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 :

Options

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

Answer

C

Explanation

Since, vessels are closed
`:.` Initial moles `=` Final moles
`(p_(i)V)/(RT_(1)) + (p_(i) V)/(RT_(1)) = (p_(f) V)/(RT_(2)) + (p_(f)V)/(RT_(1))`
`(2p_(i))/(T_(1)) = p_(f) [(1)/(T_(1)) + (1)/(T_(2))]`
`p_(f) = 2p_(i) [(T_(2))/(T_(1) + T_(2))]`