Question

Two closed bulbs of equal volume (V ) containing an ideal gas initially at pressure `P_(i)` and temperature `T_(1)` are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to `T_(2)`. The final pressure `P_(f)` is

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

Answer 1

Correct Answer - B
Initial moles `=` final moles
`(P_(i) xxV)/(RT_(1))+(P_(i)xxV)/(RT_(1))=(P_(f)xxV)/(RT_(2))+(P_(f)xxV)/(RT_(1))`
`(P_(i) )/(T_(1))+(P_(i))/(T_(1))=(P_(f))/(T_(2))+(P_(f))/(T_(1))implies(2P_(i))/(T_(1))=P_(f)[(1)/(T_(2))+(1)/(T_(1))]`
`(2P_(i))/(T_(1))=P_(f)[(T_(1)+T_(2))/(T_(1)T_(2))] implies P_(f)=2P_(i) xx ((T_(2))/(T_(1)+T_(2)))`