Thermodynamic definition of an athermic solution

In the same way as we defined a regular solution as one which has the same entropy of mixing as a perfect solution, we shall define an athermic solution as one which has the same enthalpy of mixing as a perfect solution - i.e. zero. Of course, its excess molar enthalpy is also null. 

Variation of the activity coefficients with temperature in an athermic solution 

By applying the above property of definition to expressions [A.2.24] and [A.2.8] for a perfect solution, we deduce  

As the activity coefficients do not depend on the temperature, they will be functions only of the composition and perfiaps of the pressure. Therefore, this type of solutions is referred to as athermic. 

Instantly, we can derive the following equality from this  

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