JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Heat & Thermodynamics

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According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

(A) $\frac{9}{2} R$
(B) $\frac{5}{2} R$
(C) $\frac{3}{2} R$
(D) $\frac{7}{2} R$ ✓ Correct

Answer: (D)

Solution

A diatomic molecule has three translational and two rotational degrees of freedom. An active vibrational mode adds two more, one for its kinetic and one for its potential energy, giving

f = 3 + 2 + 2 = 7

. Each degree contributes

\frac{1}{2} R

to the molar heat capacity at constant volume, so

C_{V} = \frac{f}{2} R = \frac{7}{2} R

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Single correct option

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