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

Answer

C

Explanation

(c) Heat lost by He=Heat gained by `N_2`
`n_1C_(v_1)DeltaT_1=n_2C_(v_2)DeltaT_2`
`3/2R[7/3T_0-T_f]=5/2R[T_f-T_0] rArr T_f=3/2T_0`