Two perfect monoatomic gases at absolute temperature `T_(1)` and `T_(2)` are mixed. There is no loss of energy. Find the temperature of the mixture if the number of moles in the gases are` n_(1)` and `n_(2)`.

Options

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

Answer

B

Explanation

we know , `E=(3)/(2)nKT` (K=Boltzmann's constant)
`therefore" " (3)/(2)n_(1)KT_(1)+(3)/(2)n_(2)KT_(2)=(3)/(2)(n_(1)+n_(2))KT`
`rArr " " T=(n_(1)T_(1)+n_(2)T_(2))/((n_(1)+n_(2)))`