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)^(3))/(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

Explanation

we Have `(F)/(2)n_(1)kT_(1)+(F)/(2)n_(2)kT_(2)+(F)/(2)n_(3)kT_(3)`
`(F)/(2)(n_(1)+n_(2)+n_(3))kT`
The Final Temperature of the mixture
`T=(n_(1)T_(1)+n_(2)T_(2)+n_(3)T_(3))`