If the amount of substance is specified in terms of moles $\mu$, instead of mass $m$ in $\mathrm{kg}$, we can define heat capacity per mole of the substance by

$\therefore \mathrm{C}=\frac{\mathrm{S}}{\mu}=\frac{1}{\mu} \frac{\Delta \mathrm{Q}}{\mu \Delta \mathrm{T}}$ where $\mathrm{C}$ is known as molar specific heat capacity of the substance.

$C$ depends on the nature of the substance and its temperature.

The $SI$ unit of molar specific heat capacity is $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$.

We can get molar specific heat for gases in two ways.

$(i)$ Molar specific heat at constant pressure $\left(C_{P}\right)$ : If the gas is held under constant pressure during the heat transfer, then it is called the molar specific heat capacity at constant pressure and is denoted by $\mathrm{C}_{\mathrm{p}}$.

$(ii)$ Molar specific heat at constant volume $\left(C_{V}\right):$ If the volume of the gas is maintained during the heat transfer, then the corresponding molar specific heat capacity is called molar specific heat capacity at constant volume and is denoted by $\mathrm{C}_{\mathrm{v}}$.

Water has the highest specific heat capacity compared to other substances. For this reason water is used as a coolant in automobile radiators as well as a heater in hot water bags.

Owing to its high specific heat capacity, the water warms up much more slowly than the land during summer and consequently wind from the sea has a cooling effect.

– That is why in desert areas, the earth surface warms up quickly during the day and cools quickly at night.

gas	$C_{P}\left(J \mathbf{~ m o l}^{-1} K^{-1}\right)$	$\mathrm{C}_{\mathrm{V}}\left(\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\right)$
$\mathrm{He}$	$20.8$	$12.5$
$\mathrm{H}_{2}$	$28.8$	$20.4$
$\mathrm{~N}_{2}$	$29.1$	$20.8$
$\mathrm{O}_{2}$	$29.4$	$21.1$
$\mathrm{CO}_{2}$	$37.0$	$28.5$