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A Carnot engine operates with a diatomic ideal gas as its working fluid. During the adiabatic expansion stage, the gas volume rises from V to 32V. What is the efficiency of the engine?

1. 0.50
2. 0.75
3. 0.99
4. 0.25

Correct answer: 0.75

Solution

For diatomic gas gamma=7/5. Adiabatic: T_cold/T_hot = (V/32V)^(gamma-1) = 32^(-2/5) = 1/4. Efficiency = 1 - 1/4 = 0.75.

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