[figure] 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 ?
- dq 0
- The pressure in the vessel B before opening the stopcock is zero
- dw 0
- dU 0
Answer
(2) The pressure in the vessel B before opening the stopcock is zero
Solution
This is Joule's experiment on free expansion of a gas into an evacuated vessel.
Vessel B is evacuated the pressure in B before opening the stopcock is zero.
Gas expands against zero external pressure w = -pext V = 0, so dw = 0.
No change in temperature of the water no heat exchanged dq = 0.
By the first law, dU = dq + dw = 0.
Only statement (2) is true.
Answer: (2)