performance of the cell at 25 0. Problem 5.12. Functions encountered in physics are generally well enough be- haved that their mixed partial derivatives do not depend on which derivative is taken first. Therefore, for instance, OU Ov Ov where each 8/OV is taken with S fixed. each 8/85 is taken with V fixed, and N is always held fixed. From the thermodynamic identity (for () you can evaluate the partial derivatives in parentheses to obtain OT OP OV a nontrivial identity called a Maxwell relation. Go through the derivation of this relation step by step. Then derive an analogous Maxwell relation from each ofthe other three thermodynamic identities discussed in the text (for I. F, and (). Hold A fixed in all the partial derivatives; other Maxwell relations can be derived by considering partial derivatives with respect to N, but after you've done four of them the novelty begins to wear off