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Find the molar heat capacity in a process of a diatomic gas if it does a work of $Q / 4$ when a heat of Q is supplied to it.

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5.25 R

2 R

3.33 R

answer is C.

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Detailed Solution

$\frac{Δ W}{Δ Q} = 1 - \frac{1}{γ} = \frac{C_{P} - C_{V}}{C_{P}} = \frac{C - C_{V}}{C} = \frac{1}{4}$

$\Rightarrow 1 - \frac{C_{V}}{C} = \frac{1}{4} \Rightarrow C = \frac{4}{3} \times \frac{5 R}{2} = \frac{10 R}{3} = 3.33 R$

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