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Q.

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mole of a diatomic gas. The temperature of the gas during the process $A \to B$ and $C \to D$ are T₁ and T₂ (T₁ > T₂), respectively
Choose the correct option out of the following for work done, if processes BC and DA are adiabatic.

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a

$W_{A B} = W_{D C}$

b

$W_{A D} = W_{B C}$

c

$W_{B C} + W_{D A} > 0$

d

$W_{A B} < W_{C D}$

answer is B.

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Detailed Solution

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As per question, the process BC and DA are adiabatic.
We know that work done in adiabatic process is given as
$W = \frac{- nR}{γ - 1} (T_{t} - T_{1})$ Where n = number of moles,

$γ$ = specific heat ratio R = gas constant
T_t = final temperature and T₁ = initial temperature
$W_{AD} = \frac{- nR}{γ - 1} (T_{2} - T_{1}) and W_{BC} = \frac{- nR}{γ - 1} (T_{2} - T_{1}) \Rightarrow W_{AD} = W_{BC}$

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