1. Tardigrade
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  3. Chemistry
  4. If the ratio of molar heat capacities of a gas at constant pressure and constant volume i.e., (CP/CV)=γ, the respective values of CP and CV are

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Q. If the ratio of molar heat capacities of a gas at constant pressure and constant volume i.e., $\frac{C_P}{C_V}=\gamma$, the respective values of $C_P$ and $C_V$ are

Thermodynamics

Solution:

$\frac{C_P}{C_V}=\gamma$ and $C_P-C_V=R$
$C_P-\frac{C_P}{\gamma}=R$
$\Rightarrow C_P\left(\frac{\gamma-1}{\gamma}\right)=R \Rightarrow C_P=\frac{\gamma R}{\gamma-1}$
$\gamma C_V-C_V=R$
$\Rightarrow C_V(\gamma-1)=R \Rightarrow C_V=\frac{R}{\gamma-1}$