Question

$s_p$ and $s_v$ are specific heats at constant pressure and constant volume, respectively. It is observed that $s_p-s_v=a$ for hydrogen gas, $s_p-s_v=b$ for nitrogen gas. The correct relation between $a$ and $b$ is

• A. $a=b$
• B. $a=14b$
• C. $a=28b$
• D. $14a=b$

Answer 1

The correct option is B $a=14b$

We know that, molar heat capacity $C$ and specific heat capacity $s$ are related as $C=Ms$, where $M$ is molar mass.

So, for hydrogen gas
$s_p-s_v=a$ [given]
$\Rightarrow M_H{s}_p-M_H{s}_v=M_{H}a$
$\Rightarrow C_P-C_V=M_{H}a=R$
where $R$ is the universal gas constant.
[since we know that, $C_P-C_V=R$ for any ideal gas]

$\Rightarrow C_P-C_v=2a=R$ ...$\left(1\right)$

Similarly, for nitrogen gas,
$C_P-C_v=28b=R$ ...$\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,
$2a=28b$
$\Rightarrow a=14b$

Why this question? Concept involved: This question tests if you know the difference between specific heat capacity and molar heat capacity. Importance in $JEE$: Asked in Mains $2017$.