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 $\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}}(\mathrm{T}_{\mathrm{f}}-\mathrm{T}_{\mathrm{i}})=\frac{\mathrm{nR}}{\gamma-1}(\mathrm{T}_{\mathrm{f}}-\mathrm{T}_{\mathrm{i}})$, where $\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}$, $\mathrm{T}_{\mathrm{i}}=$ initial temperature, $\mathrm{T}_{\mathrm{f}}=$ final temperature. Statement II: Relation between degree of freedom $f$ and $\gamma(=\mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}})$ is $(\gamma=1+\frac{2}{f})$ Choose the correct answer from the options given below

(B) Both A and R are true but R is NOT the correct explanation of A

(A) Both A and R are true and R is the correct explanation of A

JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Heat & Thermodynamics

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 = nC_{v} (T_{f} - T_{i}) = \frac{nR}{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})

(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✓ Correct
(C)A is true but R is false
(D)A is false but R is true

Answer: (B)

Solution

For an ideal gas

Δ U = n C_{v} (T_{f} - T_{i})

, and since

C_{p} - C_{v} = R

with

γ = C_{p} / C_{v}

, it follows that

C_{v} = \frac{R}{γ - 1}

; hence

Δ U = \frac{n R}{γ - 1} (T_{f} - T_{i})

, so the first statement is correct. The second statement is also correct: with

f

degrees of freedom,

C_{v} = \frac{f}{2} R

and

C_{p} = \frac{f + 2}{2} R

, so

γ = \frac{C _{p}}{C _{v}} = 1 + \frac{2}{f}

. The first statement follows from the relation

C_{v} = \frac{R}{γ - 1}

, not from the degrees-of-freedom relation, so the second does not explain the first. Both statements are true, but the second is not the correct explanation of the first.

JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Single correct option

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JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Heat & Thermodynamics

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