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class="vector-toc-link" href="#Particle_number_density"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Particle number density</span> </div> </a> <ul id="toc-Particle_number_density-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_quantum_mechanics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_quantum_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>In quantum mechanics</span> </div> </a> <ul id="toc-In_quantum_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_air_quality" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_air_quality"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>In air quality</span> </div> </a> <ul id="toc-In_air_quality-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" 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dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Number of particles in a thermodynamic system</div> <style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks wraplinks" style="width:18em;"><tbody><tr><td class="sidebar-above" style="background:lavender; font-size:120%;"> <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">Conjugate variables<br />of thermodynamics</a></td></tr><tr><td class="sidebar-content" style="padding:2px;"> <table class="wikitable" style="width:100%;border-collapse:collapse;border-spacing:0px 0px;border:none;margin:1px 0 0 0;"><tbody><tr style="vertical-align:top"><td> <a href="/wiki/Pressure" title="Pressure">Pressure</a></td><td> <a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">Volume</a></td></tr><tr style="vertical-align:top"><td> (<a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">Stress</a>)</td><td> (<a href="/wiki/Deformation_(physics)#Strain" title="Deformation (physics)">Strain</a>)</td></tr><tr style="vertical-align:top"><td> <a href="/wiki/Temperature" title="Temperature">Temperature</a></td><td> <a href="/wiki/Entropy" title="Entropy">Entropy</a></td></tr><tr style="vertical-align:top"><td> <a href="/wiki/Chemical_potential" title="Chemical potential">Chemical potential</a></td><td> <a class="mw-selflink selflink">Particle number</a></td></tr></tbody></table></td> </tr></tbody></table> <p>In <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>, the <b>particle number</b> (symbol <span class="texhtml mvar" style="font-style:italic;">N</span>) of a <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">thermodynamic system</a> is the <a href="/wiki/Number_of_entities" class="mw-redirect" title="Number of entities">number</a> of constituent <a href="/wiki/Particle" title="Particle">particles</a> in that system.<sup id="cite_ref-HoP_1-0" class="reference"><a href="#cite_note-HoP-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The particle number is a fundamental <a href="/wiki/List_of_thermodynamic_properties" title="List of thermodynamic properties">thermodynamic property</a> which is <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">conjugate</a> to the <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potential</a>. Unlike most <a href="/wiki/Physical_quantities" class="mw-redirect" title="Physical quantities">physical quantities</a>, the particle number is a <a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">dimensionless quantity</a>, specifically a <a href="/wiki/Countable_quantity" class="mw-redirect" title="Countable quantity">countable quantity</a>. It is an <a href="/wiki/Extensive_property" class="mw-redirect" title="Extensive property">extensive property</a>, as it is directly proportional to the size of the system under consideration and thus meaningful only for <a href="/wiki/Thermodynamic_system#Closed_system" title="Thermodynamic system">closed systems</a>. </p><p>A <b>constituent particle</b> is one that cannot be broken into smaller pieces at the scale of <a href="/wiki/Energy" title="Energy">energy</a> <span class="texhtml mvar" style="font-style:italic;">k·T</span> involved in the process (where <span class="texhtml mvar" style="font-style:italic;">k</span> is the <a href="/wiki/Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a> and <span class="texhtml mvar" style="font-style:italic;">T</span> is the <a href="/wiki/Temperature" title="Temperature">temperature</a>). For example, in a thermodynamic system consisting of a <a href="/wiki/Piston" title="Piston">piston</a> containing <a href="/wiki/Water_vapour" class="mw-redirect" title="Water vapour">water vapour</a>, the particle number is the number of water molecules in the system. The meaning of constituent particles, and thereby of particle numbers, is thus temperature-dependent. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Determining_the_particle_number">Determining the particle number</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Particle_number&action=edit&section=1" title="Edit section: Determining the particle number"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The concept of particle number plays a major role in <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical</a> considerations. In situations where the actual particle number of a given thermodynamical system needs to be determined, mainly in <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, it is not practically possible to measure it directly by <a href="/wiki/Counting" title="Counting">counting</a> the particles. If the material is homogeneous and has a known <i><a href="/wiki/Amount_of_substance" title="Amount of substance">amount of substance</a></i> <i>n</i> expressed in <i><a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a></i>, the particle number <i>N</i> can be found by the relation : <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=nN_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mi>n</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=nN_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0055322a685fbd84fce8e05c20177a101315f498" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.888ex; height:2.509ex;" alt="{\displaystyle N=nN_{A}}"></span>, where <i>N<sub>A</sub></i> is the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a>.<sup id="cite_ref-HoP_1-1" class="reference"><a href="#cite_note-HoP-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Particle_number_density">Particle number density</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Particle_number&action=edit&section=2" title="Edit section: Particle number density"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A related <a href="/wiki/Intensive_parameter" class="mw-redirect" title="Intensive parameter">intensive system parameter</a> is the <b>particle <a href="/wiki/Number_density" title="Number density">number density</a></b> （or <a href="/w/index.php?title=Particle_number_concentration&action=edit&redlink=1" class="new" title="Particle number concentration (page does not exist)">particle number concentration</a> PNC), a quantity of kind <a href="/wiki/Volumetric_number_density" class="mw-redirect" title="Volumetric number density">volumetric number density</a> obtained by dividing the particle number of a system by its <a href="/wiki/Volume" title="Volume">volume</a>. This parameter is often denoted by the lower-case letter <i>n</i>. </p> <div class="mw-heading mw-heading2"><h2 id="In_quantum_mechanics">In quantum mechanics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Particle_number&action=edit&section=3" title="Edit section: In quantum mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Quantum_mechanical" class="mw-redirect" title="Quantum mechanical">quantum mechanical</a> processes, the total number of particles may not be preserved. The concept is therefore generalized to the <a href="/wiki/Particle_number_operator" title="Particle number operator">particle number operator</a>, that is, the <a href="/wiki/Observable" title="Observable">observable</a> that counts the number of constituent particles.<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> In <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>, the particle number operator (see <a href="/wiki/Fock_state" title="Fock state">Fock state</a>) is conjugate to the phase of the <i>classical</i> wave (see <a href="/wiki/Coherent_state" title="Coherent state">coherent state</a>). </p> <div class="mw-heading mw-heading2"><h2 id="In_air_quality">In air quality</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Particle_number&action=edit&section=4" title="Edit section: In air quality"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>One measure of <a href="/wiki/Air_pollution" title="Air pollution">air pollution</a> used in air quality standards is the atmospheric concentration of <a href="/wiki/Atmospheric_particulate_matter" class="mw-redirect" title="Atmospheric particulate matter">particulate matter</a>. This measure is usually expressed in μg/m<sup>3</sup> (<a href="/wiki/Micrograms" class="mw-redirect" title="Micrograms">micrograms</a> per cubic metre). In the current EU emission norms for cars, vans, and trucks and in the upcoming EU emission norm for non-road mobile machinery, particle number measurements and limits are defined, commonly referred to as <i>PN</i>, with units [#/km] or [#/kWh]. In this case, PN expresses a quantity of particles per unit distance (or work). </p> <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=Particle_number&action=edit&section=5" 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"><ol class="references"> <li id="cite_note-HoP-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-HoP_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-HoP_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBenensonHarrisStöcker2002" class="citation book cs1">Benenson, Walter; Harris, John; Stöcker, Horst (2002). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=c60mCxGRMR8C&q=%22Particle+number%22&pg=PA637"><i>Handbook of Physics</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-95269-1" title="Special:BookSources/0-387-95269-1"><bdi>0-387-95269-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+Physics&rft.pub=Springer&rft.date=2002&rft.isbn=0-387-95269-1&rft.aulast=Benenson&rft.aufirst=Walter&rft.au=Harris%2C+John&rft.au=St%C3%B6cker%2C+Horst&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dc60mCxGRMR8C%26q%3D%2522Particle%2Bnumber%2522%26pg%3DPA637&rfr_id=info%3Asid%2Fen.wikipedia.org%3AParticle+number" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchumacherWestmoreland2010" class="citation book cs1">Schumacher, Benjamin; Westmoreland, Michael (2010). <i>Quantum Processes, Systems, and Information</i>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Processes%2C+Systems%2C+and+Information&rft.pub=Cambridge+University+Press&rft.date=2010&rft.aulast=Schumacher&rft.aufirst=Benjamin&rft.au=Westmoreland%2C+Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3AParticle+number" class="Z3988"></span></span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output 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style="width:1%">Physical quantities</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/Mass_concentration_(chemistry)" title="Mass concentration (chemistry)">Mass concentration</a></li> <li><a href="/wiki/Molar_concentration" title="Molar concentration">Molar concentration</a></li> <li><a href="/wiki/Molality" title="Molality">Molality</a></li> <li><a href="/wiki/Mass" title="Mass">Mass</a></li> <li><a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">Volume</a></li> <li><a href="/wiki/Density" title="Density">Density</a></li> <li><a href="/wiki/Mole_fraction" title="Mole fraction">Mole fraction</a></li> <li><a href="/wiki/Mass_fraction_(chemistry)" title="Mass fraction (chemistry)">Mass fraction</a></li> <li><a href="/wiki/Amount_of_substance" title="Amount of substance">Amount of substance</a></li> <li><a href="/wiki/Molar_mass" title="Molar mass">Molar mass</a></li> <li><a href="/wiki/Atomic_mass" title="Atomic mass">Atomic mass</a></li> <li><a class="mw-selflink selflink">Particle number</a></li> <li><a href="/wiki/Pressure" title="Pressure">Pressure</a></li> <li><a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">Thermodynamic temperature</a></li> <li><a href="/wiki/Molar_volume" title="Molar volume">Molar volume</a></li> <li><a href="/wiki/Specific_volume" title="Specific volume">Specific volume</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Laws</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/Charles%27s_law" title="Charles's law">Charles's law</a></li> <li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a></li> <li><a href="/wiki/Avogadro%27s_law" title="Avogadro's law">Avogadro's law</a></li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Particle_number&oldid=1236279995">https://en.wikipedia.org/w/index.php?title=Particle_number&oldid=1236279995</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Thermodynamics" title="Category:Thermodynamics">Thermodynamics</a></li><li><a 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