abibcode%2F1884AnP...258..291B&rft.aulast=Boltzmann&rft.aufirst=Ludwig&rft_id=https%3A%2F%2Fbabel.hathitrust.org%2Fcgi%2Fpt%3Fid%3Duc1.a0002763670%3Bview%3D1up%3Bseq%3D305&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-:6-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-:6_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:6_18-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:6_18-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:6_18-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFÇengelGhajar2011" class="citation book cs1">Çengel, Yunus A.; Ghajar, Afshin J. (2011). <a rel="nofollow" class="external text" href="https://www.worldcat.org/title/463634284"><i>Heat and mass transfer: fundamentals & applications</i></a> (4th ed.). New York: McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-339812-9" title="Special:BookSources/978-0-07-339812-9"><bdi>978-0-07-339812-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/463634284">463634284</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Heat+and+mass+transfer%3A+fundamentals+%26+applications&rft.place=New+York&rft.edition=4th&rft.pub=McGraw-Hill&rft.date=2011&rft_id=info%3Aoclcnum%2F463634284&rft.isbn=978-0-07-339812-9&rft.aulast=%C3%87engel&rft.aufirst=Yunus+A.&rft.au=Ghajar%2C+Afshin+J.&rft_id=https%3A%2F%2Fwww.worldcat.org%2Ftitle%2F463634284&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://archive.today/20110721181740/http://cc.oulu.fi/~kempmp/colours.html">"The Physics of Coloured Fireworks"</a>. 21 July 2011. Archived from <a rel="nofollow" class="external text" href="http://cc.oulu.fi/~kempmp/colours.html">the original</a> on 21 July 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Physics+of+Coloured+Fireworks&rft.date=2011-07-21&rft_id=http%3A%2F%2Fcc.oulu.fi%2F~kempmp%2Fcolours.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDionysius_Lardner1833" class="citation book cs1"><a href="/wiki/Dionysius_Lardner" title="Dionysius Lardner">Dionysius Lardner</a> (1833). <a rel="nofollow" class="external text" href="https://archive.org/details/treatiseonheat00lardgoog"><i>Treatise on Heat</i></a>. Longman, Rees, Orme, Brown, Green & Longman. p. <a rel="nofollow" class="external text" href="https://archive.org/details/treatiseonheat00lardgoog/page/n364">341</a>. <q>The state in which a heated body, naturally incapable of emitting light, becomes <a href="/wiki/Luminosity" title="Luminosity">luminous</a>, is called a state of <i>incandescence</i>.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Treatise+on+Heat&rft.pages=341&rft.pub=Longman%2C+Rees%2C+Orme%2C+Brown%2C+Green+%26+Longman&rft.date=1833&rft.au=Dionysius+Lardner&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ftreatiseonheat00lardgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohn_E._Bowman1856" class="citation book cs1">John E. Bowman (1856). <a rel="nofollow" class="external text" href="https://archive.org/details/anintroductiont01bowmgoog"><i>An Introduction to Practical Chemistry, Including Analysis</i></a> (Second American ed.). Philadelphia: Blanchard and Lea. p. <a rel="nofollow" class="external text" href="https://archive.org/details/anintroductiont01bowmgoog/page/n289">283</a>. <q>incandesce 0-1860.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Practical+Chemistry%2C+Including+Analysis&rft.pages=283&rft.edition=Second+American&rft.pub=Philadelphia%3A+Blanchard+and+Lea&rft.date=1856&rft.au=John+E.+Bowman&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fanintroductiont01bowmgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-:2-22"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_22-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_22-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:2_22-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:2_22-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:2_22-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:2_22-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-:2_22-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-:2_22-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-:2_22-8"><sup><i><b>i</b></i></sup></a> <a href="#cite_ref-:2_22-9"><sup><i><b>j</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIncroperaDeWittBergmanLavine2013" class="citation book cs1">Incropera, Frank P.; DeWitt, David P.; Bergman, Theodore L.; Lavine, Adrienne S., eds. 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Retrieved <span class="nowrap">24 January</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Optical+Properties+and+Radiative+Cooling+Power+of+White+Paints&rft_id=http%3A%2F%2Fwire0.ises.org%2Fwire%2Fdoclibs%2FSWC1999.nsf%2Fid%2FD33990A41EA63969C1256920003D6148%2F%24File%2F038.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span> ISES 1999 Solar World Congress</span> </li> <li id="cite_note-rtps-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-rtps_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShao2019" class="citation journal cs1">Shao, Gaofeng; et al. (2019). "Improved oxidation resistance of high emissivity coatings on fibrous ceramic for reusable space systems". <i>Corrosion Science</i>. <b>146</b>: 233–246. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1902.03943">1902.03943</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2019Corro.146..233S">2019Corro.146..233S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.corsci.2018.11.006">10.1016/j.corsci.2018.11.006</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118927116">118927116</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Corrosion+Science&rft.atitle=Improved+oxidation+resistance+of+high+emissivity+coatings+on+fibrous+ceramic+for+reusable+space+systems&rft.volume=146&rft.pages=233-246&rft.date=2019&rft_id=info%3Aarxiv%2F1902.03943&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118927116%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.corsci.2018.11.006&rft_id=info%3Abibcode%2F2019Corro.146..233S&rft.aulast=Shao&rft.aufirst=Gaofeng&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliam_Elgin_Wickenden1910" class="citation book cs1">William Elgin Wickenden (1910). <a rel="nofollow" class="external text" href="https://archive.org/details/illuminationphot00wickrich"><i>Illumination and Photometry</i></a>. McGraw-Hill. p. <a rel="nofollow" class="external text" href="https://archive.org/details/illuminationphot00wickrich/page/3">3</a>. <q>incandescent low-efficiency blackbody.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Illumination+and+Photometry&rft.pages=3&rft.pub=McGraw-Hill&rft.date=1910&rft.au=William+Elgin+Wickenden&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Filluminationphot00wickrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKoones2012" class="citation book cs1">Koones, Sheri (1 October 2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Tdrp2F3BExAC&q=fluorescent+light+and+LEDs%2C+do+not+function+by+incandescence.&pg=PT115"><i>Prefabulous + Almost Off the Grid: Your Path to Building an Energy-Independent Home</i></a>. 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"Ultrabroadband photonic structures to achieve high-performance daytime radiative cooling". <i>Nano Letters</i>. <b>13</b> (4): 1457–1461. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013NanoL..13.1457R">2013NanoL..13.1457R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fnl4004283">10.1021/nl4004283</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23461597">23461597</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:27762117">27762117</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nano+Letters&rft.atitle=Ultrabroadband+photonic+structures+to+achieve+high-performance+daytime+radiative+cooling&rft.volume=13&rft.issue=4&rft.pages=1457-1461&rft.date=2013&rft_id=info%3Adoi%2F10.1021%2Fnl4004283&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A27762117%23id-name%3DS2CID&rft_id=info%3Apmid%2F23461597&rft_id=info%3Abibcode%2F2013NanoL..13.1457R&rft.aulast=Rephaeli&rft.aufirst=Eden&rft.au=Raman%2C+Aaswath&rft.au=Fan%2C+Shanhui&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=45" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSiegel,_John_R._HowellHowell._John_R.2001" class="citation book cs1">Siegel, John R. Howell, Robert; Howell. John R. (November 2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=O389yQ0-fecC&q=Thermal+radiation&pg=PA1"><i>Thermal radiation heat transfer</i></a>. New York: Taylor & Francis, Inc. pp. (xix – xxvi <i>list of symbols for thermal radiation formulas</i>). <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56032-839-1" title="Special:BookSources/978-1-56032-839-1"><bdi>978-1-56032-839-1</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">23 July</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermal+radiation+heat+transfer&rft.place=New+York&rft.pages=%28xix+-+xxvi+%27%27list+of+symbols+for+thermal+radiation+formulas%27%27%29&rft.pub=Taylor+%26+Francis%2C+Inc.&rft.date=2001-11&rft.isbn=978-1-56032-839-1&rft.aulast=Siegel%2C+John+R.+Howell&rft.aufirst=Robert&rft.au=Howell.+John+R.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DO389yQ0-fecC%26q%3DThermal%2Bradiation%26pg%3DPA1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+radiation" class="Z3988"></span></li> <li><a href="/wiki/Ephraim_M._Sparrow" title="Ephraim M. Sparrow">E.M. Sparrow</a> and <a href="/wiki/Robert_D._Cess" title="Robert D. Cess">R.D. Cess</a>. Radiation Heat Transfer. Hemisphere Publishing Corporation, 1978.</li> <li>Kuenzer, C. and S. Dech (2013): Thermal Infrared Remote Sensing: Sensors, Methods, Applications (= Remote Sensing and Digital Image Processing 17). Dordrecht: Springer.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_radiation&action=edit&section=46" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.spectralcalc.com/blackbody_calculator/blackbody.php">Black Body Emission Calculator</a></li> <li><a rel="nofollow" class="external text" href="http://www.veliyaththermostatics.com/resources.php">Heat transfer</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060620133121/http://www.du.edu/~etuttle/weather/atmrad.htm">Atmospheric Radiation</a></li> <li><a rel="nofollow" class="external text" href="http://www.hartscientific.com/publications/pdfs/3187781_A_w.pdf">Infrared Temperature Calibration 101</a></li></ul> <div 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href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li> <li><a class="mw-selflink selflink">Thermal radiation</a></li> <li><a href="/wiki/Black-body_radiation" title="Black-body radiation">Black-body radiation</a></li> <li><a href="/wiki/Particle_radiation" title="Particle radiation">Particle radiation</a></li> <li><a href="/wiki/Gravitational_radiation" class="mw-redirect" title="Gravitational radiation">Gravitational radiation</a></li> <li><a href="/wiki/Cosmic_background_radiation" title="Cosmic background radiation">Cosmic background radiation</a></li> <li><a href="/wiki/Cherenkov_radiation" title="Cherenkov radiation">Cherenkov radiation</a></li> <li><a href="/wiki/Askaryan_radiation" title="Askaryan radiation">Askaryan radiation</a></li> <li><a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li> <li><a href="/wiki/Unruh_radiation" class="mw-redirect" title="Unruh radiation">Unruh radiation</a></li> <li><a href="/wiki/Dark_radiation" title="Dark radiation">Dark radiation</a></li> <li><a href="/wiki/Radiation_exposure" title="Radiation exposure">Radiation exposure</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Radiation <br />and health</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Radiation syndrome <ul><li><a href="/wiki/Acute_radiation_syndrome" title="Acute radiation syndrome">acute</a></li> <li><a href="/wiki/Chronic_radiation_syndrome" title="Chronic radiation syndrome">chronic</a></li></ul></li> <li><a href="/wiki/Health_physics" title="Health physics">Health physics</a></li> <li><a href="/wiki/Dosimetry" title="Dosimetry">Dosimetry</a></li> <li><a href="/wiki/Electromagnetic_radiation_and_health" title="Electromagnetic radiation and health">Electromagnetic radiation and health</a></li> <li><a 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de Dios radiotherapy accident">1996 Costa Rica accident</a></li> <li><a href="/wiki/Goi%C3%A2nia_accident" title="Goiânia accident">1987 Goiânia accident</a></li> <li><a href="/wiki/1984_Moroccan_radiation_accident" title="1984 Moroccan radiation accident">1984 Moroccan accident</a></li> <li><a href="/wiki/1990_Clinic_of_Zaragoza_radiotherapy_accident" class="mw-redirect" title="1990 Clinic of Zaragoza radiotherapy accident">1990 Zaragoza accident</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related articles</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Half-life" title="Half-life">Half-life</a></li> <li><a href="/wiki/Nuclear_physics" title="Nuclear physics">Nuclear physics</a></li> <li><a href="/wiki/Radioactive_source" title="Radioactive source">Radioactive source</a></li> <li><a href="/wiki/Radiation_hardening" title="Radiation 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