PHY 3513 Fall 1999 – Homework 9
Due at the start of class on Wednesday, November 17.
Answer all questions. 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 4.5–1,2.
Make sure that you give an algebraic final answer to each part of these problems before
inserting the data provided to obtain a numerical result. You should use the maximum work
theorem for the first problem but not in the second, where you should calculate the work
and heat transfers directly.
2. Callen Problem 4.5–5.
Do the problem assuming a heat capacity C(T ) = A + BT . Only substitute the specific
values A = 2R and B = R/150 at the very end.
Note: You will obtain a transcendental equation F (TRHS,f ) = 0 for the final temperature of
the reversible heat source. You will not be able to solve the equation algebraically, so you
may leave TRHS,f in your expression for the maximum work delivered to the reversible work
source.
When you carry out the numerical part of the problem at the end, you should determine
TRHS,f numerically (to within ±5 K). You should be able to show that F (x) is a monotonic
increasing function of x, so the zero of F (x) can be found using simple bisection on a scientific
calculator.
3. Callen Problem 4.7–2.
4. Consider a Carnot engine in which the hot and cold reversible heat sources (RHS’s) have
finite, temperature-independent heat capacities, Ch and Cc , respectively; Cc is several (2–3)
times bigger than Ch . The auxiliary system (AS) operates between S = Si and S = Si + dS.
Let the initial temperatures of the RHS’s be Th,i and Tc,i and assume that the AS starts at
S = Si , T = Th,i .
(a) Draw a T -S diagram for the AS, showing the first 5 steps of the Carnot cycle. Be careful
to show the relative slopes of the lines in a qualitatively correct fashion.
(b) Assuming that dS is an infinitesimal quantity, find the common temperature Tf at which
the hot and cold RHS eventually equilibrate.
(c) Find the total heat drawn from the hot RHS before it reaches equilibrium with the cold
RHS.
(d) Find the total reversible work output to the reversible work source.
(e) Find the overall engine efficiency.