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 :

Answer

9

Explanation

`q = 0 rArr DeltaU = w`
`nC_(v)(T_(2) - T_(1)) = - P_(ext.)(V_(2) - V_(1))`
`C_(v)(T_(2) - 300) = -2 ((R xx T_(2))/(2.4) - (R xx 300)/(12))`
`rArr (5)/(2)(T_(2) - 300) = (360)/(6) - (T_(2))/(1.2)`
`5T_(2) - 1500 = 100 - (5T_(2))/(3)`
`(20T_(2))/(3) = 1600 :. T_(2) = 240 K`
`W = 4 xx (5R)/(2)(-60) = - 600R`
`DeltaH = gammaDeltaU`
or `DeltaH = (7)/(5) xx -600 R = -840 R`