Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure pi 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 :

Question

$\begin{array}{1 1} (1)P_i \bigg(\large\frac{T_1T_2}{T_1+T_2}\bigg) \\ (2)2P_i \bigg(\large\frac{T_1}{T_1+T_2}\bigg) \\ (3)2P_i \bigg(\large\frac{T_2}{T_1+T_2}\bigg) \\ (4) 2P_i \bigg(\large\frac{T_1T_2}{T_1+T_2}\bigg)\end{array}$