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A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is

1. 0.5
2. 0.75
3. 0.99
4. 0.25

Correct answer: 0.75

Solution

For a diatomic gas (gamma = 7/5), adiabatic expansion V -> 32V gives T2/T1 = (V1/V2)^(gamma-1) = (1/32)^0.4 = 1/4. Carnot efficiency = 1 - T2/T1 = 1 - 1/4 = 0.75.

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