Читать книгу Geochemistry - William M. White - Страница 79

The reciprocity* relationship, which we discussed earlier, leads to a number of useful relationships. These relationships are known as the Maxwell relations. Consider the equation:

(2.58)

If we write the partial differential of U in terms of S and V we have:

(2.143)

From a comparison of these two equations, we see that:

(2.144a)

and

(2.144b)

And since the cross-differentials are equal, it follows that:

(2.145)

The other Maxwell relations can be derived in an exactly analogous way from other state functions. They are:

 From dH (eqn 2.65):(2.146)

 from dA (eqn. 2.121)(2.147)

 from dG (eqn. 2.122)(2.148)