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_(1))/( T_(1) -T_(2))`
D. `(2P_(1))/( T_(1)+ T_(2))`

Answer

D

Explanation

Let `T_(1) gt T_(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) xx 2V = 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))`