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 othe 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_(1))`
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_(1))/(P_(1)V_(1) + P_(2)V_(2))`
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

A

Explanation

`U = U_(1) + U_(2) implies (n_(1) + n_(2)) C_(V)T = n_(1)C_(V)T_(1)+ n_(2)C_(V)T_(2)`
`implies T = ((P_(1)V_(1) + P_(2)V_(2)) T_(1)T_(2))/((P_(1)V_(1)T_(2) + P_(2)V_(2)T_(2)))`