Chapter 9, Problem 24E

The diagram shows two systems that may exchange both thermal and mechanical energy via a movable, heat−conducting partition. Because both E and V may change, we consider the entropy of each system to be a function of both: $S\left(E,V\right)$ . Considering the exchange of thermal energy only, we argued in Section 9.2 that it was reasonable to define 1/T as $\delta S/\delta E$ . In the more general case, P/T is also defined as something. (a) Why should pressure come into play, and to what might P/T be equated? (Note: Check to see whether the units make sense.) (b) Given this relationship, show that $dS=dQ/T$ . (Remember the first law of thermodynamics.)