Physlib.StatisticalMechanics.MicroCanonicalEnsemble.IdealGas

For an ideal gas of $n$ particles in a cubic box of volume $V > 0$, the partition function $Z$ at thermodynamic beta $\beta > 0$ is given by $$Z = V^n \left( \frac{2\pi}{\beta} \right)^{\frac{3n}{2}}.$$

For an ideal gas consisting of $n$ particles in a volume $V > 0$ at temperature $T > 0$, the Helmholtz free energy $A$ is given by $$A = -n T \left( \ln V + \frac{3}{2} \ln (2\pi T) \right).$$

For an ideal gas consisting of $n$ particles in a volume $V > 0$ at temperature $T > 0$, the pressure $P$ (defined as the thermodynamic conjugate to the volume) satisfies the ideal gas law: $$PV = nRT$$ where $R = 1$ is the gas constant in the unitless system.