Define two specific heats of a gas. Write the relation between them.

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(N/A) For gases,the specific heat capacity is defined as the molar specific heat capacity.
$1$. Molar specific heat capacity at constant volume $(C_{V})$: It is the amount of heat required to raise the temperature of $1$ mole of a gas by $1 \ K$ (or $1^{\circ}C$) while keeping the volume constant.
$2$. Molar specific heat capacity at constant pressure $(C_{P})$: It is the amount of heat required to raise the temperature of $1$ mole of a gas by $1 \ K$ (or $1^{\circ}C$) while keeping the pressure constant.
The relation between these two molar specific heat capacities is given by Mayer's relation: $C_{P} - C_{V} = R$,where $R$ is the universal gas constant.

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The molar specific heat of an ideal gas at constant pressure and constant volume is $C_p$ and $C_v$ respectively. If $R$ is the universal gas constant and the ratio of $C_p$ to $C_v$ is $\gamma$,then $C_v=$

The molar specific heat of an ideal gas at constant pressure and constant volume is $C_{p}$ and $C_{v}$ respectively. If $R$ is the universal gas constant and $\gamma = \frac{C_p}{C_v}$,then $C_v =$

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