One mole of NH3 gas (gamma = 1.33) initially at 27 degrees C is expanded reversibly and adiabatically until its volume becomes 8 times the original volume. Which of the following statements is/are correct?

The final temperature of the gas is 150 K
The work done by the gas is -400 cal
The final temperature of the gas is 250 K
The work done by the gas is -900 cal

Correct answer: The final temperature of the gas is 150 K

Solution

T2 = 300*(1/8)^(0.33) = 300*(2³)^(-0.33) = 300*2^(-1) = 150 K; and W = nR(T2-T1)/(gamma-1) = 1*2*(150-300)/0.33 ~ -900 cal, so both T=150 K and W=-900 cal are correct.

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