The molar specific heat at constant pressure of an ideal gas is $\frac{7}{2} R$. The gas is made up of…
The molar specific heat at constant pressure of an ideal gas is $\frac{7}{2} R$. The gas is made up of molecules which are ( $R$ is the universal gas constant)
Polyatomic
triatomic
monoatomic
diatomic
Solution
Given: $C_P=\frac{7}{2} R$, and $C_P-C_V=R$
$\therefore C_V=C_P-R=\frac{7}{2} R-R=\frac{5}{2} R$
$\therefore \gamma=\frac{C_P}{C_V}=\frac{\frac{7}{2}}{\frac{5}{2}}=\frac{7}{5}$ which matches the $\gamma_{\text {diatomic }}=\frac{7}{5}$
$\therefore$ The gas consists of diatomic molecules!