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(A) Statement $I$ is correct. The change in internal energy for an ideal gas is given by $\Delta U = nC_v \Delta T$. Since $C_v = \frac{R}{\gamma - 1}

Vedclass · Accepted Answer

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Vedclass · Answer

(A) Statement $I$ is correct. The change in internal energy for an ideal gas is given by $\Delta U = nC_v \Delta T$. Since $C_v = \frac{R}{\gamma - 1}$, substituting this gives $\Delta U = \frac{nR}{\gamma - 1}(T_f - T_i)$.Statement $II$ is also correct. The molar heat capacity at constant volume is $C_v = \frac{fR}{2}$ and at constant pressure is $C_p = C_v + R = (\frac{f}{2} + 1)R$. Therefore, $\gamma = \frac{C_p}{C_v} = \frac{(\frac{f}{2} + 1)R}{\frac{fR}{2}} = \frac{f+2}{f} = 1 + \frac{2}{f}$.Since both statements are true and the definition of $\gamma$ in terms of $f$ is a fundamental property used to derive the expression in Statement $I$, $R$ is the correct explanation of $A$.

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