$A$. The motion of the gas molecules freezes at $0^{\circ} C$
$B$. The mean free path of gas molecules decreases if the density of molecules is increased.
$C$. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.
$D$. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2} k_{B} T$ (for monoatomic gases)
Choose the most appropriate answer from the options given below
$(i)$ The pressure of a gas is proportional to the mean speed of the molecules.
$(ii)$ The root mean square speed of the molecules is proportional to the pressure.
$(iii)$ The rate of diffusion is proportional to the mean speed of the molecules.
$(iv)$ The mean translational kinetic energy of a gas is proportional to its kelvin temperature.
$c_P - c_V = a$ for hydrogen gas
$c_P - c_V = b$ for nitrogen gas
The correct relation between $a$ and $b$ is