Helium gas goes through a cycle ABCDA as shown in figure. Efficiency of cycle is (Assume the gas to be close to ideal gas)

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$\frac{3}{17}$

$\frac{5}{14}$

$\frac{7}{15}$

$\frac{2}{13}$

answer is A.

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Detailed Solution

$η = \frac{Δ w}{Q_{A B} + Q_{B C}}$

$η = \frac{p_{0} V_{0}}{\frac{3}{2} n R (T_{B} - T_{A}) + \frac{5}{2} n R (T_{C} - T_{D})} = \frac{p_{0} V_{0}}{\frac{3}{2} (2 p_{0} V_{0} - p_{0} V_{0}) + \frac{5}{2} (4 p_{0} V_{0} - 2 p_{0} V_{0})}$

$\Rightarrow η = \frac{2}{13}$

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