# Heat Capacity of gases

Specific and molar heat capacity of gases

Specific heat (or heat capacity) of a substance may be defined as the quantity of heat required to raise the temperature of 1 g of that substance by $1^0C$. it is expressed in calories or joules. Molar heat capacity may be defined as :

Molar heat capacity = Sp. Heat × Mol. Mass

Since the gases expand on heating, hence molar heat capacity of gases is termed as follows:

(i) Molar heat capacity at constant pressure (Cp): it is the amount of heat in calories required to raise the temperature of one mole of a gas through $1^0C$ at constant pressure, while the volume is allowed to increase.

(ii) Molar heat capacity at constant volume (Cv): it is the amount of heat in calories required to raise the temperature of one mole of a gas through $1^0C$ at constant volume, while the pressure is allowed to increase.

With the help of kinetic gas euation it is calculated that, $Cv = \dfrac{3}{2}R$ (for mono atomic gas)

And Cp – Cv = R

Or, $Cp = R + Cv = R + \dfrac{3}{2}R$

Or, $Cp = \dfrac{5}{2}R$

Or, $\dfrac{Cp}{Cv}$ = $\dfrac{\left(\dfrac{5}{2} R \right) }{ \left( \dfrac{3}{2}R \right)}$ = 1.66

It means that ratio of Cp and Cv is equal to 1.66 for mono atomic gases.

This ratio changes with the atomicity of the gas. Its general equation is given below:

For any gas; $\dfrac{Cp}{Cv}$ = $\dfrac{\frac{5}{2}R + X}{\frac{3}{2}R + X}$

where X = 0, R and 3/2 R for mono-, di- and poly-atomic gases. By putting the value of X in the above equation, the ratio comes to 1.66, 1.40 and 1.33 for mono-, di- and poly-atomic gases, respectively.

The value indicates the atomicity of the gases; hereby atomic weight of the gas can be calculated as: $\text{Atomic weight} = \dfrac{\text{Molecular weight}}{\text{Atomicity}}$

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