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

`because " "q = 0 " "thereforeDeltaU=w`
`implies nC_(v,m)(T_(2)-T_(1))=-P_("ext")[(nRT_(2))/(P_(2))-(nRT_(1))/(P_(1))]`
`thereforeC_(v,m)[T_(2)-T_(1)]=P_("ext").R[(T_(1))/(P_(1))-(T_(2))/(P_(2))]`
`implies (5)/(2)R[T_(2)-300]=2xxR[(300)/(5)-(T_(2))/(2)]`
`implies " "T_(2)=248.5 K`