Particle number

The particle number (or number of particles) of a thermodynamic system, conventionally indicated with the letter N, is the number of constituent particles in that system. The particle number is a fundamental parameter in thermodynamics which is conjugate to the chemical potential. Unlike most physical quantities, particle number is a dimensionless quantity. It is an extensive parameter, 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 energy k·T involved in the process (where k is the Boltzmann constant and T is the temperature). For example, for 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 particle, and thereby of particle number, is thus temperature-dependent.

The concept of particle number has a main 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 N_A is the Avogadro constant.

A related intensive system parameter is given by the particle number density, obtained by dividing the particle number of a system by its volume. This parameter is often denoted by a lower-case letter n.

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