Study of thermodynamic properties of atomic hydrogen gas

Partition function is the sum over energy states and from which various thermodynamic properties are obtained. Specifically for an isolated atom due to existence of infinite number of energy levels, it presents critical difficulty in writing electronic partition function. Present study is aimed to derive an analytic form of partition function for hydrogenic atom assuming that the average energy per degree of freedom is equal to the linear atomic energy density. Further to test the theoretical formulation, a particular case of hydrogen atoms in a gas with partial ionization is discussed and its thermodynamic properties such as internal energy, entropy, and specific heat etc. is calculated. These calculated values are found to be in excellent agreement with benchmarked NIST database.