JEE Main 2026 · 5 Apr · Shift 1 · Physics Q32

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PhysicsSingle correct+4 / -1Question 32 of 75

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 $\Delta U=nC_v\left(T_f-T_i\right)=\dfrac{nR}{\gamma-1}\left(T_f-T_i\right)$ , where $\gamma=\dfrac{C_p}{C_v}$ , $T_i$ = initial temperature, $T_f$ = final temperature.

Statement II: Relation between degree of freedom $f$ and $\gamma\ (=C_p/C_v)$ is $\left(\gamma=1+\dfrac2f\right)$

Choose the correct answer from the options given below

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

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

A is true but R is false

A is false but R is true

Answer and worked solution

Official answer: B

Statement I (A). $\Delta U=nC_v\Delta T$ holds for an ideal gas in any process, and $C_v=\dfrac R{\gamma-1}$ . True.

Statement II (R). $C_v=\tfrac f2R$ and $C_p=\left(\tfrac f2+1\right)R$ , so $\gamma=1+\tfrac2f$ . True.

Explanation? R relates γ to the degrees of freedom; it does not explain why $\Delta U=\tfrac{nR}{\gamma-1}\Delta T$ . So R is not the explanation of A.

(B)

Topics:Specific heats of gases First law and internal energy

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JEE Main 2026 · 5 Apr · Shift 1, Physics question 32