The molar heat capacity in a process of a dia | vedclass

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(C) For a diatomic gas,the internal energy change is given by $dU = C_V dT = \frac{5}{2} R dT$. From the first law of thermodynamics,$dU = dQ - dW$. G

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$\frac{10}{3}R$

Vedclass · Answer

(C) For a diatomic gas,the internal energy change is given by $dU = C_V dT = \frac{5}{2} R dT$. From the first law of thermodynamics,$dU = dQ - dW$. Given $dQ = Q$ and $dW = \frac{Q}{4}$,we have $dU = Q - \frac{Q}{4} = \frac{3Q}{4}$. Substituting $dU$ into the internal energy equation: $\frac{3Q}{4} = \frac{5}{2} R dT$,which gives $dT = \frac{3Q}{4} 	imes \frac{2}{5R} = \frac{3Q}{10R}$. The molar heat capacity $C$ is defined as $C = \frac{dQ}{dT}$. Substituting the values: $C = \frac{Q}{\frac{3Q}{10R}} = \frac{10}{3}R$.

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:

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