MSE 308
Thermodynamics of Materials
Dept. of Materials Science & Engineering
Spring 2005/Bill Knowlton
Problem Set 2
1. Prove that the inexact differential, dw is equal to mechanical work, pdV:
i.e, dw = pdV
when the change in all other work is constant. Use the fact that
dw = Fdx
where F is force and x is distance.
2. Prove that mechanical work on a system is negative. Use a drawing of a cylinder and
piston to prove this and the concept of state 1 with variable V1 and P1 and state 2 with
variables V2 and P2.
3. The equation I provided in class that describes the 1st Law of Thermodynamics has an
opposite sign as equation (2.2) provided by Gaskell on page 19. Explain why there is a
difference.
4. Contrast the relative magnitudes of the entropy transfer versus entropy production in the
following processes:
a. A thermally insulated container has two compartments of equal size. Initially, one
side is filled with a gas and the other is evacuated. A valve is opened and the gas
expands to fill both compartments.
b. A gas contained in a steel cylinder is slowly expanded to twice its volume.
5. The notion of a “reversible process is a fiction in the real world. What make this concept,
which at first glance would appear to be only of academic interest, so useful in applying
thermodynamics to real-world “irreversible” process?:
6. Prove that the entropy in the universe is always increasing. Use the method we described
in class using the change of entropy for the universe, surroundings and system.