#### Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure $\mathrm{P_{i}}$ and temperature $\mathrm{T_{i}}$ are connected through a narrow tube of negligible volume,The temperature of one of the bulbs is then raised to $\mathrm{T_{2}}$,The final pressure $\mathrm{P_{f}}$ is _________Option: 1 Option: 2 Option: 3 Option: 4 None

Initially,

Number of moles pf gases in each container $\mathrm{=\frac{P_i V}{R T_1}}$

Total number of moles of gases in both container $\mathrm{=\frac{2 P_1 V}{R T_1}}$

After mixing,

No. of moles of gases left is chamber$\mathrm{=\frac{P_f v}{R T_1}}$

No. of moles in right chamber $\mathrm{=\frac{P_{f V}}{R T_2}}$

$\mathrm{\therefore }$ Total number of moles $\mathrm{\frac{P_f V}{R T_1}+\frac{P_f V}{R T_2}=\frac{P_f V}{R}\left(\frac{1}{T_1}+\frac{1}{T_2}\right) }$

As total number of moles remains constant.

Hence, $\mathrm{\frac{2 P_i V}{R T_1}=\frac{P_f V}{R T_1}+\frac{P_f V}{R T_2} \Rightarrow P_f=2 P_i\left(\frac{T_2}{T_1+T_2}\right) }$