Q83 / 90 · KVPY 2019 (SB/SX) · Physics
Two containers and of volumes and respectively, hold the same ideal gas and are connected by a thin horizontal tube of negligible volume with a valve which is initially closed. The initial pressures of the gas in and are and , respectively. Heat baths are employed to maintain the temperatures in the containers at and , respectively. The valve is now opened. Select the correct statement.
Two containers and of volumes and respectively, hold the same ideal gas and are connected by a thin horizontal tube of negligible volume with a valve which is initially closed. The initial pressures of the gas in and are and , respectively. Heat baths are employed to maintain the temperatures in the containers at and , respectively. The valve is now opened. Select the correct statement.
- AThe gas will flow from the hot container to the cold one and the process is reversible.
- BThe gas will flow from one container to the other till the number of moles in two containers are equal.
- CA long time after the valve is opened, the pressure in both the containers will be .
- Correct answerDA long time after the valve is opened, number of moles of gas in the hot container will be thrice that of the cold one.
Solution
Let and are number of moles of gas present in container and respectively, before the value is opened.
Then, using .
and

When value is opened gas flows from to till pressure in and is equal. Let after equalisation of pressure in both and , its value is ,
Then, using .
(Container )
and (Container )
So,
As no gas is leaked from containers,
So,
Now,
Finally number of moles of is thrice of .
Hence, the correct answer is option: 'D'.