Stability with respect to adiabatic perturbations

As an example of the application of the most general condition of stability (15.52) we now consider adiabatic perturbations at constant pressure. From (2.13) 

For a transformation of this kind, therefore, the condition of stability (15.52) may be written (c/. 15.3) 

Provided that the system is in stable thermal equilibrium ((7 positive), and is stable with respect to changes at constant T, p negative), then it is also stable with respect to adiabatic perturbations at constant pressure. 

So far we have only considered stabihty in the two cases in which either 

It may happen, however, that at P, all the successive differentials of A with respect to up to the n - 2)th are zero. The uncompensated heat is therefore given according to (15.5) by 

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