A classical model of a diatomic molecule is a springy dumbbell, as shown, where the dumbbell is free to rotate about axes perpendicular to the spring. At high temperature when vibrational degree of freedom is excited, the specific heat per mole at constant volume, is

Engineering

Physics

Degree of Freedom Internal Energy of Gas and Specific Heat Capacity of Gases

Question

$\frac{7}{2} R$

$\frac{5}{2} R$

$\frac{9}{2} R$

$\frac{3}{2} R$

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A diatomic molecule has translational (3), rotational (2), and vibrational (1) degrees of freedom. The equipartition theorem states each quadratic term contributes $\frac{1}{2} R$ per mole. Vibration has both kinetic and potential energy terms, contributing $1 R$ . The total specific heat is $\frac{3}{2} R + \frac{2}{2} R + R = \frac{7}{2} R$ .

Final Answer: $\frac{7}{2} R$