Temperature-Dependent Specific Heat of a Monoatomic Gas Based on a Stretched Exponential Partition Function

Accurate modeling of complex systems often requires the application of advanced mathematical tools. In this work, we investigate the thermodynamic behavior of monoatomic gases using a stretched exponential probability density function. By constructing the partition function Z within this framework, we derive expressions for the internal energy and temperature-dependent specific heat of the system. The results are shown to be consistent with classical kinetic theory for ideal gases. Furthermore, comparisons with experimental data are presented, highlighting the viability of this approach.