Question

An isolated box is divided into two equal compartments by a partition (see figure). One compartment contains a van der Waals gas while the other compartment is empty. The partition between the two compartments is now removed. After the gas has filled the entire box and equilibrium has been achieved, which of the following statement(s) is (are) correct?

• A. Internal energy of the gas has not changed.
• B. Internal energy of the gas has decreased.
• C. Temperature of the gas has increased.
• D. Temperature of the gas has decreased.

Hint:

In an irreversible expansion in an isolated system, the internal energy of the gas does not change, but its temperature typically decreases.

Answer 1

The Correct Option is A, D

Step 1: Understanding the effect of partition removal.
When the partition is removed, the gas expands to fill the entire volume. This expansion is an irreversible process, and in most cases, it will result in a decrease in the temperature of the gas, assuming no heat exchange with the surroundings. However, the internal energy of the gas does not change in an isolated system because the expansion work is done without heat exchange.
Step 2: Conclusion.
Thus, the correct answer is options (A) and (D).