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Q.

A diatomic 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 32V, the efficiency of the engine is

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a

0.25

b

0.5

c

0.75

d

0.99

answer is C.

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Detailed Solution

$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$

$T_{1} = T_{2} {(32)}^{γ - 1}$

$T_{1} = T_{2} {(2^{5})}^{\frac{7}{5} - 1}$

$T_{1} = T_{2} {(2^{5})}^{2 / 5}$

$T_{1} = 4 T_{2}$

$η = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{1}{4}$

$η = 0.75$

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A diatomic 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 32V, the efficiency of the engine is