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)dw=0
(B)dq=0
(C)dU=0
(D)The pressure in the vessel B before opening the stopcock is zero.✓ Correct
Answer: (D)
Solution
No temperature change accompanies the expansion, and the internal energy of an ideal gas depends only on temperature, so ΔU=0. The gas expands into the second vessel against nothing, so the external pressure is zero and no work is done; with ΔU=0 and w=0 the heat exchanged is also zero. Such a free expansion, yielding no work and no temperature change, is possible only if the second vessel was evacuated beforehand, so its pressure before the stopcock was opened must have been zero.
JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Single correct option
