`1.0 mol` of an ideal gas initially present in a `2.0L` insulated cylinder at `300K` is allowed to expand against vacuum to `8.0L`. Determine `w, DeltaU, Delta_("total")S`, and `DeltaG`.

Explanation

`w =- P_(ext)DeltaV = 0, q =0`(insulated cylinder)
`rArr DeltaU = 0 = DeltaH`
`rArr T_(f) = 300K`
`Delta_(sys)S = nR"In"(V_(2))/(V_(1)) = 2RIn 2 = 11.52 J K^(-1)`
and `Delta_(surr)S = 0 :. Q_(sys) = q_(surr) = 0`
`rArr Delta_("total")S = 11.52JK^(-1)`
`rArr DeltaG =- TDelta_("total")S =- 300 xx 11.52 =- 3456J`