Two perfect gases at absolute temperature `T_(1) and T_(2)` are mixed. There is no loss of energy. The masses of the molecules are `m_(1) and m_(2)`. The number of molecules in the gases are `n_(1) and n_(2)`. The temperature of the mixture is

Options

A. `T_(1) + T_(2)`
B. `T_(1) + T_(2)/2`
C. `n_(1)T_(1) + n_(2)T_(2)/n_(1) +n_(2)`
D. None of these

Answer

C

Explanation

`3/2 kT_(1) xx n_(1)+3/2 KT_(2) xx n_(2) = (n_(1)+n_(2))3/2 kT`
or `T = (n_(1)T_(1)+n_(2)T_(2))/(n_(1)+n_(2))`.