Particle number

In thermodynamics, the particle number (symbol N) of a thermodynamic system is the number of constituent particles in that system. The particle number is a fundamental thermodynamic property which is 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 closed systems.

Conjugate variables
of thermodynamics
Pressure Volume
(Stress) (Strain)
Temperature Entropy
Chemical potential Particle number

A constituent particle is one that cannot be broken into smaller pieces at the scale of energy k·T involved in the process (where k is the Boltzmann constant and 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.

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