Two thermally insulated vessels 1 and 2 are filled with air at temperatures $$(T_1, T_2)$$, volume $$(V_1, V_2)$$ and pressure $$(P_1, P_2)$$ respectively. If the valve joining two vessels is opened, the temperature inside the vessel at equilibrium will be

A

$$T_1 + T_2$$

B

$$(T_1 + T_2)/2$$

C

$$\frac{T_1 T_2 (P_1 V_1 + P_2 V_2)}{P_1 V_1 T_2 + P_2 V_2 T_1}$$

D

$$\frac{T_1 T_2 (P_1 V_1 + P_2 V_2)}{P_1 V_1 T_1 + P_2 V_2 T_2}$$