Two thermally insulated vessel 1 and 2 are filled with air at temperature `(T_1T_2), volume (V_1V_2)` and pressure `(P_1P_2)` respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

Options

A. `T_1 = T_2`
B. `(T_1 + T_2 )//2`
C. `(T_1 T_2 P(V_1 + V_2))/(E_1 V_1 T_2 + P_2 V_2 T_1)`
D. `(T_1 T_2 P(P_2 V_1 + P_2V_2))/(P_1 V_1 T_2 + P_2 V_2 T_1)`

Answer

C

Explanation

Initial No. of moles = final No. of moles
`rArr" "(P_1 V_1)/(RT_1) + (P_2 V_2)/(RT_2) = (P(V_1 + V_2))/(RT) rArr T = (P(V_1 +V_2)T_3T_4)/(P_1V_1 T_2 + P_2 V_2 T_1)`