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</div> </a> <ul id="toc-Absorption-compression_heat_pump-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Coefficient_of_performance" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Coefficient_of_performance"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Coefficient of performance</span> </div> </a> <ul id="toc-Coefficient_of_performance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div 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Available in 14 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-14" 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">14 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D9%88%D8%B1%D8%A9_%D8%A7%D9%84%D8%AA%D8%A8%D8%B1%D9%8A%D8%AF_%D9%88%D9%85%D8%B6%D8%AE%D8%A9_%D8%A7%D9%84%D8%AD%D8%B1%D8%A7%D8%B1%D8%A9" title="دورة التبريد ومضخة الحرارة – Arabic" lang="ar" hreflang="ar" data-title="دورة التبريد ومضخة الحرارة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B9%E0%A6%BF%E0%A6%9F_(%E0%A6%A4%E0%A6%BE%E0%A6%AA%E0%A7%80%E0%A6%AF%E0%A6%BC)_%E0%A6%AA%E0%A6%BE%E0%A6%AE%E0%A7%8D%E0%A6%AA_%E0%A6%8F%E0%A6%AC%E0%A6%82_%E0%A6%B6%E0%A7%80%E0%A6%A4%E0%A6%B2%E0%A7%80%E0%A6%95%E0%A6%B0%E0%A6%A3_%E0%A6%9A%E0%A6%95%E0%A7%8D%E0%A6%B0" title="হিট (তাপীয়) পাম্প এবং শীতলীকরণ চক্র – Bangla" lang="bn" hreflang="bn" data-title="হিট (তাপীয়) পাম্প এবং শীতলীকরণ চক্র" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Bomba_de_calor_y_ciclo_de_refrigeraci%C3%B3n" title="Bomba de calor y ciclo de refrigeración – Spanish" lang="es" hreflang="es" data-title="Bomba de calor y ciclo de refrigeración" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%86%D8%B1%D8%AE%D9%87_%D9%BE%D9%85%D9%BE_%D8%AD%D8%B1%D8%A7%D8%B1%D8%AA%DB%8C_%D9%88_%D8%AE%D9%86%DA%A9%E2%80%8C%D8%B3%D8%A7%D8%B2" title="چرخه پمپ حرارتی و خنک‌ساز – Persian" lang="fa" hreflang="fa" data-title="چرخه پمپ حرارتی و خنک‌ساز" 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/Cycle_frigorifique" title="Cycle frigorifique – French" lang="fr" hreflang="fr" data-title="Cycle frigorifique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Kalora_pumpilo_e_frigorizo_cikli" title="Kalora pumpilo e frigorizo cikli – Ido" lang="io" hreflang="io" data-title="Kalora pumpilo e frigorizo cikli" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ciclo_frigorifero" title="Ciclo frigorifero – Italian" lang="it" hreflang="it" data-title="Ciclo frigorifero" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Ciclo_rinfrescant" title="Ciclo rinfrescant – Lombard" lang="lmo" hreflang="lmo" data-title="Ciclo rinfrescant" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ciclo_de_refrigera%C3%A7%C3%A3o" title="Ciclo de refrigeração – Portuguese" lang="pt" hreflang="pt" data-title="Ciclo de refrigeração" 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/Ciclul_ma%C8%99inilor_frigorifice_%C8%99i_al_pompelor_de_c%C4%83ldur%C4%83" title="Ciclul mașinilor frigorifice și al pompelor de căldură – Romanian" lang="ro" hreflang="ro" data-title="Ciclul mașinilor frigorifice și al pompelor de căldură" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/Tziclu_frigor%C3%ACferu" title="Tziclu frigorìferu – Sardinian" lang="sc" hreflang="sc" data-title="Tziclu frigorìferu" data-language-autonym="Sardu" data-language-local-name="Sardinian" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Heat_pump_and_refrigeration_cycle" title="Heat pump and refrigeration cycle – Simple English" lang="en-simple" hreflang="en-simple" data-title="Heat pump and refrigeration cycle" 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-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/So%C4%9Futma_%C3%A7evrimi" title="Soğutma çevrimi – Turkish" lang="tr" hreflang="tr" data-title="Soğutma çevrimi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-zh 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title" style="padding-bottom:0.3em;border-bottom:1px solid #aaa;"><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a></th></tr><tr><td class="sidebar-image" style="display:block;margin:0.3em 0 0.4em;"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/Carnot_heat_engine" title="Carnot heat engine"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/220px-Carnot_heat_engine_2.svg.png" decoding="async" width="220" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/330px-Carnot_heat_engine_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/440px-Carnot_heat_engine_2.svg.png 2x" data-file-width="840" data-file-height="370" /></a></span><div class="sidebar-caption">The classical <a href="/wiki/Carnot_heat_engine" title="Carnot heat engine">Carnot heat engine</a></div></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)">Branches</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Thermodynamics" title="Thermodynamics">Classical</a></li> <li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical</a></li> <li><a href="/wiki/Quantum_thermodynamics" title="Quantum thermodynamics">Quantum thermodynamics</a></li></ul> </div> <ul><li><a href="/wiki/Equilibrium_thermodynamics" title="Equilibrium thermodynamics">Equilibrium</a> / <a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">Laws</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Zeroth_law_of_thermodynamics" title="Zeroth law of thermodynamics">Zeroth</a></li> <li><a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">First</a></li> <li><a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">Second</a></li> <li><a href="/wiki/Third_law_of_thermodynamics" title="Third law of thermodynamics">Third</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Thermodynamic_system" title="Thermodynamic system">Systems</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Closed_system" title="Closed system">Closed system</a></li> <li><a href="/wiki/Thermodynamic_system#Open_system" title="Thermodynamic system">Open system</a></li> <li><a href="/wiki/Isolated_system" title="Isolated system">Isolated system</a></li></ul> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_state" title="Thermodynamic state">State</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Equation_of_state" title="Equation of state">Equation of state</a></li> <li><a href="/wiki/Ideal_gas" title="Ideal gas">Ideal gas</a></li> <li><a href="/wiki/Real_gas" title="Real gas">Real gas</a></li> <li><a href="/wiki/State_of_matter" title="State of matter">State of matter</a></li> <li><a href="/wiki/Phase_(matter)" title="Phase (matter)">Phase (matter)</a></li> <li><a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">Equilibrium</a></li> <li><a href="/wiki/Control_volume" title="Control volume">Control volume</a></li> <li><a href="/wiki/Thermodynamic_instruments" title="Thermodynamic instruments">Instruments</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_process" title="Thermodynamic process">Processes</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Isobaric_process" title="Isobaric process">Isobaric</a></li> <li><a href="/wiki/Isochoric_process" title="Isochoric process">Isochoric</a></li> <li><a href="/wiki/Isothermal_process" title="Isothermal process">Isothermal</a></li> <li><a href="/wiki/Adiabatic_process" title="Adiabatic process">Adiabatic</a></li> <li><a href="/wiki/Isentropic_process" title="Isentropic process">Isentropic</a></li> <li><a href="/wiki/Isenthalpic_process" title="Isenthalpic process">Isenthalpic</a></li> <li><a href="/wiki/Quasistatic_process" title="Quasistatic process">Quasistatic</a></li> <li><a href="/wiki/Polytropic_process" title="Polytropic process">Polytropic</a></li> <li><a href="/wiki/Free_expansion" class="mw-redirect" title="Free expansion">Free expansion</a></li> <li><a href="/wiki/Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">Reversibility</a></li> <li><a href="/wiki/Irreversible_process" title="Irreversible process">Irreversibility</a></li> <li><a href="/wiki/Endoreversible_thermodynamics" title="Endoreversible thermodynamics">Endoreversibility</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_cycle" title="Thermodynamic cycle">Cycles</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Heat_engine" title="Heat engine">Heat engines</a></li> <li><a class="mw-selflink selflink">Heat pumps</a></li> <li><a href="/wiki/Thermal_efficiency" title="Thermal efficiency">Thermal efficiency</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/List_of_thermodynamic_properties" title="List of thermodynamic properties">System properties</a></div><div class="sidebar-list-content mw-collapsible-content"><div style="font-size:90%;padding-bottom:0.2em;border-bottom:1px solid #aaa;">Note: <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">Conjugate variables</a> in <i>italics</i></div> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none;margin-top:0.4em;"><tbody><tr><td class="sidebar-content" style="padding-bottom:0.7em;"> <ul><li><a href="/wiki/Thermodynamic_diagrams" title="Thermodynamic diagrams">Property diagrams</a></li> <li><a href="/wiki/Intensive_and_extensive_properties" title="Intensive and extensive properties">Intensive and extensive properties</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Process_function" title="Process function">Process functions</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;;padding-bottom:0.4em;"> <div class="hlist"> <ul><li><a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">Work</a></li> <li><a href="/wiki/Heat" title="Heat">Heat</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/State_function" title="State function">Functions of state</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;"> <ul><li><a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">Temperature</a> / <i><a href="/wiki/Entropy" title="Entropy">Entropy</a></i> (<a href="/wiki/Introduction_to_entropy" title="Introduction to entropy">introduction</a>)</li> <li><a href="/wiki/Pressure" title="Pressure">Pressure</a> / <i><a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">Volume</a></i></li> <li><a href="/wiki/Chemical_potential" title="Chemical potential">Chemical potential</a> / <i><a href="/wiki/Particle_number" title="Particle number">Particle number</a></i></li> <li><a href="/wiki/Vapor_quality" title="Vapor quality">Vapor quality</a></li> <li><a href="/wiki/Reduced_properties" title="Reduced properties">Reduced properties</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Material_properties_(thermodynamics)" title="Material properties (thermodynamics)">Material properties</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Thermodynamic_databases_for_pure_substances" title="Thermodynamic databases for pure substances">Property databases</a></li></ul> <div style="font-size:90%;margin-top:0.4em;border-top:1px solid #aaa;text-align:center;"> <table> <tbody><tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Heat_capacity" title="Heat capacity">Specific heat capacity</a> </td> <td style="vertical-align:middle; text-align:left"><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> <mo>=</mo> </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/891d40a9b18752b04065caee655d008b3ec11428" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.46ex; height:1.676ex;" alt="{\displaystyle c=}"></span></td> <td><table><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><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 \partial S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c609f4d3c5692ea4495479ef47594dc67f9fa464" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.817ex; height:2.176ex;" alt="{\displaystyle \partial S}"></span></td></tr><tr><td style="border-top:solid 1px black;"><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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span></td><td style="border-top:solid 1px black;"><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 \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}"></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Compressibility" title="Compressibility">Compressibility</a> </td> <td style="vertical-align:middle; text-align:left"><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 \beta =-}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =-}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b01c042bf1456bd4d2a8caed1f4912820a7ecbb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.239ex; height:2.509ex;" alt="{\displaystyle \beta =-}"></span></td> <td><table><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 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span></td><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 \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}"></span></td></tr><tr><td style="border-top:solid 1px black;"><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 V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span></td><td style="border-top:solid 1px black;"><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 \partial p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebc4a48eb2412f08b54fe438b5139c88f9cfa372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.487ex; height:2.509ex;" alt="{\displaystyle \partial p}"></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Thermal_expansion" title="Thermal expansion">Thermal expansion</a> </td> <td style="vertical-align:middle; text-align:left"><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> <mo>=</mo> </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/a92d4583d351f08c1c70985f0c843b2fff1b01e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.941ex; height:1.676ex;" alt="{\displaystyle \alpha =}"></span></td> <td><table><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 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span></td><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 \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}"></span></td></tr><tr><td style="border-top:solid 1px black;"><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 V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span></td><td style="border-top:solid 1px black;"><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 \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}"></span></td></tr></tbody></table></td></tr> </tbody></table></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Thermodynamic_equations" title="Thermodynamic equations">Equations</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Carnot%27s_theorem_(thermodynamics)" title="Carnot's theorem (thermodynamics)">Carnot's theorem</a></li> <li><a href="/wiki/Clausius_theorem" title="Clausius theorem">Clausius theorem</a></li> <li><a href="/wiki/Fundamental_thermodynamic_relation" title="Fundamental thermodynamic relation">Fundamental relation</a></li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li></ul> </div> <ul><li><a href="/wiki/Maxwell_relations" title="Maxwell relations">Maxwell relations</a></li> <li><a href="/wiki/Onsager_reciprocal_relations" title="Onsager reciprocal relations">Onsager reciprocal relations</a></li> <li><a href="/wiki/Bridgman%27s_thermodynamic_equations" title="Bridgman's thermodynamic equations">Bridgman's equations</a></li> <li><i><a href="/wiki/Table_of_thermodynamic_equations" title="Table of thermodynamic equations">Table of thermodynamic equations</a></i></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><a href="/wiki/Thermodynamic_potential" title="Thermodynamic potential">Potentials</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">Free energy</a></li> <li><a href="/wiki/Free_entropy" title="Free entropy">Free entropy</a></li></ul> </div> <div class="plainlist"><ul><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Internal_energy" title="Internal energy">Internal energy</a><br /><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 U(S,V)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(S,V)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/921f33f9c6551562ec836007b035c2de6323d2d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.912ex; height:2.843ex;" alt="{\displaystyle U(S,V)}"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Enthalpy" title="Enthalpy">Enthalpy</a><br /><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(S,p)=U+pV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(S,p)=U+pV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6407d78e5f39d07f70e2414a92e08e2e068519f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.254ex; height:2.843ex;" alt="{\displaystyle H(S,p)=U+pV}"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a><br /><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(T,V)=U-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(T,V)=U-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e93692f031ba6484d82731c54db83a69daed3f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.867ex; height:2.843ex;" alt="{\displaystyle A(T,V)=U-TS}"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a><br /><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 G(T,p)=H-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(T,p)=H-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dd7a8f0b8ae04963da133e3b202432e1b6caed4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.614ex; height:2.843ex;" alt="{\displaystyle G(T,p)=H-TS}"></span></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)"><div class="hlist"><ul><li>History</li><li>Culture</li></ul></div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> History</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">General</a></li> <li><a href="/wiki/History_of_entropy" title="History of entropy">Entropy</a></li> <li><a href="/wiki/Gas_laws" title="Gas laws">Gas laws</a></li></ul> </div> <ul><li><a href="/wiki/History_of_perpetual_motion_machines" title="History of perpetual motion machines">"Perpetual motion" machines</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Philosophy_of_thermal_and_statistical_physics" class="mw-redirect" title="Philosophy of thermal and statistical physics">Philosophy</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Entropy_(arrow_of_time)" class="mw-redirect" title="Entropy (arrow of time)">Entropy and time</a></li> <li><a href="/wiki/Entropy_and_life" title="Entropy and life">Entropy and life</a></li> <li><a href="/wiki/Brownian_ratchet" title="Brownian ratchet">Brownian ratchet</a></li> <li><a href="/wiki/Maxwell%27s_demon" title="Maxwell's demon">Maxwell's demon</a></li> <li><a href="/wiki/Heat_death_paradox" title="Heat death paradox">Heat death paradox</a></li> <li><a href="/wiki/Loschmidt%27s_paradox" title="Loschmidt's paradox">Loschmidt's paradox</a></li> <li><a href="/wiki/Synergetics_(Haken)" title="Synergetics (Haken)">Synergetics</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> Theories</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Caloric_theory" title="Caloric theory">Caloric theory</a></li></ul> </div> <ul><li><a href="/wiki/Vis_viva" title="Vis viva"><i>Vis viva</i> <span style="font-size:85%;">("living force")</span></a></li> <li><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">Mechanical equivalent of heat</a></li> <li><a href="/wiki/Power_(physics)" title="Power (physics)">Motive power</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/List_of_important_publications_in_physics" title="List of important publications in physics">Key publications</a></th></tr><tr><td class="sidebar-content"> <ul><li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/An_Inquiry_Concerning_the_Source_of_the_Heat_Which_Is_Excited_by_Friction" title="An Inquiry Concerning the Source of the Heat Which Is Excited by Friction">An Inquiry Concerning the<br />Source ... Friction</a></i></div></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of<br />Heterogeneous Substances</a></i></div></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/Reflections_on_the_Motive_Power_of_Fire" title="Reflections on the Motive Power of Fire">Reflections on the<br />Motive Power of Fire</a></i></div></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> Timelines</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Timeline_of_thermodynamics" title="Timeline of thermodynamics">Thermodynamics</a></li> <li><a href="/wiki/Timeline_of_heat_engine_technology" title="Timeline of heat engine technology">Heat engines</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <div class="hlist"><ul><li>Art</li><li>Education</li></ul></div></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">Maxwell's thermodynamic surface</a></li> <li><a href="/wiki/Entropy_(energy_dispersal)" title="Entropy (energy dispersal)">Entropy as energy dispersal</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Boltzmann</a></li> <li><a href="/wiki/Percy_Williams_Bridgman" title="Percy Williams Bridgman">Bridgman</a></li> <li><a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Carathéodory</a></li> <li><a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Carnot</a></li> <li><a href="/wiki/Beno%C3%AEt_Paul_%C3%89mile_Clapeyron" class="mw-redirect" title="Benoît Paul Émile Clapeyron">Clapeyron</a></li> <li><a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Clausius</a></li> <li><a href="/wiki/Th%C3%A9ophile_de_Donder" title="Théophile de Donder">de Donder</a></li> <li><a href="/wiki/Pierre_Duhem" title="Pierre Duhem">Duhem</a></li> <li><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">von Helmholtz</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Lewis</a></li> <li><a href="/wiki/Fran%C3%A7ois_Massieu" title="François Massieu">Massieu</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Julius_von_Mayer" title="Julius von Mayer">von Mayer</a></li> <li><a href="/wiki/Walther_Nernst" title="Walther Nernst">Nernst</a></li> <li><a href="/wiki/Lars_Onsager" title="Lars Onsager">Onsager</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">Rankine</a></li> <li><a href="/wiki/John_Smeaton" title="John Smeaton">Smeaton</a></li> <li><a href="/wiki/Georg_Ernst_Stahl" title="Georg Ernst Stahl">Stahl</a></li> <li><a href="/wiki/Peter_Tait_(physicist)" class="mw-redirect" title="Peter Tait (physicist)">Tait</a></li> <li><a href="/wiki/Benjamin_Thompson" title="Benjamin Thompson">Thompson</a></li> <li><a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">van der Waals</a></li> <li><a href="/wiki/John_James_Waterston" title="John James Waterston">Waterston</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;;color: var(--color-base)">Other</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Nucleation" title="Nucleation">Nucleation</a></li> <li><a href="/wiki/Self-assembly" title="Self-assembly">Self-assembly</a></li> <li><a href="/wiki/Self-organization" title="Self-organization">Self-organization</a></li> <li><a href="/wiki/Order_and_disorder" title="Order and disorder">Order and disorder</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below"> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Thermodynamics" title="Category:Thermodynamics">Category</a></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Thermodynamics_sidebar" title="Template:Thermodynamics sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Thermodynamics_sidebar" title="Template talk:Thermodynamics sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Thermodynamics_sidebar" title="Special:EditPage/Template:Thermodynamics sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>Thermodynamic <b>heat pump cycles</b> or <b>refrigeration cycles</b> are the conceptual and <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical models</a> for <a href="/wiki/Heat_pump" title="Heat pump">heat pump</a>, <a href="/wiki/Air_conditioning" title="Air conditioning">air conditioning</a> and <a href="/wiki/Refrigeration" title="Refrigeration">refrigeration</a> systems.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A heat pump is a mechanical system that transmits <a href="/wiki/Heat" title="Heat">heat</a> from one location (the "source") at a certain temperature to another location (the "sink" or "heat sink") at a higher temperature.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Thus a heat pump may be thought of as a "heater" if the objective is to warm the heat sink (as when warming the inside of a home on a cold day), or a "refrigerator" or “cooler” if the objective is to cool the heat source (as in the normal operation of a freezer). The operating principles in both cases are the same;<sup id="cite_ref-Cengel2008_3-0" class="reference"><a href="#cite_note-Cengel2008-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> energy is used to move heat from a colder place to a warmer place. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Thermodynamic_cycles">Thermodynamic cycles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_pump_and_refrigeration_cycle&action=edit&section=1" title="Edit section: Thermodynamic cycles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a>, heat cannot spontaneously flow from a colder location to a hotter area; <a href="/wiki/Mechanical_work" class="mw-redirect" title="Mechanical work">work</a> is required to achieve this.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> An air conditioner requires work to cool a living space, moving heat from the interior being cooled (the heat source) to the outdoors (the heat sink). Similarly, a refrigerator moves heat from inside the cold icebox (the heat source) to the warmer room-temperature air of the kitchen (the heat sink). The operating principle of an ideal <a href="/wiki/Carnot_heat_engine" title="Carnot heat engine">heat engine</a> was described mathematically using the <a href="/wiki/Carnot_cycle" title="Carnot cycle">Carnot cycle</a> by <a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Sadi Carnot</a> in 1824. An ideal refrigerator or heat pump can be thought of as an ideal <a href="/wiki/Heat_engine" title="Heat engine">heat engine</a> that is operating in a reverse Carnot cycle.<sup id="cite_ref-ASHRAE_5-0" class="reference"><a href="#cite_note-ASHRAE-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Heat pump cycles and refrigeration cycles can be classified as <i>vapor compression</i>, <i>vapor absorption</i>, <i>gas cycle</i>, or <i>Stirling cycle</i> types. </p> <div class="mw-heading mw-heading3"><h3 id="Vapor-compression_cycle">Vapor-compression cycle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_pump_and_refrigeration_cycle&action=edit&section=2" title="Edit section: Vapor-compression cycle"><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/Vapor-compression_refrigeration" title="Vapor-compression refrigeration">Vapor-compression refrigeration</a></div> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/File:Refrigeration.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/5d/Refrigeration.png" decoding="async" width="299" height="281" class="mw-file-element" data-file-width="299" data-file-height="281" /></a><figcaption>Vapor-compression refrigeration<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Heatpump2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Heatpump2.svg/300px-Heatpump2.svg.png" decoding="async" width="300" height="154" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Heatpump2.svg/450px-Heatpump2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Heatpump2.svg/600px-Heatpump2.svg.png 2x" data-file-width="715" data-file-height="367" /></a><figcaption>For comparison, a simple stylized diagram of a heat pump's <a href="/wiki/Vapor-compression_refrigeration" title="Vapor-compression refrigeration">vapor-compression refrigeration</a> cycle: 1) <a href="/wiki/Condenser_(heat_transfer)" title="Condenser (heat transfer)">condenser</a>, 2) <a href="/wiki/Thermal_expansion_valve" title="Thermal expansion valve">expansion valve</a>, 3) <a href="/wiki/Evaporator" title="Evaporator">evaporator</a>, 4) <a href="/wiki/Compressor" title="Compressor">compressor</a> (Note that this diagram is flipped vertically and horizontally compared to the previous one)<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></figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/File:RefrigerationTS.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/f7/RefrigerationTS.png" decoding="async" width="387" height="319" class="mw-file-element" data-file-width="387" data-file-height="319" /></a><figcaption><a href="/wiki/Temperature%E2%80%93entropy_diagram" title="Temperature–entropy diagram">Temperature–entropy diagram</a> of the vapor-compression cycle.</figcaption></figure> <p>The vapor-compression cycle is used by many refrigeration, <a href="/wiki/Air_conditioning" title="Air conditioning">air conditioning</a>, and other cooling applications and also within <a href="/wiki/Heat_pump" title="Heat pump">heat pump</a> for heating applications. There are two heat exchangers, one being the <a href="/wiki/Condenser_(heat_transfer)" title="Condenser (heat transfer)">condenser</a>, which is hotter and releases heat, and the other being the evaporator, which is colder and accepts heat. For applications which need to operate in both heating and cooling modes, a <a href="/wiki/Reversing_valve" title="Reversing valve">reversing valve</a> is used to switch the roles of these two heat exchangers.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2021)">citation needed</span></a></i>]</sup> </p><p>At the start of the <a href="/wiki/Thermodynamics" title="Thermodynamics"> thermodynamic</a> cycle the <a href="/wiki/Refrigerant" title="Refrigerant">refrigerant</a> enters the <a href="/wiki/Gas_compressor" class="mw-redirect" title="Gas compressor">compressor</a> as a low pressure and low temperature vapor. In heat pumps, this refrigerant is typically R32 refrigerant or R290 refrigerant. Then the pressure is increased and the refrigerant leaves as a higher temperature and higher pressure <a href="/wiki/Superheated_steam" title="Superheated steam">superheated</a> gas. This hot pressurised gas then passes through the <a href="/wiki/Condenser_(heat_transfer)" title="Condenser (heat transfer)">condenser</a> where it releases heat to the surroundings as it cools and condenses completely. The cooler high-pressure liquid next passes through the <a href="/wiki/Thermal_expansion_valve" title="Thermal expansion valve">expansion valve</a> (throttle valve) which reduces the pressure abruptly causing the temperature to drop dramatically.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The cold low pressure mixture of liquid and vapor next travels through the evaporator where it vaporizes completely as it accepts heat from the surroundings before returning to the compressor as a low pressure low temperature gas to start the cycle again.<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>Some simpler applications with fixed operating temperatures, such as a domestic <a href="/wiki/Refrigerator" title="Refrigerator">refrigerator</a>, may use a fixed speed compressor and fixed aperture expansion valve. Applications that need to operate at a high <a href="/wiki/Coefficient_of_performance" title="Coefficient of performance">coefficient of performance</a> in very varied conditions, as is the case with <a href="/wiki/Heat_pump" title="Heat pump">heat pumps</a> where external temperatures and internal heat demand vary considerably through the seasons, typically use a variable speed inverter compressor and an adjustable expansion valve to control the pressures of the cycle more accurately.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2021)">citation needed</span></a></i>]</sup> </p><p>The above discussion is based on the ideal vapor-compression refrigeration cycle and does not take into account real-world effects like frictional pressure drop in the system, slight <a href="/wiki/Thermodynamic_reversibility" class="mw-redirect" title="Thermodynamic reversibility">thermodynamic irreversibility</a> during the compression of the refrigerant vapor, or <a href="/wiki/Ideal_gas" title="Ideal gas">non-ideal gas</a> behavior (if any).<sup id="cite_ref-ASHRAE_5-1" class="reference"><a href="#cite_note-ASHRAE-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Vapor_absorption_cycle">Vapor absorption cycle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_pump_and_refrigeration_cycle&action=edit&section=3" title="Edit section: Vapor absorption cycle"><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/Absorption_refrigerator" title="Absorption refrigerator">Absorption refrigerator</a></div> <p>In the early years of the twentieth century, the vapor absorption cycle using water-ammonia systems was popular and widely used but, after the development of the vapor compression cycle, it lost much of its importance because of its low <a href="/wiki/Coefficient_of_performance" title="Coefficient of performance">coefficient of performance</a> (about one fifth of that of the vapor compression cycle). Nowadays, the vapor absorption cycle is used only where heat is more readily available than electricity, such as industrial <a href="/wiki/Waste_heat" title="Waste heat">waste heat</a>, <a href="/wiki/Solar_thermal_energy" title="Solar thermal energy">solar thermal energy</a> by <a href="/wiki/Solar_thermal_collector" title="Solar thermal collector">solar collectors</a>, or <a href="/wiki/Propane#Refrigerant" title="Propane">off-the-grid refrigeration</a> in <a href="/wiki/Recreational_vehicle" title="Recreational vehicle">recreational vehicles</a>. </p><p>The absorption cycle is similar to the compression cycle, but depends on the partial pressure of the refrigerant vapor. In the absorption system, the compressor is replaced by an absorber and a generator. The absorber dissolves the refrigerant in a suitable liquid (dilute solution) and therefore the dilute solution becomes a strong solution. In the generator, on heat addition, the temperature increases, and with it, the partial pressure of the refrigerant vapor is released from the strong solution. However, the generator requires a heat source, which would consume energy unless waste heat is used. In an absorption refrigerator, a suitable combination of refrigerant and absorbent is used. The most common combinations are <a href="/wiki/Ammonia" title="Ammonia">ammonia</a> (refrigerant) and water (absorbent), and water (refrigerant) and <a href="/wiki/Lithium_bromide" title="Lithium bromide">lithium bromide</a> (absorbent). </p><p>Absorption refrigeration systems can be powered by <a href="/wiki/Combustion" title="Combustion">combustion</a> of <a href="/wiki/Fossil_fuel" title="Fossil fuel">fossil fuels</a> (e.g., <a href="/wiki/Coal" title="Coal">coal</a>, <a href="/wiki/Oil" title="Oil">oil</a>, <a href="/wiki/Natural_gas" title="Natural gas">natural gas</a>, etc.) or <a href="/wiki/Renewable_energy" title="Renewable energy">renewable energy</a> (e.g., <a href="/wiki/Waste_heat" title="Waste heat">waste-heat</a> recovery, <a href="/wiki/Biomass" title="Biomass">biomass</a> combustion, or <a href="/wiki/Solar_energy" title="Solar energy">solar energy</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Gas_cycle">Gas cycle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_pump_and_refrigeration_cycle&action=edit&section=4" title="Edit section: Gas cycle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Heat_pump_and_refrigeration_cycle" title="Special:EditPage/Heat pump and refrigeration cycle">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">June 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>When the <a href="/wiki/Working_fluids" class="mw-redirect" title="Working fluids">working fluid</a> is a gas that is compressed and expanded but does not change phase, the refrigeration cycle is called a <i>gas cycle</i>. <a href="/wiki/Air" class="mw-redirect" title="Air">Air</a> is most often this working fluid. As there is no condensation and evaporation intended in a gas cycle, components corresponding to the condenser and evaporator in a vapor compression cycle are the hot and cold gas-to-gas <a href="/wiki/Heat_exchanger" title="Heat exchanger">heat exchangers</a>. </p><p>For given extreme temperatures, a gas cycle may be less efficient than a vapor compression cycle because the gas cycle works on the reverse <a href="/wiki/Brayton_cycle" title="Brayton cycle">Brayton cycle</a> instead of the reverse <a href="/wiki/Rankine_cycle" title="Rankine cycle">Rankine cycle</a>. As such, the working fluid never receives or rejects heat at constant temperature. In the gas cycle, the refrigeration effect is equal to the product of the specific heat of the gas and the rise in temperature of the gas in the low temperature side. Therefore, for the same cooling load, gas refrigeration cycle machines require a larger mass flow rate, which in turn increases their size. </p><p>Because of their lower efficiency and larger bulk, <i>air cycle</i> coolers are not often applied in terrestrial refrigeration. The <a href="/wiki/Air_cycle_machine" title="Air cycle machine">air cycle machine</a> is very common, however, on <a href="/wiki/Gas_turbine" title="Gas turbine">gas turbine</a>-powered <a href="/wiki/Jet_airliner" title="Jet airliner">jet airliners</a> since compressed air is readily available from the engines' compressor sections. These jet aircraft's cooling and ventilation units also serve the purpose of heating and pressurizing the <a href="/wiki/Aircraft_cabin" title="Aircraft cabin">aircraft cabin</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Stirling_engine">Stirling engine</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_pump_and_refrigeration_cycle&action=edit&section=5" title="Edit section: Stirling engine"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Heat_pump_and_refrigeration_cycle" title="Special:EditPage/Heat pump and refrigeration cycle">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">June 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Stirling_engine" title="Stirling engine">Stirling engine</a></div> <p>The <a href="/wiki/Stirling_cycle" title="Stirling cycle">Stirling cycle</a> heat engine<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> can be driven in reverse, using a mechanical energy input to drive heat transfer in a reversed direction (i.e. a heat pump, or refrigerator). There are several design configurations for such devices that can be built. Several such setups require rotary or sliding seals, which can introduce difficult tradeoffs between frictional losses and refrigerant leakage. </p> <div class="mw-heading mw-heading3"><h3 id="Reversed_Carnot_cycle">Reversed Carnot cycle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_pump_and_refrigeration_cycle&action=edit&section=6" title="Edit section: Reversed Carnot cycle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Carnot_cycle" title="Carnot cycle">Carnot cycle</a>, which has a quantum equivalent,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> is reversible so the four processes that comprise it, two isothermal and two isentropic, can also be reversed. When a Carnot cycle runs in reverse, it is called a <i>reverse Carnot cycle</i>. A refrigerator or heat pump that acts according to the reversed Carnot cycle is called a Carnot refrigerator or Carnot heat pump, respectively. In the first stage of this cycle, the refrigerant absorbs heat isothermally from a low-temperature source, <span class="texhtml">T<sub>L</sub></span>, in the amount <span class="texhtml">Q<sub>L</sub></span>. Next, the refrigerant is compressed isentropically (adiabatically, without heat transfer) and its temperature rises to that of the high-temperature source, <span class="texhtml">T<sub>H</sub></span>. Then at this high temperature, the refrigerant isothermally rejects heat in the amount <span class="texhtml">Q<sub>H</sub> < 0</span> (negative according to the <a href="/wiki/Heat" title="Heat">sign convention for heat</a> lost by the system). Also during this stage, the refrigerant changes from a saturated vapor to a saturated liquid in the condenser. Lastly, the refrigerant expands isentropically until its temperature falls to that of the low-temperature source, <span class="texhtml">T<sub>L</sub></span>.<sup id="cite_ref-Cengel2008_3-1" class="reference"><a href="#cite_note-Cengel2008-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Absorption-compression_heat_pump">Absorption-compression heat pump</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_pump_and_refrigeration_cycle&action=edit&section=7" title="Edit section: Absorption-compression heat pump"><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/Absorption-compression_heat_pump" title="Absorption-compression heat pump">Absorption-compression heat pump</a></div> <p>An <a href="/wiki/Absorption-compression_heat_pump" title="Absorption-compression heat pump">absorption-compression heat pump</a> <b>(ACHP)</b> is a device that integrate an electric <a href="/wiki/Compressor" title="Compressor">compressor</a> in an <a href="/wiki/Absorption_heat_pump" title="Absorption heat pump">absorption heat pump</a>. In some cases this is obtained by combining a <a href="/wiki/Heat_pump" title="Heat pump">vapor-compression heat pump</a> and an <a href="/wiki/Absorption_heat_pump" title="Absorption heat pump">absorption heat pump</a>. It is also referred to as a hybrid heat pump<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> which is however a broader field. Thanks to this integration, the device can obtain <a href="/wiki/Cooling" title="Cooling">cooling</a> and <a href="/wiki/Heating" class="mw-redirect" title="Heating">heating</a> effects using both <a href="/wiki/Thermal_energy" title="Thermal energy">thermal</a> and <a href="/wiki/Electrical_energy" title="Electrical energy">electrical</a> energy sources.<sup id="cite_ref-swinney2001_13-0" class="reference"><a href="#cite_note-swinney2001-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_14-0" class="reference"><a href="#cite_note-:0-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> This type of systems is well coupled with <a href="/wiki/Cogeneration" title="Cogeneration">cogeneration</a> systems where both heat and electricity are produced. Depending on the configuration, the system can maximise heating and cooling production from a given amount of fuel, or can improve the <a href="/wiki/Temperature" title="Temperature">temperature</a> (hence the quality) of <a href="/wiki/Waste_heat" title="Waste heat">waste heat</a> from other processes.<sup id="cite_ref-:1_15-0" class="reference"><a href="#cite_note-:1-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> This second use is the most studied one and has been applied to several industrial applications.<sup id="cite_ref-:2_16-0" class="reference"><a href="#cite_note-:2-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Coefficient_of_performance">Coefficient of performance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_pump_and_refrigeration_cycle&action=edit&section=8" title="Edit section: Coefficient of performance"><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/Coefficient_of_performance" title="Coefficient of performance">Coefficient of performance</a></div> <p>The merit of a refrigerator or heat pump is given by a parameter called the <a href="/wiki/Coefficient_of_performance" title="Coefficient of performance">coefficient of performance</a> (COP). The equation is: </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 {\rm {COP}}={\frac {|Q|}{W_{net,in}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">O</mi> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>e</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {COP}}={\frac {|Q|}{W_{net,in}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5344897f9a9bb39a61d8928146050b157bd4fae2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:15.787ex; height:6.343ex;" alt="{\displaystyle {\rm {COP}}={\frac {|Q|}{W_{net,in}}}}"></span></dd></dl> <p>where </p> <ul><li><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 Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> is the useful <a href="/wiki/Heat" title="Heat">heat</a> given off or taken up by the considered system.</li> <li><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 W_{net,in}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>e</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{net,in}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3faa3cac2d49b26906d4277e189ff02281f90e11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.783ex; height:2.843ex;" alt="{\displaystyle W_{net,in}}"></span> is the net <a href="/wiki/Mechanical_work" class="mw-redirect" title="Mechanical work">work</a> done on the considered system in one cycle.</li></ul> <p>The detailed COP of a refrigerator is given by the following 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 {\rm {COP_{R}}}={\frac {\text{Desired Output}}{\text{Required Input}}}={\frac {\text{Cooling Effect}}{\text{Work Input}}}={\frac {Q_{L}}{W_{\text{net,in}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">O</mi> <msub> <mi mathvariant="normal">P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> </mrow> </msub> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>Desired Output</mtext> <mtext>Required Input</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>Cooling Effect</mtext> <mtext>Work Input</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>net,in</mtext> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {COP_{R}}}={\frac {\text{Desired Output}}{\text{Required Input}}}={\frac {\text{Cooling Effect}}{\text{Work Input}}}={\frac {Q_{L}}{W_{\text{net,in}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ecee173581d6f52304afbd97adc254dd733ce36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:54.845ex; height:6.009ex;" alt="{\displaystyle {\rm {COP_{R}}}={\frac {\text{Desired Output}}{\text{Required Input}}}={\frac {\text{Cooling Effect}}{\text{Work Input}}}={\frac {Q_{L}}{W_{\text{net,in}}}}}"></span></dd></dl> <p>The COP of a heat pump (sometimes referred to as coefficient of amplification COA) is given by the following equations, where the <a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">first law of thermodynamics</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 W_{net,in}+Q_{L}+Q_{H}=\Delta _{cycle}U=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>e</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>y</mi> <mi>c</mi> <mi>l</mi> <mi>e</mi> </mrow> </msub> <mi>U</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{net,in}+Q_{L}+Q_{H}=\Delta _{cycle}U=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d330f61c4f747dfa038a2b96c297195f32ed40f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:33.991ex; height:2.843ex;" alt="{\displaystyle W_{net,in}+Q_{L}+Q_{H}=\Delta _{cycle}U=0}"></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 |Q_{H}|=-Q_{H}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |Q_{H}|=-Q_{H}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/331268ddb235764750089a07516fd94e3df8de1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.26ex; height:2.843ex;" alt="{\displaystyle |Q_{H}|=-Q_{H}}"></span> was used in one of the last steps: </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 {\rm {COP_{HP}}}={\frac {\text{Desired Output}}{\text{Required Input}}}={\frac {\text{Heating Effect}}{\text{Work Input}}}={\frac {|Q_{H}|}{W_{\text{net,in}}}}={\frac {W_{net,in}+Q_{L}}{W_{\text{net,in}}}}=1+{\frac {Q_{L}}{W_{\text{net,in}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">O</mi> <msub> <mi mathvariant="normal">P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">P</mi> </mrow> </msub> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>Desired Output</mtext> <mtext>Required Input</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>Heating Effect</mtext> <mtext>Work Input</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>net,in</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>e</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>net,in</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>net,in</mtext> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {COP_{HP}}}={\frac {\text{Desired Output}}{\text{Required Input}}}={\frac {\text{Heating Effect}}{\text{Work Input}}}={\frac {|Q_{H}|}{W_{\text{net,in}}}}={\frac {W_{net,in}+Q_{L}}{W_{\text{net,in}}}}=1+{\frac {Q_{L}}{W_{\text{net,in}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f2dbc7619bc6eea149b242e4cd707e5739f505b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:87.403ex; height:6.343ex;" alt="{\displaystyle {\rm {COP_{HP}}}={\frac {\text{Desired Output}}{\text{Required Input}}}={\frac {\text{Heating Effect}}{\text{Work Input}}}={\frac {|Q_{H}|}{W_{\text{net,in}}}}={\frac {W_{net,in}+Q_{L}}{W_{\text{net,in}}}}=1+{\frac {Q_{L}}{W_{\text{net,in}}}}}"></span></dd></dl> <p>Both the COP of a refrigerator and a heat pump can be greater than one. Combining these two equations results in: </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 {\rm {COP_{HP}}}=1+{\rm {COP_{R}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">O</mi> <msub> <mi mathvariant="normal">P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">P</mi> </mrow> </msub> </mrow> </mrow> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">O</mi> <msub> <mi mathvariant="normal">P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> </mrow> </msub> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {COP_{HP}}}=1+{\rm {COP_{R}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5aebf84c0c48abf703d9e7dd2576b9ab4b19309" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.265ex; height:2.509ex;" alt="{\displaystyle {\rm {COP_{HP}}}=1+{\rm {COP_{R}}}}"></span> for fixed values of <span class="texhtml">Q<sub>H</sub></span> and <span class="texhtml">Q<sub>L</sub></span>.</dd></dl> <p>This implies that <span class="texhtml">COP<sub>HP</sub></span> will be greater than one because <span class="texhtml">COP<sub>R</sub></span> will be a positive quantity. In a worst-case scenario, the heat pump will supply as much energy as it consumes, making it act as a resistance heater. However, in reality, as in home heating, some of <span class="texhtml">Q<sub>H</sub></span> is lost to the outside air through piping, insulation, etc., thus making the <span class="texhtml">COP<sub>HP</sub></span> drop below unity when the outside air temperature is too low.<sup id="cite_ref-Cengel2008_3-2" class="reference"><a href="#cite_note-Cengel2008-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>For Carnot refrigerators and heat pumps, the COP can be expressed in terms of temperatures: </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 {\rm {COP_{R,Carnot}}}={\frac {T_{L}}{T_{H}-T_{L}}}={\frac {1}{(T_{H}/T_{L})-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">O</mi> <msub> <mi mathvariant="normal">P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mo>,</mo> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">t</mi> </mrow> </msub> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {COP_{R,Carnot}}}={\frac {T_{L}}{T_{H}-T_{L}}}={\frac {1}{(T_{H}/T_{L})-1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6896cddf1880500e5a42313f80e480332ae9c399" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:41.197ex; height:6.009ex;" alt="{\displaystyle {\rm {COP_{R,Carnot}}}={\frac {T_{L}}{T_{H}-T_{L}}}={\frac {1}{(T_{H}/T_{L})-1}}}"></span></dd></dl> <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 {\rm {COP_{HP,Carnot}}}={\frac {T_{H}}{T_{H}-T_{L}}}={\frac {1}{1-(T_{L}/T_{H})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">O</mi> <msub> <mi mathvariant="normal">P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">P</mi> <mo>,</mo> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">t</mi> </mrow> </msub> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {COP_{HP,Carnot}}}={\frac {T_{H}}{T_{H}-T_{L}}}={\frac {1}{1-(T_{L}/T_{H})}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4407f69cc0bf81a232bc8092727774f3975076b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:42.34ex; height:6.009ex;" alt="{\displaystyle {\rm {COP_{HP,Carnot}}}={\frac {T_{H}}{T_{H}-T_{L}}}={\frac {1}{1-(T_{L}/T_{H})}}}"></span></dd> <dd>These are the upper limits for the COP of any system operating between <span class="texhtml">T<sub>L</sub></span> and <span class="texhtml">T<sub>H</sub></span>.</dd></dl> <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=Heat_pump_and_refrigeration_cycle&action=edit&section=9" 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-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></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="CITEREFyifei2024" class="citation web cs1">yifei (2024-10-21). <a rel="nofollow" class="external text" href="https://www.newntide.com/blog/heat-pump-vs-air-conditioner/">"Heat Pump Vs Air Conditioner"</a>. <i>NEWNTIDE</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-08-30</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=NEWNTIDE&rft.atitle=Heat+Pump+Vs+Air+Conditioner&rft.date=2024-10-21&rft.au=yifei&rft_id=https%3A%2F%2Fwww.newntide.com%2Fblog%2Fheat-pump-vs-air-conditioner%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">The Systems and Equipment volume of the <i><a href="/wiki/ASHRAE_Handbook" title="ASHRAE Handbook">ASHRAE Handbook</a></i>, ASHRAE, Inc., Atlanta, GA, 2004</span> </li> <li id="cite_note-Cengel2008-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Cengel2008_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Cengel2008_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Cengel2008_3-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCengel,_Yunus_A._and_Michael_A._Boles2008" class="citation book cs1">Cengel, Yunus A. and Michael A. Boles (2008). <i>Thermodynamics: An Engineering Approach</i> (6th ed.). McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-330537-0" title="Special:BookSources/978-0-07-330537-0"><bdi>978-0-07-330537-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics%3A+An+Engineering+Approach&rft.edition=6th&rft.pub=McGraw-Hill&rft.date=2008&rft.isbn=978-0-07-330537-0&rft.au=Cengel%2C+Yunus+A.+and+Michael+A.+Boles&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><i>Fundamentals of Engineering Thermodynamics</i>, by Howell and Buckius, McGraw-Hill, New York.</span> </li> <li id="cite_note-ASHRAE-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-ASHRAE_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ASHRAE_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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ashrae.org/technical-resources/ashrae-handbook/description-2017-ashrae-handbook-fundamentals">"Description 2017 ASHRAE Handbook—Fundamentals"</a>. <i>www.ashrae.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-06-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.ashrae.org&rft.atitle=Description+2017+ASHRAE+Handbook%E2%80%94Fundamentals&rft_id=https%3A%2F%2Fwww.ashrae.org%2Ftechnical-resources%2Fashrae-handbook%2Fdescription-2017-ashrae-handbook-fundamentals&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://web.me.unr.edu/me372/Spring2001/Vapor%20Compression%20Refrigeration%20Cycles.pdf">The Ideal Vapor-Compression Cycle</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070226113352/http://web.me.unr.edu/me372/Spring2001/Vapor%20Compression%20Refrigeration%20Cycles.pdf">Archived</a> 2007-02-26 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></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"><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/20060630164309/http://iehmtu.edata-center.com/toc/chapt_r/ch18s82.html">"Scroll down to "The Basic Vapor Compression Cycle and Components"<span class="cs1-kern-right"></span>"</a>. Archived from <a rel="nofollow" class="external text" href="http://iehmtu.edata-center.com/toc/chapt_r/ch18s82.html">the original</a> on 2006-06-30<span class="reference-accessdate">. Retrieved <span class="nowrap">2007-06-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Scroll+down+to+%22The+Basic+Vapor+Compression+Cycle+and+Components%22&rft_id=http%3A%2F%2Fiehmtu.edata-center.com%2Ftoc%2Fchapt_r%2Fch18s82.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</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://www.ac-heatingconnect.com/facility-managers/guide-to-txv/">"Thermostatic Expansion Values: A Guide to Understanding TXVs"</a>. <i>AC & Heating Connect</i>. 2013-06-24<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-06-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=AC+%26+Heating+Connect&rft.atitle=Thermostatic+Expansion+Values%3A+A+Guide+to+Understanding+TXVs&rft.date=2013-06-24&rft_id=https%3A%2F%2Fwww.ac-heatingconnect.com%2Ffacility-managers%2Fguide-to-txv%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" 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="CITEREFAlthouse2004" class="citation book cs1">Althouse, Andrew (2004). <i>Modern Refrigeration and Air Conditioning</i>. The Goodheart-Wilcox Company, Inc. p. 109. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-59070-280-8" title="Special:BookSources/1-59070-280-8"><bdi>1-59070-280-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Refrigeration+and+Air+Conditioning&rft.pages=109&rft.pub=The+Goodheart-Wilcox+Company%2C+Inc.&rft.date=2004&rft.isbn=1-59070-280-8&rft.aulast=Althouse&rft.aufirst=Andrew&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" 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="CITEREFMartini1983" class="citation journal cs1">Martini, W. R. (1983-01-01). <a rel="nofollow" class="external text" href="https://ntrs.nasa.gov/citations/19830022057">"Stirling engine design manual, 2nd edition"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Stirling+engine+design+manual%2C+2nd+edition&rft.date=1983-01-01&rft.aulast=Martini&rft.aufirst=W.+R.&rft_id=https%3A%2F%2Fntrs.nasa.gov%2Fcitations%2F19830022057&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Cite journal requires <code class="cs1-code">|journal=</code> (<a href="/wiki/Help:CS1_errors#missing_periodical" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGeusicSchulz-DuBiosScovil1967" class="citation journal cs1">Geusic, J. 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Berntsson, Thore (1999). <a rel="nofollow" class="external text" href="https://doi.org/10.1016/S0140-7007(98)00047-4">"The compression/absorption cycle – influence of some major parameters on COP and a comparison with the compression cycle"</a>. <i>International Journal of Refrigeration</i>. <b>22</b> (2): 91–106. <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%2Fs0140-7007%2898%2900047-4">10.1016/s0140-7007(98)00047-4</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/0140-7007">0140-7007</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Refrigeration&rft.atitle=The+compression%2Fabsorption+cycle+%E2%80%93+influence+of+some+major+parameters+on+COP+and+a+comparison+with+the+compression+cycle&rft.volume=22&rft.issue=2&rft.pages=91-106&rft.date=1999&rft_id=info%3Adoi%2F10.1016%2Fs0140-7007%2898%2900047-4&rft.issn=0140-7007&rft.aulast=Hult%C3%A9n&rft.aufirst=Magnus&rft.au=Berntsson%2C+Thore&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%2FS0140-7007%2898%2900047-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></span> </li> <li id="cite_note-swinney2001-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-swinney2001_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSwinneyJonesWilson2001" class="citation journal cs1">Swinney, J; Jones, W.E; Wilson, J.A (2001). <a rel="nofollow" class="external text" href="https://doi.org/10.1016/S0140-7007(00)00025-6">"A novel hybrid absorption–compression refrigeration cycle"</a>. <i>International Journal of Refrigeration</i>. <b>24</b> (3): 208–219. <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%2Fs0140-7007%2800%2900025-6">10.1016/s0140-7007(00)00025-6</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/0140-7007">0140-7007</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Refrigeration&rft.atitle=A+novel+hybrid+absorption%E2%80%93compression+refrigeration+cycle&rft.volume=24&rft.issue=3&rft.pages=208-219&rft.date=2001&rft_id=info%3Adoi%2F10.1016%2Fs0140-7007%2800%2900025-6&rft.issn=0140-7007&rft.aulast=Swinney&rft.aufirst=J&rft.au=Jones%2C+W.E&rft.au=Wilson%2C+J.A&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%2FS0140-7007%2800%2900025-6&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></span> </li> <li id="cite_note-:0-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_14-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><span class="citation patent" id="CITEREFShiflettYokozeki2006"><a rel="nofollow" class="external text" href="https://patents.google.com/patent/WO2006124776A2/en">WO2006124776A2</a>, Shiflett, Mark Brandon & Yokozeki, Akimichi, "Hybrid vapor compression-absorption cycle", issued 2006-11-23</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=WO2006124776A2&rft.cc=&rft.title=Hybrid+vapor+compression-absorption+cycle&rft.inventor=Shiflett&rft.date=2006-11-23"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-:1-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-:1_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBHM2017" class="citation journal cs1">B, Wersland M.; H, Kvalsvik K.; M, Bantle (2017). <a rel="nofollow" class="external text" href="https://iifiir.org/en/fridoc/off-design-of-high-temperature-compression-absorption-heat-pump-33107">"Off-design of high temperature compression-absorption heat pump"</a>. <i>7th Conference on Ammonia and CO2 Refrigeration Technology. Proceedings: Ohrid, North Macedonia, May 11-13, 2017</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.18462%2Fiir.nh3-co2.2017.0040">10.18462/iir.nh3-co2.2017.0040</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=7th+Conference+on+Ammonia+and+CO2+Refrigeration+Technology.+Proceedings%3A+Ohrid%2C+North+Macedonia%2C+May+11-13%2C+2017.&rft.atitle=Off-design+of+high+temperature+compression-absorption+heat+pump.&rft.date=2017&rft_id=info%3Adoi%2F10.18462%2Fiir.nh3-co2.2017.0040&rft.aulast=B&rft.aufirst=Wersland+M.&rft.au=H%2C+Kvalsvik+K.&rft.au=M%2C+Bantle&rft_id=https%3A%2F%2Fiifiir.org%2Fen%2Ffridoc%2Foff-design-of-high-temperature-compression-absorption-heat-pump-33107&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></span> </li> <li id="cite_note-:2-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-:2_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAhrensLothTolstorebrovHafner2021" class="citation journal cs1">Ahrens, Marcel Ulrich; Loth, Maximilian; Tolstorebrov, Ignat; Hafner, Armin; Kabelac, Stephan; Wang, Ruzhu; Eikevik, Trygve Magne (2021-05-19). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fapp11104635">"Identification of Existing Challenges and Future Trends for the Utilization of Ammonia-Water Absorption–Compression Heat Pumps at High Temperature Operation"</a>. <i>Applied Sciences</i>. <b>11</b> (10): 4635. <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/10.3390%2Fapp11104635">10.3390/app11104635</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/11250%2F2756158">11250/2756158</a></span>. <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/2076-3417">2076-3417</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Applied+Sciences&rft.atitle=Identification+of+Existing+Challenges+and+Future+Trends+for+the+Utilization+of+Ammonia-Water+Absorption%E2%80%93Compression+Heat+Pumps+at+High+Temperature+Operation&rft.volume=11&rft.issue=10&rft.pages=4635&rft.date=2021-05-19&rft_id=info%3Ahdl%2F11250%2F2756158&rft.issn=2076-3417&rft_id=info%3Adoi%2F10.3390%2Fapp11104635&rft.aulast=Ahrens&rft.aufirst=Marcel+Ulrich&rft.au=Loth%2C+Maximilian&rft.au=Tolstorebrov%2C+Ignat&rft.au=Hafner%2C+Armin&rft.au=Kabelac%2C+Stephan&rft.au=Wang%2C+Ruzhu&rft.au=Eikevik%2C+Trygve+Magne&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Fapp11104635&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></span> </li> </ol></div></div> <dl><dt>Notes</dt></dl> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTurns2006" class="citation book cs1">Turns, Stephen (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=fy5hs04OeMQC&q=Heat+pump+and+refrigeration+cycle"><i>Thermodynamics: Concepts and Applications</i></a>. Cambridge University Press. p. 756. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-85042-8" title="Special:BookSources/0-521-85042-8"><bdi>0-521-85042-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics%3A+Concepts+and+Applications&rft.pages=756&rft.pub=Cambridge+University+Press&rft.date=2006&rft.isbn=0-521-85042-8&rft.aulast=Turns&rft.aufirst=Stephen&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dfy5hs04OeMQC%26q%3DHeat%2Bpump%2Band%2Brefrigeration%2Bcycle&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDincer2003" class="citation book cs1">Dincer, Ibrahim (2003). <i>Refrigeration Systems and Applications</i>. John Wiley and Sons. p. 598. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-62351-2" title="Special:BookSources/0-471-62351-2"><bdi>0-471-62351-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Refrigeration+Systems+and+Applications&rft.pages=598&rft.pub=John+Wiley+and+Sons&rft.date=2003&rft.isbn=0-471-62351-2&rft.aulast=Dincer&rft.aufirst=Ibrahim&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhitman2008" class="citation book cs1">Whitman, Bill (2008). <i>Refrigeration and Air conditioning Technology</i>. Delmar.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Refrigeration+and+Air+conditioning+Technology&rft.pub=Delmar&rft.date=2008&rft.aulast=Whitman&rft.aufirst=Bill&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeat+pump+and+refrigeration+cycle" class="Z3988"></span></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=Heat_pump_and_refrigeration_cycle&action=edit&section=10" 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.central-air-conditioner-and-refrigeration.com/basic-refrigeration-cycle.html">"The Basic Refrigeration Cycle"</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style 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.navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Thermodynamic_cycles" style="padding:3px"><table class="nowraplinks mw-collapsible uncollapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Thermodynamic_cycles" title="Template:Thermodynamic cycles"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Thermodynamic_cycles" title="Template talk:Thermodynamic cycles"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Thermodynamic_cycles" title="Special:EditPage/Template:Thermodynamic cycles"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Thermodynamic_cycles" style="font-size:114%;margin:0 4em"><a href="/wiki/Thermodynamic_cycle" title="Thermodynamic cycle">Thermodynamic cycles</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/External_combustion_engine" title="External combustion engine">External<br />combustion / thermal</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Without phase change<br />(<a href="/wiki/Hot_air_engine" title="Hot air engine">hot air engines</a>)</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Brayton_cycle#Reverse_Brayton_cycle" title="Brayton cycle">Bell Coleman</a></li> <li><a href="/wiki/Brayton_cycle" title="Brayton cycle">Brayton/Joule</a></li> <li><a href="/wiki/Carnot_cycle" title="Carnot cycle">Carnot</a></li> <li><a href="/wiki/Ericsson_cycle" title="Ericsson cycle">Ericsson</a></li> <li><a href="/wiki/Stirling_cycle" title="Stirling cycle">Stirling</a></li> <li><a href="/wiki/Pseudo_Stirling_cycle" title="Pseudo Stirling cycle">Stirling (pseudo/adiabatic)</a></li> <li><a href="/wiki/Stoddard_cycle" class="mw-redirect" title="Stoddard cycle">Stoddard</a></li> <li><a href="/wiki/Manson_engine" title="Manson engine">Manson</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">With phase change</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kalina_cycle" title="Kalina cycle">Kalina</a></li> <li><a href="/wiki/Hygroscopic_cycle" title="Hygroscopic cycle">Hygroscopic</a></li> <li><a href="/wiki/Rankine_cycle" title="Rankine cycle">Rankine</a> (<a href="/wiki/Organic_Rankine_cycle" title="Organic Rankine cycle">Organic Rankine</a>)</li> <li><a href="/wiki/Regenerative_cycle" class="mw-redirect" title="Regenerative cycle">Regenerative</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Internal_combustion_engine" title="Internal combustion engine">Internal <br />combustion / thermal</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Atkinson_cycle" title="Atkinson cycle">Atkinson</a></li> <li><a href="/wiki/Brayton_cycle" title="Brayton cycle">Brayton/Joule</a></li> <li><a href="/wiki/Diesel_cycle" title="Diesel cycle">Diesel</a></li> <li><a href="/wiki/Expander_cycle" title="Expander cycle">Expander</a></li> <li><a href="/wiki/Gas-generator_cycle" title="Gas-generator cycle">Gas-generator</a></li> <li><a href="/wiki/Homogeneous_charge_compression_ignition" title="Homogeneous charge compression ignition">Homogeneous charge compression ignition</a></li> <li><a href="/wiki/Humphrey_cycle" title="Humphrey cycle">Humphrey</a></li> <li><a href="/wiki/Lenoir_cycle" title="Lenoir cycle">Lenoir</a></li> <li><a href="/wiki/Miller_cycle" title="Miller cycle">Miller</a></li> <li><a href="/wiki/Otto_cycle" title="Otto cycle">Otto</a></li> <li><a href="/wiki/Scuderi_cycle" title="Scuderi cycle">Scuderi</a></li> <li><a href="/wiki/Staged_combustion_cycle" title="Staged combustion cycle">Staged combustion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mixed</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/Combined_cycle" class="mw-redirect" title="Combined cycle">Combined</a></li> <li><a href="/wiki/High-efficiency_hybrid_cycle" title="High-efficiency hybrid cycle">HEHC</a></li> <li><a href="/wiki/Mixed/dual_cycle" title="Mixed/dual cycle">Mixed/dual</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Refrigeration</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hampson%E2%80%93Linde_cycle" title="Hampson–Linde cycle">Hampson–Linde</a></li> <li><a href="/wiki/Kleemenko_cycle" title="Kleemenko cycle">Kleemenko</a></li> <li><a href="/wiki/Pulse_tube_refrigerator" title="Pulse tube refrigerator">Pulse tube</a></li> <li><a href="/wiki/Regenerative_cooling" title="Regenerative cooling">Regenerative cooling</a></li> <li><a href="/wiki/Transcritical_cycle" title="Transcritical cycle">Transcritical</a></li> <li><a href="/wiki/Absorption_refrigerator" title="Absorption refrigerator">Vapor absorption</a></li> <li><a href="/wiki/Vapor-compression_refrigeration" title="Vapor-compression refrigeration">Vapor-compression</a></li> <li><a href="/wiki/Siemens_cycle" title="Siemens cycle">Siemens</a></li> <li><a href="/wiki/Vuilleumier_cycle" title="Vuilleumier cycle">Vuilleumier</a></li> <li><a href="/wiki/Ionocaloric_refrigeration" title="Ionocaloric refrigeration">Ionocaloric</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Heating,_ventilation,_and_air_conditioning" style="vertical-align: middle;;padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:HVAC" title="Template:HVAC"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:HVAC" title="Template talk:HVAC"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:HVAC" title="Special:EditPage/Template:HVAC"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Heating,_ventilation,_and_air_conditioning" style="font-size:114%;margin:0 4em"><a href="/wiki/Heating,_ventilation,_and_air_conditioning" title="Heating, ventilation, and air conditioning">Heating, ventilation, and air conditioning</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fundamental <br />concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Air_changes_per_hour" title="Air changes per hour">Air changes per hour</a></li> <li><a href="/wiki/Bake-out" title="Bake-out">Bake-out</a></li> <li><a href="/wiki/Building_envelope" title="Building envelope">Building envelope</a></li> <li><a href="/wiki/Convection" title="Convection">Convection</a></li> <li><a href="/wiki/Dilution_(equation)" title="Dilution (equation)">Dilution</a></li> <li><a href="/wiki/Domestic_energy_consumption" title="Domestic energy consumption">Domestic energy consumption</a></li> <li><a href="/wiki/Enthalpy" title="Enthalpy">Enthalpy</a></li> <li><a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Fluid dynamics</a></li> <li><a href="/wiki/Gas_compressor" class="mw-redirect" title="Gas compressor">Gas compressor</a></li> <li><a class="mw-selflink selflink">Heat pump and refrigeration cycle</a></li> <li><a href="/wiki/Heat_transfer" title="Heat transfer">Heat transfer</a></li> <li><a href="/wiki/Humidity" title="Humidity">Humidity</a></li> <li><a href="/wiki/Infiltration_(HVAC)" title="Infiltration (HVAC)">Infiltration</a></li> <li><a href="/wiki/Latent_heat" title="Latent heat">Latent heat</a></li> <li><a href="/wiki/Noise_control" title="Noise control">Noise control</a></li> <li><a href="/wiki/Outgassing" title="Outgassing">Outgassing</a></li> <li><a href="/wiki/Particulates" title="Particulates">Particulates</a></li> <li><a href="/wiki/Psychrometrics" title="Psychrometrics">Psychrometrics</a></li> <li><a href="/wiki/Sensible_heat" title="Sensible heat">Sensible heat</a></li> <li><a href="/wiki/Stack_effect" title="Stack effect">Stack effect</a></li> <li><a href="/wiki/Thermal_comfort" title="Thermal comfort">Thermal comfort</a></li> <li><a href="/wiki/Thermal_destratification" title="Thermal destratification">Thermal destratification</a></li> <li><a href="/wiki/Thermal_mass" title="Thermal mass">Thermal mass</a></li> <li><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a></li> <li><a href="/wiki/Vapour_pressure_of_water" title="Vapour pressure of water">Vapour pressure of water</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technology</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Absorption-compression_heat_pump" title="Absorption-compression heat pump">Absorption-compression heat pump</a></li> <li><a href="/wiki/Absorption_refrigerator" title="Absorption refrigerator">Absorption refrigerator</a></li> <li><a href="/wiki/Air_barrier" title="Air barrier">Air barrier</a></li> <li><a href="/wiki/Air_conditioning" title="Air conditioning">Air conditioning</a></li> <li><a href="/wiki/Antifreeze" title="Antifreeze">Antifreeze</a></li> <li><a href="/wiki/Automobile_air_conditioning" class="mw-redirect" title="Automobile air conditioning">Automobile air conditioning</a></li> <li><a href="/wiki/Autonomous_building" title="Autonomous building">Autonomous building</a></li> <li><a href="/wiki/Building_insulation_material" title="Building insulation material">Building insulation materials</a></li> <li><a href="/wiki/Central_heating" title="Central heating">Central heating</a></li> <li><a href="/wiki/Central_solar_heating" title="Central solar heating">Central solar heating</a></li> <li><a href="/wiki/Chilled_beam" title="Chilled beam">Chilled beam</a></li> <li><a href="/wiki/Chilled_water" title="Chilled water">Chilled water</a></li> <li><a href="/wiki/Constant_air_volume" title="Constant air volume">Constant air volume</a> (CAV)</li> <li><a href="/wiki/Coolant" title="Coolant">Coolant</a></li> <li><a href="/wiki/Cross_ventilation" title="Cross ventilation">Cross ventilation</a></li> <li><a href="/wiki/Dedicated_outdoor_air_system" title="Dedicated outdoor air system">Dedicated outdoor air system</a> (DOAS)</li> <li><a href="/wiki/Deep_water_source_cooling" title="Deep water source cooling">Deep water source cooling</a></li> <li><a href="/wiki/Demand_controlled_ventilation" title="Demand controlled ventilation">Demand controlled ventilation</a> (DCV)</li> <li><a href="/wiki/Displacement_ventilation" title="Displacement ventilation">Displacement ventilation</a></li> <li><a href="/wiki/District_cooling" title="District cooling">District cooling</a></li> <li><a href="/wiki/District_heating" title="District heating">District heating</a></li> <li><a href="/wiki/Electric_heating" title="Electric heating">Electric heating</a></li> <li><a href="/wiki/Energy_recovery_ventilation" class="mw-redirect" title="Energy recovery ventilation">Energy recovery ventilation</a> (ERV)</li> <li><a href="/wiki/Firestop" title="Firestop">Firestop</a></li> <li><a href="/wiki/Forced-air" title="Forced-air">Forced-air</a></li> <li><a href="/wiki/Forced-air_gas" title="Forced-air gas">Forced-air gas</a></li> <li><a href="/wiki/Free_cooling" title="Free cooling">Free cooling</a></li> <li><a href="/wiki/Heat_recovery_ventilation" title="Heat recovery ventilation">Heat recovery ventilation</a> (HRV)</li> <li><a href="/wiki/Hybrid_heat" title="Hybrid heat">Hybrid heat</a></li> <li><a href="/wiki/Hydronics" title="Hydronics">Hydronics</a></li> <li><a href="/wiki/Ice_storage_air_conditioning" title="Ice storage air conditioning">Ice storage air conditioning</a></li> <li><a href="/wiki/Kitchen_ventilation" title="Kitchen ventilation">Kitchen ventilation</a></li> <li><a href="/wiki/Mixed-mode_ventilation" title="Mixed-mode ventilation">Mixed-mode ventilation</a></li> <li><a href="/wiki/Microgeneration" title="Microgeneration">Microgeneration</a></li> <li><a href="/wiki/Passive_cooling" title="Passive cooling">Passive cooling</a></li> <li><a href="/wiki/Passive_daytime_radiative_cooling" title="Passive daytime radiative cooling">Passive daytime radiative cooling</a></li> <li><a href="/wiki/Passive_house" title="Passive house">Passive house</a></li> <li><a href="/wiki/Passive_ventilation" title="Passive ventilation">Passive ventilation</a></li> <li><a href="/wiki/Radiant_heating_and_cooling" title="Radiant heating and cooling">Radiant heating and cooling</a></li> <li><a href="/wiki/Radiant_cooling" class="mw-redirect" title="Radiant cooling">Radiant cooling</a></li> <li><a href="/wiki/Radiant_heating" class="mw-redirect" title="Radiant heating">Radiant heating</a></li> <li><a href="/wiki/Radon_mitigation" title="Radon mitigation">Radon mitigation</a></li> <li><a href="/wiki/Refrigeration" title="Refrigeration">Refrigeration</a></li> <li><a href="/wiki/Renewable_heat" title="Renewable heat">Renewable heat</a></li> <li><a href="/wiki/Room_air_distribution" title="Room air distribution">Room air distribution</a></li> <li><a href="/wiki/Solar_air_heat" title="Solar air heat">Solar air heat</a></li> <li><a href="/wiki/Solar_combisystem" title="Solar combisystem">Solar combisystem</a></li> <li><a href="/wiki/Solar_cooling" class="mw-redirect" title="Solar cooling">Solar cooling</a></li> <li><a href="/wiki/Solar_heating" class="mw-redirect" title="Solar heating">Solar heating</a></li> <li><a href="/wiki/Thermal_insulation" title="Thermal insulation">Thermal insulation</a></li> <li><a href="/wiki/Thermosiphon" title="Thermosiphon">Thermosiphon</a></li> <li><a href="/wiki/Underfloor_air_distribution" title="Underfloor air distribution">Underfloor air distribution</a></li> <li><a href="/wiki/Underfloor_heating" title="Underfloor heating">Underfloor heating</a></li> <li><a href="/wiki/Vapor_barrier" title="Vapor barrier">Vapor barrier</a></li> <li><a href="/wiki/Vapor-compression_refrigeration" title="Vapor-compression refrigeration">Vapor-compression refrigeration</a> (VCRS)</li> <li><a href="/wiki/Variable_air_volume" title="Variable air volume">Variable air volume</a> (VAV)</li> <li><a href="/wiki/Variable_refrigerant_flow" title="Variable refrigerant flow">Variable refrigerant flow</a> (VRF)</li> <li><a href="/wiki/Ventilation_(architecture)" title="Ventilation (architecture)">Ventilation</a></li> <li><a href="/wiki/Water_heat_recycling" title="Water heat recycling">Water heat recycling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Components</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Air_conditioner_inverter" class="mw-redirect" title="Air conditioner inverter">Air conditioner inverter</a></li> <li><a href="/wiki/Air_door" title="Air door">Air door</a></li> <li><a href="/wiki/Air_filter" title="Air filter">Air filter</a></li> <li><a href="/wiki/Air_handler" title="Air handler">Air handler</a></li> <li><a href="/wiki/Air_ioniser" title="Air ioniser">Air ionizer</a></li> <li><a href="/wiki/Air-mixing_plenum" title="Air-mixing plenum">Air-mixing plenum</a></li> <li><a href="/wiki/Air_purifier" title="Air purifier">Air purifier</a></li> <li><a href="/wiki/Air_source_heat_pump" title="Air source heat pump">Air source heat pump</a></li> <li><a href="/wiki/Attic_fan" title="Attic fan">Attic fan</a></li> <li><a href="/wiki/Automatic_balancing_valve" title="Automatic balancing valve">Automatic balancing valve</a></li> <li><a href="/wiki/Back_boiler" title="Back boiler">Back boiler</a></li> <li><a href="/wiki/Barrier_pipe" title="Barrier pipe">Barrier pipe</a></li> <li><a href="/wiki/Blast_damper" title="Blast damper">Blast damper</a></li> <li><a href="/wiki/Boiler" title="Boiler">Boiler</a></li> <li><a href="/wiki/Centrifugal_fan" title="Centrifugal fan">Centrifugal fan</a></li> <li><a href="/wiki/Ceramic_heater" title="Ceramic heater">Ceramic heater</a></li> <li><a href="/wiki/Chiller" title="Chiller">Chiller</a></li> <li><a href="/wiki/Condensate_pump" title="Condensate pump">Condensate pump</a></li> <li><a href="/wiki/Condenser_(heat_transfer)" title="Condenser (heat transfer)">Condenser</a></li> <li><a href="/wiki/Condensing_boiler" title="Condensing boiler">Condensing boiler</a></li> <li><a href="/wiki/Convection_heater" title="Convection heater">Convection heater</a></li> <li><a href="/wiki/Compressor" title="Compressor">Compressor</a></li> <li><a href="/wiki/Cooling_tower" title="Cooling tower">Cooling tower</a></li> <li><a href="/wiki/Damper_(flow)" title="Damper (flow)">Damper</a></li> <li><a href="/wiki/Dehumidifier" title="Dehumidifier">Dehumidifier</a></li> <li><a href="/wiki/Duct_(flow)" title="Duct (flow)">Duct</a></li> <li><a href="/wiki/Economizer" title="Economizer">Economizer</a></li> <li><a href="/wiki/Electrostatic_precipitator" title="Electrostatic precipitator">Electrostatic precipitator</a></li> <li><a href="/wiki/Evaporative_cooler" title="Evaporative cooler">Evaporative cooler</a></li> <li><a href="/wiki/Evaporator" title="Evaporator">Evaporator</a></li> <li><a href="/wiki/Exhaust_hood" class="mw-redirect" title="Exhaust hood">Exhaust hood</a></li> <li><a href="/wiki/Expansion_tank" title="Expansion tank">Expansion tank</a></li> <li><a href="/wiki/Fan_(machine)" title="Fan (machine)">Fan</a></li> <li><a href="/wiki/Fan_coil_unit" title="Fan coil unit">Fan coil unit</a></li> <li><a href="/wiki/Fan_filter_unit" title="Fan filter unit">Fan filter unit</a></li> <li><a href="/wiki/Fan_heater" title="Fan heater">Fan heater</a></li> <li><a href="/wiki/Fire_damper" title="Fire damper">Fire damper</a></li> <li><a href="/wiki/Fireplace" title="Fireplace">Fireplace</a></li> <li><a href="/wiki/Fireplace_insert" title="Fireplace insert">Fireplace insert</a></li> <li><a href="/wiki/Freeze_stat" title="Freeze stat">Freeze stat</a></li> <li><a href="/wiki/Flue" title="Flue">Flue</a></li> <li><a href="/wiki/Freon" title="Freon">Freon</a></li> <li><a href="/wiki/Fume_hood" title="Fume hood">Fume hood</a></li> <li><a href="/wiki/Furnace_(house_heating)" class="mw-redirect" title="Furnace (house heating)">Furnace</a></li> <li><a href="/wiki/Gas_compressor" class="mw-redirect" title="Gas compressor">Gas compressor</a></li> <li><a href="/wiki/Gas_heater" title="Gas heater">Gas heater</a></li> <li><a href="/wiki/Gasoline_heater" title="Gasoline heater">Gasoline heater</a></li> <li><a href="/wiki/Grease_duct" title="Grease duct">Grease duct</a></li> <li><a href="/wiki/Grille_(architecture)" title="Grille (architecture)">Grille</a></li> <li><a href="/wiki/Ground-coupled_heat_exchanger" title="Ground-coupled heat exchanger">Ground-coupled heat exchanger</a></li> <li><a href="/wiki/Ground_source_heat_pump" title="Ground source heat pump">Ground source heat pump</a></li> <li><a href="/wiki/Heat_exchanger" title="Heat exchanger">Heat exchanger</a></li> <li><a href="/wiki/Heat_pipe" title="Heat pipe">Heat pipe</a></li> <li><a href="/wiki/Heat_pump" title="Heat pump">Heat pump</a></li> <li><a href="/wiki/Heating_film" title="Heating film">Heating film</a></li> <li><a href="/wiki/Heating_system" title="Heating system">Heating system</a></li> <li><a href="/wiki/HEPA" title="HEPA">HEPA</a></li> <li><a href="/wiki/High_efficiency_glandless_circulating_pump" title="High efficiency glandless circulating pump">High efficiency glandless circulating pump</a></li> <li><a href="/wiki/High-pressure_cut-off_switch" class="mw-redirect" title="High-pressure cut-off switch">High-pressure cut-off switch</a></li> <li><a href="/wiki/Humidifier" title="Humidifier">Humidifier</a></li> <li><a href="/wiki/Infrared_heater" title="Infrared heater">Infrared heater</a></li> <li><a href="/wiki/Inverter_compressor" title="Inverter compressor">Inverter compressor</a></li> <li><a href="/wiki/Kerosene_heater" title="Kerosene heater">Kerosene heater</a></li> <li><a href="/wiki/Louver" title="Louver">Louver</a></li> <li><a href="/wiki/Mechanical_room" title="Mechanical room">Mechanical room</a></li> <li><a href="/wiki/Oil_heater" title="Oil heater">Oil heater</a></li> <li><a href="/wiki/Packaged_terminal_air_conditioner" title="Packaged terminal air conditioner">Packaged terminal air conditioner</a></li> <li><a href="/wiki/Plenum_space" title="Plenum space">Plenum space</a></li> <li><a href="/wiki/Pressurisation_ductwork" title="Pressurisation ductwork">Pressurisation ductwork</a></li> <li><a href="/wiki/Process_duct_work" title="Process duct work">Process duct work</a></li> <li><a href="/wiki/Radiator_(heating)" title="Radiator (heating)">Radiator</a></li> <li><a href="/wiki/Radiator_reflector" title="Radiator reflector">Radiator reflector</a></li> <li><a href="/wiki/Recuperator" title="Recuperator">Recuperator</a></li> <li><a href="/wiki/Refrigerant" title="Refrigerant">Refrigerant</a></li> <li><a href="/wiki/Register_(air_and_heating)" title="Register (air and heating)">Register</a></li> <li><a href="/wiki/Reversing_valve" title="Reversing valve">Reversing valve</a></li> <li><a href="/wiki/Run-around_coil" title="Run-around coil">Run-around coil</a></li> <li><a href="/wiki/Sail_switch" title="Sail switch">Sail switch</a></li> <li><a href="/wiki/Scroll_compressor" title="Scroll compressor">Scroll compressor</a></li> <li><a href="/wiki/Solar_chimney" title="Solar chimney">Solar chimney</a></li> <li><a href="/wiki/Solar-assisted_heat_pump" title="Solar-assisted heat pump">Solar-assisted heat pump</a></li> <li><a href="/wiki/Space_heater" title="Space heater">Space heater</a></li> <li><a href="/wiki/Smoke_canopy" title="Smoke canopy">Smoke canopy</a></li> <li><a href="/wiki/Smoke_damper" title="Smoke damper">Smoke damper</a></li> <li><a href="/wiki/Smoke_exhaust_ductwork" title="Smoke exhaust ductwork">Smoke exhaust ductwork</a></li> <li><a href="/wiki/Thermal_expansion_valve" title="Thermal expansion valve">Thermal expansion valve</a></li> <li><a href="/wiki/Thermal_wheel" title="Thermal wheel">Thermal wheel</a></li> <li><a href="/wiki/Thermostatic_radiator_valve" title="Thermostatic radiator valve">Thermostatic radiator valve</a></li> <li><a href="/wiki/Trickle_vent" title="Trickle vent">Trickle vent</a></li> <li><a href="/wiki/Trombe_wall" title="Trombe wall">Trombe wall</a></li> <li><a href="/wiki/TurboSwing" title="TurboSwing">TurboSwing</a></li> <li><a href="/wiki/Turning_vanes_(HVAC)" title="Turning vanes (HVAC)">Turning vanes</a></li> <li><a href="/wiki/Ultra-low_particulate_air" title="Ultra-low particulate air">Ultra-low particulate air</a> (ULPA)</li> <li><a href="/wiki/Whole-house_fan" title="Whole-house fan">Whole-house fan</a></li> <li><a href="/wiki/Windcatcher" title="Windcatcher">Windcatcher</a></li> <li><a href="/wiki/Wood-burning_stove" title="Wood-burning stove">Wood-burning stove</a></li> <li><a href="/wiki/Zone_valve" title="Zone valve">Zone valve</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Measurement<br />and control</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Air_flow_meter" title="Air flow meter">Air flow meter</a></li> <li><a href="/wiki/Aquastat" title="Aquastat">Aquastat</a></li> <li><a href="/wiki/BACnet" title="BACnet">BACnet</a></li> <li><a href="/wiki/Blower_door" title="Blower door">Blower door</a></li> <li><a href="/wiki/Building_automation" title="Building automation">Building automation</a></li> <li><a href="/wiki/Carbon_dioxide_sensor" title="Carbon dioxide sensor">Carbon dioxide sensor</a></li> <li><a href="/wiki/Clean_air_delivery_rate" title="Clean air delivery rate">Clean air delivery rate</a> (CADR)</li> <li><a href="/wiki/Control_valve" title="Control valve">Control valve</a></li> <li><a href="/wiki/Gas_detector" title="Gas detector">Gas detector</a></li> <li><a href="/wiki/Home_energy_monitor" title="Home energy monitor">Home energy monitor</a></li> <li><a href="/wiki/Humidistat" title="Humidistat">Humidistat</a></li> <li><a href="/wiki/HVAC_control_system" title="HVAC control system">HVAC control system</a></li> <li><a href="/wiki/Infrared_thermometer" title="Infrared thermometer">Infrared thermometer</a></li> <li><a href="/wiki/Intelligent_buildings" class="mw-redirect" title="Intelligent buildings">Intelligent buildings</a></li> <li><a href="/wiki/LonWorks" title="LonWorks">LonWorks</a></li> <li><a href="/wiki/Minimum_efficiency_reporting_value" title="Minimum efficiency reporting value">Minimum efficiency reporting value</a> (MERV)</li> <li><a href="/wiki/Normal_temperature_and_pressure" class="mw-redirect" title="Normal temperature and pressure">Normal temperature and pressure</a> (NTP)</li> <li><a href="/wiki/OpenTherm" title="OpenTherm">OpenTherm</a></li> <li><a href="/wiki/Programmable_communicating_thermostat" title="Programmable communicating thermostat">Programmable communicating thermostat</a></li> <li><a href="/wiki/Programmable_thermostat" title="Programmable thermostat">Programmable thermostat</a></li> <li><a href="/wiki/Psychrometrics" title="Psychrometrics">Psychrometrics</a></li> <li><a href="/wiki/Room_temperature" title="Room temperature">Room temperature</a></li> <li><a href="/wiki/Smart_thermostat" title="Smart thermostat">Smart thermostat</a></li> <li><a href="/wiki/Standard_temperature_and_pressure" title="Standard temperature and pressure">Standard temperature and pressure</a> (STP)</li> <li><a href="/wiki/Thermographic_camera" class="mw-redirect" title="Thermographic camera">Thermographic camera</a></li> <li><a href="/wiki/Thermostat" title="Thermostat">Thermostat</a></li> <li><a href="/wiki/Thermostatic_radiator_valve" title="Thermostatic radiator valve">Thermostatic radiator valve</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Professions,<br />trades,<br />and services</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Architectural_acoustics" title="Architectural acoustics">Architectural acoustics</a></li> <li><a href="/wiki/Architectural_engineering" title="Architectural engineering">Architectural engineering</a></li> <li><a href="/wiki/Architectural_technologist" title="Architectural technologist">Architectural technologist</a></li> <li><a href="/wiki/Building_services_engineering" title="Building services engineering">Building services engineering</a></li> <li><a href="/wiki/Building_information_modeling" title="Building information modeling">Building information modeling</a> (BIM)</li> <li><a href="/wiki/Deep_energy_retrofit" title="Deep energy retrofit">Deep energy retrofit</a></li> <li><a href="/wiki/Duct_cleaning" class="mw-redirect" title="Duct cleaning">Duct cleaning</a></li> <li><a href="/wiki/Duct_leakage_testing" title="Duct leakage testing">Duct leakage testing</a></li> <li><a href="/wiki/Environmental_engineering" title="Environmental engineering">Environmental engineering</a></li> <li><a href="/wiki/Hydronic_balancing" title="Hydronic balancing">Hydronic balancing</a></li> <li><a href="/wiki/Kitchen_exhaust_cleaning" title="Kitchen exhaust cleaning">Kitchen exhaust cleaning</a></li> <li><a href="/wiki/Mechanical_engineering" title="Mechanical engineering">Mechanical engineering</a></li> <li><a href="/wiki/Mechanical,_electrical,_and_plumbing" title="Mechanical, electrical, and plumbing">Mechanical, electrical, and plumbing</a></li> <li><a href="/wiki/Mold_growth,_assessment,_and_remediation" class="mw-redirect" title="Mold growth, assessment, and remediation">Mold growth, assessment, and remediation</a></li> <li><a href="/wiki/Refrigerant_reclamation" title="Refrigerant reclamation">Refrigerant reclamation</a></li> <li><a href="/wiki/Testing,_adjusting,_balancing" title="Testing, adjusting, balancing">Testing, adjusting, balancing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Industry <br />organizations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Air_Conditioning,_Heating_and_Refrigeration_Institute" title="Air Conditioning, Heating and Refrigeration Institute">AHRI</a></li> <li><a href="/wiki/Air_Movement_and_Control_Association" title="Air Movement and Control Association">AMCA</a></li> <li><a href="/wiki/ASHRAE" title="ASHRAE">ASHRAE</a></li> <li><a href="/wiki/ASTM_International" title="ASTM International">ASTM International</a></li> <li><a href="/wiki/Building_Research_Establishment" title="Building Research Establishment">BRE</a></li> <li><a href="/wiki/BSRIA" title="BSRIA">BSRIA</a></li> <li><a href="/wiki/Chartered_Institution_of_Building_Services_Engineers" title="Chartered Institution of Building Services Engineers">CIBSE</a></li> <li><a href="/wiki/Institute_of_Refrigeration" title="Institute of Refrigeration">Institute of Refrigeration</a></li> <li><a href="/wiki/International_Institute_of_Refrigeration" title="International Institute of Refrigeration">IIR</a></li> <li><a href="/wiki/Leadership_in_Energy_and_Environmental_Design" class="mw-redirect" title="Leadership in Energy and Environmental Design">LEED</a></li> <li><a href="/wiki/Sheet_Metal_and_Air_Conditioning_Contractors%27_National_Association" title="Sheet Metal and Air Conditioning Contractors' National Association">SMACNA</a></li> <li><a href="/wiki/Uniform_Mechanical_Code" title="Uniform Mechanical Code">UMC</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Health and safety</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Indoor_air_quality" title="Indoor air quality">Indoor air quality</a> (IAQ)</li> <li><a href="/wiki/Passive_smoking" title="Passive smoking">Passive smoking</a></li> <li><a href="/wiki/Sick_building_syndrome" title="Sick building syndrome">Sick building syndrome</a> (SBS)</li> <li><a href="/wiki/Volatile_organic_compound" title="Volatile organic compound">Volatile organic compound</a> (VOC)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;text-align: middle;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ASHRAE_Handbook" title="ASHRAE Handbook">ASHRAE Handbook</a></li> <li><a href="/wiki/Building_science" 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