If 2 mol of an ideal monatomic gas at temperature `T_(0)` are mixed with 4 mol of another ideal monatomic gas at temperature `2 T_(0)` then the temperature of the mixture is

Options

A. `5/3 T_(0)`
B. `3/2 T_(0)`
C. `4/3 T_(0)`
D. `5/4 T_(0)`

Answer

A

Explanation

Let `T` be temperature of the mixture
then `U = U_(1)+U_(2)`
or `f/2(n_(1)_n_(2))RT = f/2(n_1)(R)(T_0)`
`+f/2(n_2)(R)(2T_0)`
or `(2+4)T=2T_(0)+8T_(0) ( :'n_(1)=2, n_(2)=4)`
`:. = T = 5/3 T_(0)`.