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

`because n_(1)C_(V_(1))T_(1) + n_(2)C_(V_(2))T_(2)= (n_(1)C_(V_(1)) + n_(2)C_(V_(2)))T_(1)`
`therefore T_(f) = (n_(1)C_(V_(1))T_(1) + n_(2)C_(V_(2))T_(2))/(n_(1)C_(V_(1) + n_(2)C_(V_(2)))`
`= (1xx(1)/(5)RT_(0)+ 1 xx(3)/(2)R((7)/(3)T_(0)))/(1xx(5)/(2)R + 1 xx(3)/(2)R)= (6RT_(0))/(4R) = (3)/(2)T_(0)`