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 gases, `T_(f)` , in terms of `T_(0)` is -

Options

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

Answer

D

Explanation

`DeltaE_"int"=(DeltaE_"int")_(N_2)+(DeltaE_"int")_(He)`…(1)
but `DeltaE_"int"=0`
`(DeltaE_"int")_(N_2)=(mu C_V DeltaT)_(N_2)(C_V)_(N_2)=5/2R`
`(DeltaE_"int")_(He)=(mu C_V DeltaT)_(He) (C_V)_(He)=3/2R`
From equation (1),
`0=1xx5/2(T_f-T_0)+1xx3/2xx(T_f-7/3T_0)`
`therefore 0=5 T_f-5T_0+3T_f - 7T_0`
`therefore 12T_0 =8T_f`
`therefore T_f=3/2T_0`