Q 11-12-154JEE MainJEE Main 2017 (2 Apr)Easy
$C_p - C_v = \dfrac{R}{M}$, where $C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_p - C_v = a$ for hydrogen gas and $C_p - C_v = b$ for nitrogen gas. The correct relation between $a$ and $b$ is:
Answer: (D) $a = 14b$
Here $M$ is the molar mass, so the difference of the specific heats (per unit mass) is inversely proportional to $M$:
$$a = \frac{R}{2},\qquad b = \frac{R}{28}$$
$$\frac{a}{b} = \frac{28}{2} = 14 \;\Rightarrow\; a = 14b$$
Solution by Sreeraj P, M.Sc Physics