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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.