Two closed bulb of euqal 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 released to `T_(2)`. The final pressure `p_(t)` is :

Options

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

Answer

B

Explanation

Initially number of moles of gas in each bulb is :
`n_(1) = (P_(i)V)/(RT_(1))` and `n_(2) = (P_(i)V)/(RT_(2))`
After the temperature of second bulb is raised to `T_(2)`, the number of moles of gas in both the bulbs are :
`n_(1)^(') = (P_(i)V)/(RT_(1))` and `n_(2)^(') = (P_(1)V)/(RT_(2))`
Number of moles of two gases in both the bulbs remain unchanged.
`n_(1) + n_(2) = n_(1^(')) + n_(2^('))`
`(2P_(i)V)/(RT_(1)) = (P_(f)V)/(RT_(1)) + (P_(f)V)/(RT_(2))`
or `(2P_(i))/(T_(1)) = P_(f) [(T_(1) + T_(2))/(T_(1)T_(2))]`
or `P_(f) = (2P_(i)T_(2))/(T_(1) + T_(2))`