JEE Chemistry 2025 Question with Solution

Given: Gas in vessel A expands into vessel B after opening the stopcock, and no temperature change is observed.

Find: Which statement is certainly true.

This setup represents free expansion only when vessel B is initially a vacuum. In free expansion, the gas expands against zero external pressure.

Using the work relation,

for free expansion,

therefore,

However, whether $dq = 0$ and $du = 0$ are always true depends on the nature of the gas and the interpretation of the process. The solution discussion states that these conclusions can be conditional, whereas the condition for free expansion itself is unambiguous.

So the universally correct statement is that vessel B must have been empty before opening the stopcock, i.e. its pressure was zero.

Therefore, the correct option is D.

Given: The gas initially occupies vessel A. After the stopcock is opened, it expands into vessel B while the assembly is in a water bath, and no change in temperature is observed.

Find: The true statement among the four options.

Step 1: Identify the process

The described process is a free expansion. For a gas to expand freely, the region into which it expands must offer no opposing pressure. Therefore vessel B must be evacuated.

That means the pressure in vessel B before opening the stopcock is

Step 2: Check the work term

For expansion work,

Since the gas expands into vacuum,

so,

Step 3: Check heat and internal energy statements

The thermometer shows no temperature change, but the solution notes that the conclusions about $dq$ and $du$ can depend on whether the gas is treated as ideal or real. Hence these are not taken as the most universally valid statements here.

Step 4: Conclude

The defining condition of the process is that vessel B was initially vacuum. Therefore, the pressure in vessel B before opening the stopcock is zero.

Hence, the correct option is D.