First slide

Heat engine

Question

A heat engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is (Take Cv = 3R/2, where R is molar gas constant)

Moderate

A

0.24
B

0.15
C

0.32
D

0.08

Solution

Heat is absorbed in the process AB (isochoric) and BC (isobaric). The temperature rise ΔT in AB = (2PoVo-PoVo)/nR and heat absorbed = nCVΔT = 1.5PoVo. The temperature rise ΔT in BC = (4PoVo-2PoVo)/nR and heat absorbed = nCPΔT = 5PoVo. Total heat absorbed = 6.5PoVo. Work done is area ABCD = PoVo. Thermal efficiency = PoVo/6.5PoVo = 0.15

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