Two thermally insulated vessels (1) and (2) are filled with air at temperature `(T_1,T_2)` volumes `(V_1,V_2)` and pressures `(p_1,p_2)` respectively. If the valve joining the two vessela is opened, the temperature inside the vessel at equilibrium will be `(P = common pressure)`.

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)`