Question

$C_p$ 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
$C_p-C_v$ = b for nitrogen gas
The correct relation between $a$ and $b$ is :

• A. $a = \frac{1}{14} b $
• B. $a = b $
• C. $a = 14 \, b $
• D. $a = 28 \, b $

Answer 1

Answer: (C)

Let molar heat capacity at constant pressure = $X_p$
and molar heat capacity at constant volume = $X_v$
$X_p - X_{v} = R $
$MC_p - MC_{v} = R$
$C_p - C_v = \frac{R}{M}$
For hydrogen; $a = \frac{R}{2}$
For $N_2 ; b = \frac{R}{28}$
$\frac{a}{b} = 14$
$ a = 14 b$