Well in our textbook the formula is listed with (k-1), but I can't find any similar formula online so I can't double check.
Although in the example problem the teacher uses the same formula and finds a positive value for W. That's what makes me think that my V2 must be wrong.
You're right about...
First i calculate n:
500000 g / 32 g/mol = 15625 mol
Then I calculate V1:
(100000 Pa * V1)/288.15 K = 15625 mol * 8.31 J/mol.k
so V1 = 374.145 m^3
I calculate V2:
100000¨ Pa * (374.145 m^3)^1.3 = 300000 Pa * (V2)^1.3
So V2 = 160.703 m^3
W = ((100000 Pa * 374.145 m^3)-(300000 Pa * 160.703...