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, $C_p-C_v=R$, which is the gas constant.

Hence be it any gas, hydrogen or nitrogen, its value is same.

Here, for ideal gas, $C_p–C_v=R/M$, where $M$ is the mass of one mole of gas.

Mass of one mole of hydrogen $M=2$ g and that of nitrogen $M=28$ g

$\therefore$ $a=C_p-C_v=R/2$ (for hydrogen)

And $b=C_p-C_v=R/28$ (for nitrogen)

$⟹a=14b$