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  4. 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 is

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Q. The molar heat capacity in a process of a diatomic gas, if it does a work of $ \frac{Q}{4} $ when a heat of Q is supplied to it is

VMMC MedicalVMMC Medical 2009

Solution:

$ dU={{C}_{V}}dT=\left[ \frac{5}{2}R \right]dT $ $ \Rightarrow $ $ dT=\frac{2(dU)}{5R} $ From first law of thermodynamics $ dU=dQ-dW=Q-\frac{Q}{4}=\frac{3Q}{4} $ Now, molar heat capacity $ C=\frac{dQ}{dT}=\frac{Q}{\frac{2(dU)}{5R}}=\frac{5RQ}{2\left[ \frac{3Q}{4} \right]}=\frac{10}{3}R $