First slide

Law of equipartition of energy

Question

The value of $γ (= \frac{C_{p}}{C_{v}})$ for hydrogen, helium and another ideal diatomic gas X (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to,

Difficult

A

$\frac{7}{5}, \frac{5}{3}, \frac{7}{5}$
B

$\frac{7}{5}, \frac{5}{3}, \frac{9}{7}$
C

$\frac{5}{3}, \frac{7}{5}, \frac{9}{7}$
D

$\frac{5}{3}, \frac{7}{5}, \frac{7}{5}$

Solution

Diatomic gases have 5 degrees of freedom, if vibrational mode is neglected. And if vibrational mode is also considered then degrees of freedom of diatomic gas molecules are 7.
For Hydrogen $γ = 1 + \frac{2}{f} = 1 + \frac{2}{5} = \frac{7}{5}$
For Helium $γ = 1 + \frac{2}{f} = 1 + \frac{2}{3} = \frac{5}{3}$
For gas X (vibrational mode also considered) f = 7.
$γ = 1 + \frac{2}{f} = 1 + \frac{2}{7} = \frac{9}{7} So, (\frac{7}{5}, \frac{5}{3}, \frac{9}{7})$

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