JEE Main 2026 Apr 5 Shift 1, Physics Q7: Law of Equipartition of Energy

JEE Main2026Apr 5, Shift 1Physics

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Statement I: Change in internal energy of a system containing n mole of ideal gas can be written as $Δ U = n C_{v} (T_{f} - T_{i}) = \frac{n R}{γ - 1} (T_{f} - T_{i})$ , where $γ = \frac{C _{p}}{C _{v}}$ , $T_{i}$ = initial temperature, $T_{f}$ = final temperature.

Statement II: Relation between degree of freedom $f$ and $γ$ ( $= C_{p} / C_{v}$ ) is $(γ = 1 + \frac{2}{f})$ .

Choose the correct answer from the options given below:

A
Both A and R are true and R is the correct explanation of A
B
Both A and R are true but R is NOT the correct explanation of A
C
A is true but R is false
D
A is false but R is true

Solution

Statement I follows from $C_{v} = \frac{R}{γ - 1}$ combined with $Δ U = n C_{v} Δ T$ for an ideal gas. True.

Statement II is the standard equipartition result: with $f$ active degrees of freedom, $C_{v} = \frac{f R}{2}$ and $C_{p} = C_{v} + R$ , giving $γ = 1 + \frac{2}{f}$ . True.

However, the formula in Statement I is a direct consequence of $C_{v} = R / (γ - 1)$ , which can be derived independently of the equipartition theorem. So Statement II is true but not the logical cause of Statement I.

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JEE Main 2026 Apr 5 Shift 1, Physics Q7: Law of Equipartition of Energy

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