Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Statement I : Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = nC_v(T_f - T_i) = \dfrac{nR}{\gamma - 1}(T_f - T_i)$, where $\gamma = \dfrac{C_p}{C_v}$, $T_i =$ initial temperature, $T_f =$ final temperature.
Statement II : Relation between degree of freedom $f$ and $\gamma\ (= C_p/C_v)$ is $\left(\gamma = 1 + \dfrac{2}{f}\right)$
Choose the correct answer from the options given below
Answer: (B) Both A and R are true but R is NOT the correct explanation of A
Statement I: $C_p - C_v = R$ gives $C_v = \dfrac{R}{\gamma - 1}$, so $\Delta U = nC_v\Delta T = \dfrac{nR}{\gamma - 1}\Delta T$. True.
Statement II: $C_v = \dfrac{f}{2}R$ and $C_p = \left(\dfrac{f}{2} + 1\right)R$, so $\gamma = 1 + \dfrac{2}{f}$. True.
Statement I follows from Mayer's relation, not from the degrees-of-freedom formula, so R does not explain A.
Solution by Sreeraj P, M.Sc Physics