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_(1)V_(1)+ P_(2)V_(2)))/(P_(1)V_(1)T_(2) + P_(2)V_(2)T_(1))`
D. `(T_(1)T_(2)(P_(1)V_(1)+ P_(2)V_(2)))/(P_(1)V_(1)T_(1) + P_(2)V_(2)T_(2))`

Answer

C

Explanation

Assume `T_(1) gt T_(2)`
Heat given = Heat taken
`mu_(1)C_(V_(1))(T_(1) - T_(2)) = mu_(2)C_(V_(2))(T- T_(2))`
Here `C_(V_(1)) = C_(V_(2))` & `mu_(1) = (P_(1)V_(1))/(T_(1)), mu_(2) = (P_(2)V_(2))/(T_(2))`