For a diatomic gas, if for rigid molecules and for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? ( and are specific heats of the gas at constant pressure and volume) [2025]

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Solution

Q.
For a diatomic gas, if $γ_{1} = (\frac{C_{p}}{C_{v}})$ for rigid molecules and $γ_{2} = (\frac{C_{p}}{C_{v}})$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct

( $C_{p}$ and $C_{v}$ are specific heats of the gas at constant pressure and volume) [2025]

1 $γ_{2} > γ_{1}$

2 $γ_{2} = γ_{1}$

3 $2 γ_{2} > γ_{1}$

4 $γ_{2} < γ_{1}$

Ans.
(4)

$γ = \frac{2}{f} + 1$

without vibration : f = 5 : $γ_{1}$ = 1.4

without vibration : f = 7 : $γ_{2}$ = 1.14

$∴ γ_{2} < γ_{1}$

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