Question

Two vessels A and B are connected via stopcock. Vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and 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

Hint:

In a free expansion, there is no work done, no heat transfer, and no change in internal energy, as the process is adiabatic and occurs without a temperature change.

Answer 1

The Correct Option is D

Since there is no change in temperature after the stopcock is opened, it is a free expansion, implying: \[ w = 0, \quad q = 0, \quad \Delta U = 0 \] Thus, the correct answer is option (4). The pressure in vessel B before opening the stopcock is zero.