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

Answer 1

The correct option is D $a=14b$

For any gas, difference between molar specific heats $C_p^{\prime }-C_v^{\prime }=R$, which is the gas constant.
Hence, be it any gas, hydrogen or nitrogen, its value is same.
Specific heats $C_p=\frac{C_p^{\prime }}{M}$
and $C_v=\frac{C_v^{\prime }}{M}$
$\therefore C_p-C_v=\frac{R}{M}$
where $M$ is the mass of one mole of gas.
Mass of one mole of hydrogen $M_{H_2}=2$ g and that of nitrogen $M_{N_2}=28$ g
$\therefore$ $a=C_p-C_v=R/2$ (for hydrogen)
And $b=C_p-C_v=R/28$ (for nitrogen)
$⟹a=14b$