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) = (7)/(3) T_0`
B. `T_(f) = (3)/(2) T_0`
C. `T_(f) = (5)/(2) T_0`
D. `T_f = (3)/(7) T_0`

Answer

B

Explanation

Heat lost by `H_e` = Heat gained by `N_(2)`
`n_1 C_(v_1) Delta T_1 = n_2 C_(v_2) Delta T_2`
`rArr 1 xx (3)/(2) R xx (7/3 T_0 - T_f) = (5)/(2) R (T_f - T_0)`
`rArr T T_0 - 3T_f = 5T_f - 5T_0`
`T_f = (3)/(2) T_0`.