First slide

Law of equipartition of energy

Question

Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass $\large \frac{m}{4}$ . The ratio of the specific heats $\large \left( {C_V^A\,and\,C_V^B} \right)\$ of gas A and B, respectively is :

Moderate

A

7 : 9
B

5 : 7
C

3: 5
D

5 : 9

Solution

Degree of freedom of a diatomic molecule
if vibration is absent = 5
Degree of freedom of a diatomic molecule
if vibration is present = 7
$\therefore \,C_v^A\, = \,\frac{{{f_A}}}{2}R\, = \,\frac{5}{2}R\& \,C_V^B\, = \,\frac{{{f_B}}}{2}R\, = \,\frac{7}{2}R$
$\therefore \,\frac{{C_v^A}}{{C_v^B}}\, = \,\frac{5}{7}$

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