PHY 3513 Fall 2000 – Homework 5
Due at the start of class on Friday, October 13.
Answer all questions, including any additions to textbook problems. To obtain full credit,
you must explain your reasoning and show all working. Please write neatly and include your
name on the front page of your answers.
1. Callen Problem 3.2-1. This problem illustrates the point that for a single-component
simple system, there are two (not three) independent first partial derivatives of the
fundamental equation.
You should start by inverting a pair of simultaneous equations for T(s, v)andP(s, v)
to obtain s(T,P)andv(T,P). You should then determine µ(T,P) via three separate
methods (do them all!):
(a) calculate µ(s, v) from the fundamental relation, then substitute for sand v;
(b) use the Euler equation;
(c) integrate the Gibbs-Duhem relation.
2. Callen Problem 3.3-2.
You should write down the total differential ds and integrate it to obtain s(u, v). (Don’t
forget to check your final result by comparing its partial derivatives against the total
differential you began with.)
3. Callen Problem 3.4-5, modified as follows:
(i) Rather than assuming that the gas is monatomic ideal (as stated by Callen),
instead take it to be simple ideal with an arbitrary value of c.
(ii) Replace part (e) by the following: “From the result of (c) or (d), for what value
of ηis Q= 0? For this case, show that PV γ= constant, and express γin terms
of c.”
In part (c) you should use the First Law, while in part (d) you should start with the
fundamental equation for S.