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Q.

A cyclic process $A B C$ is performed on one mole of an ideal gas $T_{A} = 350 K$ and $T_{B} = 370 K$ . A total of 50 R of heat is withdrawn from the gas in the complete cycle. Magnitude of work done by the gas during process $B \to C$ is kR. The value of k is ____

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answer is 70.

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Detailed Solution

In a cyclic process,
$Δ U = 0$
$\Rightarrow Q_{C y c l e} = W_{C y c l e}$
$\Rightarrow W_{C A} = 0$ (Isochoric process)
$\Rightarrow W_{A \to B} = P Δ V = n R Δ T$
$= 1 \times R \times (370 - 350)$
$= 20 R$
Now, $- 50 R = 20 R + W_{B C}$
$\Rightarrow W_{B C} = - 70 R$

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