An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume `V_1` and contains ideal gas at pressure `P_1` and temperature `T_1`.The other chamber has volume `V_2` and contains ideal gas at pressure `P_2` and temperature `T_2`. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

Options

A. `(T _(1) T_(2) (p_(1) V_(1) + P_(2) V_(2)))/(p _(1) V _(1) T_(2 ) + p _(2) V _(2) T _(2))`
B. `(p _(1) V_(1) T _(1)+ p _(2) V _(2) T_(2))/(p _(1) V _(1 ) + p _(2) V_(2))`
C. `(p_(1) V _1 T_(2) + p_(2) V _(2) T_(2))/(p _(1) V_(2) + p_(2) V _(2))`
D. `(T _(1) T _(2) (p_(1) V _(1) + p _(1) V _(2)))/(p _(1) V _(1) T _(1) + p_(2) V _(2) T _(2))`

Answer

A