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 value joining two vessels is opened, the temperature inside the vessel at equilibrium will be

Question

( A ) $(T_1 + T_2)/2$
( B ) $\frac{T_1T_2 (P_1V_1 + P_2V_2)}{P_1V_1T_1 + P_2V_2T_2}$
( C ) $\frac{T_1T_2 (P_1V_1 + P_2V_2)}{P_1V_1T_2 + P_2V_2T_1}$
( D ) $T_1 + T_2$