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

Internal energy `U=nC_(V)dT`
In this case, dU = 0. As nitrogen is diatomic `C_(V)=5/2R`
and helium is monoatomic `" "thereforeC_(V)=3/2R`
If `T_(f)` is the final temperature,
`therefore1xx5/2R(T_(f)-T_(0))+1xx3/2R(T_(f)-7/3T_(0))=0`
`therefore5T_(f)-5T_(0)+3T_(f)-7T_(0)=0`
`therefore8T_(f)=12T_(0)" "thereforeT_(f)=3/2T_(0)`