Two closed vessels of equal volume containing air at pressure `P_(1)` and temperature `T_(1)` are connected to each other through a narrow tube. If the temperature in one of the vessels is now maintained at `T_(1)` and that in the other at `T_(2)`, what will be the pressure in the vessels?

Options

A. `(T_(1))/(2P_(1)T_(2))`
B. `(2P_(1)T_(2))/(T_(1)+T_(2))`
C. `(2P_(1)T_(2))/(T_(1)-T_(2))`
D. `(2P_(1))/(T_(1)+T_(2))`

Answer

b

Explanation

(b) Let `T_(1)gtT_(2)`, final pressure will be same, Let x mole transfer from A to B vessel.
`:." " P_(A)V=(n-x)RT`
and `P_(A)V=(n+x)RT_(2)`
`:." " x=(n(T_(1)-T_(2)))/(T_(1)+T_(2)),`
`"finally "P_(1)xx2V=2nRT_(1),V=(nRT_(1))/(P_(1))`
`:." " P_(A)xx(nRT_(1))/(P_(1))=(n-(n(T_(1)-T_(2)))/((T_(1)+T_(2))))RT_(1)`
`P_(A)=(2P_(1)T_(2))/(T_(1)+T_(2))`