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Q.
The ratio $\frac{C_{P}}{C_{V}}=\gamma$ for a gas. Its molecular weight is $M$. Its specific heat capacity at constant pressure is
Kinetic Theory
Solution:
According to Mayer's relation
$C_{P}-C_{V}=R$ or
$1-\frac{C_{V}}{C_{P}}=\frac{R}{C_{P}}$
or $1-\frac{1}{\gamma}=\frac{R}{C_{P}}$
$\left(\because \gamma=\frac{C_{P}}{C_{V}}\right)$
or $\frac{\gamma-1}{\gamma}=\frac{R}{C_{P}}$ or $C_{P}=\frac{\gamma R}{\gamma-1}$
Specific heat capacity $=\frac{\text { molar heat capacity }}{\text { molecular weight }}$
Specific heat capacity at constant pressure
$=\frac{\gamma R}{M(\gamma-1)}$