Problem 1. (40 pts) An ideal gas compression problem – First and Second law . On

Question

Problem 1. (40 pts) An ideal gas compression problem – First and Second law.

One mole of an ideal monatomic gas is expanded adiabatically against a 1 atm external pressure. "Adiabatically" means that no heat is transferred to or from the gas. The initial pressure of the gas is 10 atm, and its initial temperature is 500 K. The final pressure of the gas is 1 atm. Cv = 3/2R; Cp = 5/2 R, U = (3/2)RT. This is an irreversible process.

(15 pts) Show that the final temperature of the gas is 320K.

b. (25 pts) What is the entropy change, S, between the initial state of the gas at 10 atm and 500 K and the final state of the gas at 1 atm and 320 K? You can determine the answer by finding the sum of the two entropy changes, deltaS1 and deltaS2, in the following reversible processes: Leave your answer in terms of R, the gas constant.

(10 pts) deltaS1 is the entropy change in going from 10 to 1 atm at a constant temperature of 500 K. Find S1.

(10 pts) deltaS2 is the entropy change in going from 500 K to 320 K, all at a constant pressure of 1 atm. Find deltaS2.

(5 pts) deltaS = deltaS1 + deltaS2 and be sure to note what the sign of deltaS should be.

Explanation / Answer

Problem 1. (40 pts) An ideal gas compression problem – First and Second law . On

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