A system goes from A to B via two processes I and II as shown in figure. If \Delta U_1 and \Delta U_2 are the changes in internal energies in the processes I and II respectively, then

relation between \Delta U_1 and \Delta U_2 can not be determined

Heat and Thermodynamics PYQ — JEE Main 2005 · Shift 0 · Q152 with Solution

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Correct answer: B

Key thermodynamics idea
Internal energy $U$ is a state function. That means its change depends only on the initial and final states, not on the path taken.
Given situation
The system goes from the same initial state $A$ to the same final state $B$ by two different processes:
- Process $I$
- Process $II$
Apply property of state function
Since both processes start at $A$ and end at $B$ , the change in internal energy must be the same in both cases:
$Delta U_1 = U_B - U_A$ $Delta U_2 = U_B - U_A$
Therefore,
$Delta U_1 = Delta U_2$
Check options
- A: Cannot be determined Incorrect
- B: $\Delta U_1 = \Delta U_2$ Correct
- C: $\Delta U_2 < \Delta U_1$ Incorrect
- D: $\Delta U_2 > \Delta U_1$ Incorrect

Hence, the correct answer is B.