Corrections to Maxwell-Boltzmann ideal gas model from a quantum phase space approach

The Maxwell-Boltzmann ideal gas model is known to be the simplest model that is considered in classical statistical physics and thermodynamics to describe gas behavior. However, classical approach can no longer be rigorously valid if quantum effect becomes significant. In this work, we consider a study of corrections to the Maxwell-Boltzmann ideal gas model related to quantum size effect by using an approach based on the concept of quantum phase space. A canonical quantum partition function is deduced in order to obtain all thermodynamics properties. A corrected state equation for ideal gas and expressions of thermodynamic state functions such as internal energy, entropy and free energy are deduced. The corrections are expected to be particularly useful to describe the deviation from classical behavior of a Maxwell-Boltzmann gas at low temperature and in confined space. The properties of classical ideal gas are obtained as asymptotic limits at high temperature and for large volume.