Editing Ideal solution (section)

=== Enthalpy and heat capacity ===
Proceeding in a similar way but taking the derivative with respect to <math>T</math> we get a similar result for molar [[enthalpy|enthalpies]]:
:<math>\frac{g(T,P)-g^\mathrm{gas}(T,p^u)}{RT}=\ln\frac{f}{p^u}.</math>
Remembering that <math>\left( \frac{\partial \frac{g}{T}}{\partial T}\right)_P=-\frac{h}{T^2}</math> we get:
:<math>-\frac{\bar{h_i}-h_i^\mathrm{gas}}{R}=-\frac{h_i^*-h_i^\mathrm{gas}}{R}</math>
which in turn means that <math>\bar{h_i}=h_i^*</math> and that the enthalpy of the mix is equal to the sum of its component enthalpies.

Since <math>\bar{u_i}=\bar{h_i}-p\bar{v_i}</math> and <math>u_i^* = h_i^* - p v_i^*</math>, similarly
:<math>u_i^*=\bar{u_i}.</math>
It is also easily verifiable that 
:<math>C_{pi}^*=\bar{C_{pi}}.</math>