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Q.

A monoatomic gas performs a work of $\frac{Q}{4}$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ______ R during this transformation.
Where R is the gas constant.

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answer is 2.

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Detailed Solution

The molar heat capacity of the gas will be 2R during this transformation.

$Δ Q = Δ E + WD \Rightarrow Q = Δ E + \frac{Q}{4}$
$\Rightarrow n \frac{3 R}{2} Δ T = Δ E = \frac{3 Q}{4}$
$∴ n Δ T = \frac{Q}{2 R}$
$∴ C = 2 R$

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A monoatomic gas performs a work of Q4 where Q is the heat supplied to it. The molar heat capacity of the gas will be ______ R during this transformation.Where R is the gas constant.