JEE Main 2025 · 2 April · morning · Single correct · +4 / −1
Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?
- (a) dq ≠ 0
- (b) The pressure in the vessel B before opening the stopcock is zero
- (c) dw ≠ 0
- (d) dU ≠ 0
Answer and solution
Answer (b) The pressure in the vessel B before opening the stopcock is zero
Solution
Chemistry ma’am · 3 steps
No temperature change and nothing pushing back: this is free expansion of a gas into a vacuum.
- Vessel B is empty. Vessel B is evacuated before the stopcock opens, so the pressure in B is zero. The gas from A rushes into a vacuum, with no opposing pressure.
- Work and heat. Work done is w = -pₑₓₜΔ V with pₑₓₜ = 0, so w = 0. The water temperature does not change, so no heat flows between the gas and the water: q = 0.
Δ U = q + w = 0 + 0 = 0
- So. dq, dw and dU are all zero, so options (a), (c) and (d) are false. The true statement is (b): the pressure in vessel B before opening the stopcock is zero.
The idea to keep. Expansion into a vacuum means pₑₓₜ = 0, so w = 0. If the temperature also stays the same, q = 0, and the first law gives Δ U = 0 for an ideal gas.
Answer from the NTA final answer key. Solution by PrepWiser.