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 B 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 gases reach a common final temperature (Ignore the heat capacity of boxes ). then, the final temperature of the gases, `T_(f)`, in terms of `T_(0)` is

Options

A. `T_f = 7/3 r_0`
B. `r_f = 3/7 r_0`
C. `T_f = 3/2 T_0`
D. `T_f = 5/2 T_0`

Answer

C

Explanation

`U_i= (5)/(2)RT_(o)+(3)/(2)R((7)/(3)T_(o))= 6RT_(o), U_(f)= (5)/(2)RT_(f)+(3)/(2)RT_(f)=4RT_(f)`
As `U_i = U_(f) implies `T_(f)= (3)/(2)T_(o)`.