Specific Heat Capacities Of Gases

From NCERT Class 11, Chapter 12 (Thermodynamics) and its link to kinetic theory, the two molar specific heats of an ideal gas are connected by Mayer's relation, $C_P-C_V=R$, where $R$ is the universal gas constant; the difference arises because a gas heated at constant pressure also performs expansion work. For a diatomic gas the molar specific heat at constant volume is $C_V=\frac{5R}{2}$, accounting for three translational and two rotational degrees of freedom under the equipartition principle. Then $C_P=C_V+R=\frac{5R}{2}+R=\frac{7R}{2}$. The ratio of specific heats follows as $\gamma =\frac{C_P}{C_V}=\frac{7R/2}{5R/2}=\frac{7}{5}=1.4$. The option 5/3 is wrong because that is the value for a monatomic gas with $C_V=3R/2$. The option 9/7 is wrong because it corresponds to a polyatomic gas with additional vibrational modes, not a simple diatomic gas. The option 3/2 is wrong because it is a value of $C_V/R$, not a ratio of the two specific heats at all. A plausibility check confirms the answer: $\gamma$ for any gas must exceed 1 since $C_P>C_V$, and the diatomic value 1.4 matches the well-known experimental result for air, which is largely diatomic nitrogen and oxygen.