THE FIRST LAW of THERMODYNAMICS: Conservation of energy
... Since h = u + Pv and, for an ideal gas, Pv = RT, then for the ideal gas h = u + RT
R is constant, and u = u(T) only, so we conclude h = h(T) only for an ideal gas.
Aside: application of enthalpy balance in steady-flow system:
energy balance for a single-stream, steady-flow system with negligible ch ...