Physics - Heat & Thermo Question with Solution | TestHub

For monoatomic gas, $C_p=\frac{5}{2}R,C_v=\frac{3}{2}R$, $C_p-C_v=R$

For diatomic gas $C_p=\frac{7}{2}R,C_v=\frac{5}{2}R$, $C_p-C_v=R$

$C_p-C_v$ is same for both

$C_p+C_v=6R$ (diatomic), $C_p+C_v=4R$ (mono)

so ${\left(C_p+C_v\right)}_{\text{dia }}>{\left(C_p+C_v\right)}_{\text{mono }}$

$\frac{C_p}{C_v}=\frac{7}{5}=1.4$ (diatomic), $\frac{C_p}{C_v}=\frac{5}{3}=1.66$ (monoatomic)

$C_p{C}_v=\frac{35}{4}{R}^2$ (diatomic), $C_p{C}_v=\frac{15}{4}{R}^2$ (monoatomic)

so ${\left(C_p\cdot C_v\right)}_{\text{diatomic }}>{\left(C_p\cdot C_v\right)}_{\text{monoatomic }}$