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 Pf is

Options

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

B

Explanation

Number of mol of gases in each container `= (P_(i)V)/(RT_(1))`
Total mol of gases in both containers `=2 (P_(i)V)/(RT)`

In left chamber `n_(1) = (P_(f)V)/(RT_(1))` and In right chamber, `n_(2) = (P_(f)V)/(RT_(2))`
Total moles of gases should remain constant `(2P_(i)V)/(RT_(1)) = (P_(f)V)/(RT_(1)) + (P_(f)V)/(RT_(2)) rArr P_(f) = 2p ((T_(2))/(T_(1) + T_(2)))`