Editing Particle number

{{short description|Number of particles in a thermodynamic system}}
{{Conjugate variables (thermodynamics)}}

In [[thermodynamics]], the '''particle number''' (symbol {{mvar|N}}) of a [[thermodynamic system]] is the [[number of entities|number]] of constituent [[particle]]s in that system.<ref name="HoP">{{cite book|last1=Benenson|first1=Walter|last2=Harris|first2=John|last3=Stöcker|first3=Horst|title=Handbook of Physics |url=https://books.google.com/books?id=c60mCxGRMR8C&q=%22Particle+number%22&pg=PA637|publisher=Springer|isbn=0-387-95269-1|year=2002}}</ref> The particle number is a fundamental [[List of thermodynamic properties|thermodynamic property]] which is [[Conjugate variables (thermodynamics)|conjugate]] to the [[chemical potential]]. Unlike most [[physical quantities]], the particle number is a [[dimensionless quantity]], specifically a [[countable quantity]]. It is an [[extensive property]], as it is directly proportional to the size of the system under consideration and thus meaningful only for [[Thermodynamic system#Closed system|closed system]]s.

A '''constituent particle''' is one that cannot be broken into smaller pieces at the scale of [[energy]] {{mvar|k·T}} involved in the process (where {{mvar|k}} is the [[Boltzmann constant]] and {{mvar|T}} is the [[temperature]]). For example, in a thermodynamic system consisting of a [[piston]] containing [[water vapour]], 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.

==Determining the particle number==
The concept of particle number plays a major role in [[Theoretical physics|theoretical]] considerations. In situations where the actual particle number of a given thermodynamical system needs to be determined, mainly in [[chemistry]], it is not practically possible to measure it directly by [[counting]] the particles. If the material is homogeneous and has a known ''[[amount of substance]]'' ''n'' expressed in ''[[mole (unit)|mole]]s'', the particle number ''N'' can be found by the relation :
<math> N = nN_A</math>,
where ''N<sub>A</sub>'' is the [[Avogadro constant]].<ref name="HoP"/>

==Particle number density==
A related [[intensive parameter|intensive system parameter]] is the '''particle [[number density]]''' （or [[particle number concentration]] PNC), a quantity of kind [[volumetric number density]] obtained by dividing the particle number of a system by its [[volume]]. This parameter is often denoted by the lower-case letter ''n''.

==In quantum mechanics==
In [[quantum mechanical]] processes, the total number of particles may not be preserved. The concept is therefore generalized to the [[particle number operator]], that is, the [[observable]] that counts the number of constituent particles.<ref>{{cite book|last1=Schumacher|first1=Benjamin|last2=Westmoreland|first2=Michael|title=Quantum Processes, Systems, and Information |year=2010|publisher=[[Cambridge University Press]]}}</ref> In [[quantum field theory]], the particle number operator (see [[Fock state]]) is conjugate to the phase of the ''classical'' wave (see [[coherent state]]).

==In air quality==
One measure of [[air pollution]] used in air quality standards is the atmospheric concentration of [[Atmospheric particulate matter|particulate matter]]. This measure is usually expressed in μg/m<sup>3</sup> ([[micrograms]] 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 ''PN'', with units [#/km] or [#/kWh]. In this case, PN expresses a quantity of particles per unit distance (or work).

==References==
{{Reflist}}

{{Mole concepts}}
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[[Category:Thermodynamics]]
[[Category:Dimensionless numbers of thermodynamics]]
[[Category:Countable quantities]]
[[Category:State functions]]