JEE Advanced levelSingle correct optionDifficulty 3 of 3td201
Two moles of a diatomic ideal gas (CV=25R) at 400K and 5bar expand adiabatically to 1bar, once irreversibly against a constant external pressure of 1bar and once reversibly. Which statement is correct?
ATirrev≈253K, Trev≈309K, and the gas does more work in the reversible expansion
BTirrev≈309K, Trev≈253K, and the gas does more work in the irreversible expansion
CTirrev≈309K, Trev≈253K, and the gas does more work in the reversible expansion
DTirrev=Trev≈253K, and the work done is the same
Answer: C
Irreversible: 2.5(T2−400)=−(T2−0.2×400) gives T2=2.7×400/3.5=308.6K and ∣w∣=2×2.5R(400−T2)=3801J. Reversible: T2=400×(1/5)2/7=252.6K and ∣w∣=6129J. The reversible path gives the lower final temperature and more work.