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. `2p_(i)((T_(2))/(T_(1)+T_(2)))`
D. `1p_(i)((T_(1)T_(2))/(T_(1)+T_(2)))`

Answer

C

Explanation

Initial moles
`"No. of moles in first container, "n_(1)=(p_(i)V)/(RT_(1))`
`"No. of moles in second container, "n_(2)=(p_(i)V)/(RT_(1))`
`"Total moles in two containers."`
`n_(1)+n_(2)=(p_(i)V)/(RT_(1))+(p_(i)V)/(RT_(1))=(2p_(i)V)/(RT_(1))`
After heating one of hte bulbs to `T_(2)`

`"No. of moles in first container, "n._(1)=(p_(f)V)/(RT_(1))`
`"No. of moles in second container, "n._(2)=(p_(f)V)/(RT_(2))`
Total moles in two containers
`n._(1)+n._(2)=(p_(f)V)/(RT_(1))+(p_(f)V)/(RT_(2))`
Since `n_(1)+n_(2)=n._(1)+n._(2)`
`(2p_(i)V)/(RT_(1))=(p_(f)V)/(RT_(1))+(p_(f)V)/(RT_(2))`
`(2p_(i)V)/(RT_(1))=(p_(f)V)/(R)((1)/(T_(1))+(1)/(T_(2)))`
`=(p_(f)V)/(R)((T_(1)+T_(2))/(T_(1)T_(2)))`
`2p_(i)=p_(f)((T_(1)+T_(2))/(T_(2)))`
`p_(f)=2p_(i)((T_(2))/(T_(1)+T_(2)))`