Question

Consider the following:
Statement-I: Both internal energy (U) and work (w) are state functions.
Statement-II: During the free expansion of an ideal gas into vacuum, the work done is zero.
The correct answer is

• A. Both Statement-I and Statement-II are correct
• B. Both Statement-I and Statement-II are not correct
• C. Statement-I is correct, but Statement-II is not correct
• D. Statement-I is not correct, but Statement-II is correct

Hint:

State functions depend only on the system’s state, while path functions depend on the process. Free expansion into a vacuum involves no work because there’s no external pressure to oppose the expansion.

Answer 1

The Correct Option is D

Let’s break this down step by step to evaluate the statements and determine why option (4) is the correct answer.
Step 1: Evaluate Statement-I

• Internal energy ($U$) is a state function because it depends only on the state of the system.
• Work ($w$) is a path function because it depends on the process.

Statement-I is incorrect because work is not a state function.
Step 2: Evaluate Statement-II
During free expansion of an ideal gas into a vacuum:

• External pressure $P_{\text{ext}} = 0$.
• Work done, $w = -P_{\text{ext}} \Delta V = 0$.

Statement-II is correct.
Step 3: Confirm the correct answer
Statement-I is incorrect, but Statement-II is correct, matching option (4).
Thus, the correct answer is (4) Statement-I is not correct, but Statement-II is correct.