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(C) The heat supplied at constant pressure is $dQ_p = n C_p \Delta T$. The change in internal energy is $dU = n C_v \Delta T$. The fraction of heat en

Vedclass · Accepted Answer

$5/7$

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(C) The heat supplied at constant pressure is $dQ_p = n C_p \Delta T$. The change in internal energy is $dU = n C_v \Delta T$. The fraction of heat energy used to increase the internal energy is given by the ratio $\frac{dU}{dQ_p} = \frac{n C_v \Delta T}{n C_p \Delta T} = \frac{C_v}{C_p} = \frac{1}{\gamma}$. For a diatomic gas,the degrees of freedom $f = 5$. The molar heat capacity at constant volume is $C_v = \frac{f}{2} R = \frac{5}{2} R$. The molar heat capacity at constant pressure is $C_p = C_v + R = \frac{5}{2} R + R = \frac{7}{2} R$. Therefore,the required fraction is $\frac{C_v}{C_p} = \frac{\frac{5}{2} R}{\frac{7}{2} R} = \frac{5}{7}$.

$A$ diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy?

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