Question

Assertion (A) For a gas molecule with degree of freedom 6, the law of equipartition of energy gives $C_v = 2R$. Reason (R) Law of equipartition of energy holds good for all degree of freedom whether translational, rotational or vibrational. (NCERT Pg. 253)

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
• B. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
• C. Assertion (A) is true but Reason (R) is false
• D. Assertion (A) is false but Reason (R) is true

Answer 1

Answer: (D)

Option 4

Answer 2

The assertion is incorrect because for a gas molecule with 6 degrees of freedom, the molar heat capacity at constant volume ($C_v$) is calculated as $C_v = \frac{f}{2}R = \frac{6}{2}R = 3R$, not $2R$. The reason correctly states that the law of equipartition of energy applies to all types of degrees of freedom (translational, rotational, and vibrational), each contributing $\frac{1}{2}k_BT$ per independent quadratic term in the energy expression.