Ideal Gas

An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.

The Sackur–Tetrode equation expresses the entropy \(S\) of a monatomic ideal gas in terms of its thermodynamic state—specifically, its volume \(V\), internal energy \(U\), and the number of particles \(N\):

\[\displaystyle {\frac {S}{k_{\rm {B}}N}}=\ln \left[{\frac {V}{N}}\left({\frac {4\pi m}{3h^{2}}}{\frac {U}{N}}\right)^{3/2}\right]+{\frac {5}{2}},\] where \(k_{\mathrm {B}}\) is the Boltzmann constant, \(m\) is the mass of a gas particle and \(h\) is the Planck constant.