JEE Main20265 April 2026Morning ShiftPhysicsKinetic Theory of GasesActual
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 U = n C_v (T_f - T_i) = nR - 1 (T_f - T_i) , where = C_p C_v , T_i = initial temperature, T_f = final temperature. Statement II: Relation between degree of freedom f and (= C_p/C_v) is ( = 1 + 2 f ) Choose the correct a
Options
- ABoth A and R are true and R is the correct explanation of A
- BBoth A and R are true but R is NOT the correct explanation of A
- CA is true but R is false
- DA is false but R is true
Correct answer
B. Both A and R are true but R is NOT the correct explanation of A
Step-by-step solution
Statement I is true because for an ideal gas, the change in internal energy is given by U = n C_v T . Using Mayer's relation C_p - C_v = R and the ratio of specific heats = C_p C_v , we can write C_v = R - 1 . Substituting this, we get U = nR - 1 (T_f - T_i) . Statement II is true because according to the law of equipartition of energy, the molar heat capacity at constant volume is C_v = f 2 R and at constant pressure is C_p = ( f 2 + 1 )R . Therefore, = C_p C_v = 1 + 2 f . Statement II does not explain Statement I