Three perfect gases at absolute temperature `T_(1), T_(2)` and `T_(3)` are mixed. The masses f molecules are `m_(1), m_(2)` and `m_(3)` and the number of molecules are `n_(1), n_(2)` and `n_(3)` respectively. Assuming no loss of energy, the final temperature of the mixture is

Options

A. `(n _(1) T _(1) + n _(2) T _(2) + n _(3) T _(3))/(n _(1) + n _(2) + n_(3))`
B. `(n _(1) T _(1)^(2) + n _(2) T_(2) ^(2) + n _(3) T _(3) ^(2))/( n _(1) T_(1) + n _(2) T _(2) + n _(3) T _(3))`
C. `(n _(1) ^(2) T _(1) ^(2) + n _(2)^(2) T _(2) ^(2) + n _(3) ^(2) T _(3) ^(2))/( n _(1)T_(1) + n _(2) T_(2) + n _(3) T _(3))`
D. `((T _(1) + T_(2) + T_(3)))/(3)`

Answer

A