A gas is enclosed in a vessel of volume V at temperature `T_(1)` and P, the vessel is connected to another vessel of volume `V//2` by a tube and a stopcock. The second vessel is initially evacuated. If the stopcock is opened, the temperature of second vessel becomes `T_(2)`. The first vessel is maintained at a temperature `T_(1)`. What is the final pressure `P_(1)` in the apparatus ?

Options

A. `(2pT^(2))/(2T_(2)+T_(1))`
B. `(2pT^(2))/(T_(2)+2T_(1))`
C. `(pT^(2))/(2T_(2)+T_(1))`
D. `(2pT^(2))/(T_(1)+T_(2))`

Answer

A

Explanation

If n is the total nwnber of moles of gas and `n_(1)` moles are in the larger shpere and `n_(2)` moles in the smaller shpere. Then `n = n_(1) + n_(2)` and pV = nRT
`(pV)/(RT_(1))=(p.V)/(RT_(1))+(p.V)/(2RT_(2)),p.=(2pT_(2))/(2T_(2)+T_(1))`