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
Concept. For an ideal gas $\Delta U=nC_V\Delta T$ in any process, and $C_V=\dfrac{R}{\gamma-1}$. Separately, $\gamma=1+\dfrac2f$ from equipartition.
Step 1. Statement A. True.
Step 2. Statement R. True, but A follows from $C_P-C_V=R$ and $\gamma=C_P/C_V$, not from the degrees of freedom.
Answer. Option B.
Solution by Sreeraj P, M.Sc Physics
