One mole of an ideal gas `(C_(v,m)=(5)/(2)R)` at 300 K and 5 atm is expanded adiabatically to a final pressure of 2 atm against a constant pressure of 2 atm. Final temperature of the gas is :

Options

A. `270 K`
B. `273 K`
C. `248.5 K`
D. `200 K`

Answer

C

Explanation

`q=0" ":. DeltaU=w`
`rArr nC_(v.m)(T_(2)-T_(1))=-P_(ext)[(nRT_(2))/(P_(2))-(nRT_(1))/(P_(1))]`
`:. C_(v.m)[T_(2)-T_(1)]=P_(ext).R[(T_(1))/(P_(1))-(T_(2))/(P_(2))] rArr (5)/(2)R[T_(2)-300]=2xxR[(300)/(5)-(T_(2))/(2)]rArr T_(2)=248.5K`