Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature `T_0`, while Box contains one mole of helium at temperature `(7/3)T_0`. The boxes are then put into thermal contact with each other, and heat flows between them until the gasses reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gasses, `T_f` in terms of `T_0` is

Options

A. `T_(f) = (3)/(7)T_(0)`
B. `T_(f) = (7)/(3)T_(0)`
C. `T_(f) = (3)/(2)T_(0)`
D. `T_(f) =(5)/(2)T_(0)`

Answer

C

Explanation

Equarting internal energy.
`1 xx (5)/(2) RT_(0) +1 xx (3)/(2) R ((7)/(3)T_(0)) = 1 xx(3)/(2)RT_(f)+(5)/(2)RT_(f)`
`rArr T_(f) = (3)/(2)T_(0)`