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. `((T_(1) + T_(2) + T_(3)))/(3)`
B. `(n_(1)T_(1) + n_(2)T_(2) + n_(3)T_(3))/(n_(1) + n_(2) + n_(3))`
C. `(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))`
D. `(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))`

Answer

B

Explanation

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