Standard thermodynamic relations connect the partial derivatives of enthalpy and internal energy with respect to temperature through heat capacities, volume, and expansion coefficients.
The claim states that a thermodynamic relation can be proven between partial derivatives of enthalpy and internal energy with respect to temperature. This is a fundamental concept in chemical thermodynamics, where enthalpy (H = U + PV) and internal energy (U) are linked via state variables. Standard Maxwell relations and definitions of heat capacity (such as constant-pressure and constant-volume heat capacities, and internal pressure) explicitly relate their temperature derivatives. Papers [2], [6], and [7] confirm the analytical and experimental treatment of these partial derivatives with respect to temperature.