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

a. Let `T` be the 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 = 2 T_(0) + 8 T_(0)`
`( :' n_(1) = 2, n_(2) = 4)`
`:. T = (5)/(3) T_(0)`