When deriving the temperature dependence of the enthalpy change (∂H /∂T )P , the temperature
dependence of the internal energy (under constant pressure) (∂U /∂T )P is obtained. Compared with the
expression for temperature dependence of internal energy (under constant volume) (∂U /∂T )V , both
derivatives are equal for a monatomic molecular ideal gas. In this paper, two simple methods are
presented to derive the equivalence of internal energy between constant pressure and constant volume.