Work done by a sample of an ideal gas in a process A is double the work done in another process B. The temperature rises through the same amount in the two processes. If $C_{A}$ and $C_{B}$ be the molar heat capacities for the two processes :

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$C_{A} = C_{B}$

$C_{A} > C_{B}$

$C_{A} < C_{B}$

None of these

answer is B.

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Detailed Solution

If $C_{A}$ and $C_{B}$ be the molar heat capacities for the two processes :

$w_{A} = 2 w_{B}; Δ T_{A} = Δ T_{B}$

$\Rightarrow Δ U_{A} = Δ U_{B}$

$\Rightarrow C_{A} \cdot Δ T - w_{A} = C_{B} Δ T - \frac{w_{A}}{2}$

$\Rightarrow C_{B} < C_{A}$

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