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

Answer

C

Explanation

`:.q=0:.DeltaU=w`
`impliesnc_(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))]`
`implies5/2R[T_(2)-300]=2xxR[300/5-(T_(2))/2]`
`impliesT_(2)=248.5K`