Particle number
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Conjugate variables of thermodynamics | ||||||||
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In
extensive property, as it is directly proportional to the size of the system under consideration and thus meaningful only for closed systems
.
A constituent particle is one that cannot be broken into smaller pieces at the scale of
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 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 moles, the particle number N can be found by the relation : , where NA is the Avogadro constant.[1]
Particle number density
A related
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.[2] 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
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
- ^ ISBN 0-387-95269-1.
- ^ Schumacher, Benjamin; Westmoreland, Michael (2010). Quantum Processes, Systems, and Information. Cambridge University Press.