1. The problem statement, all variables and given/known data I'm given a initial and final pressure and temperature of an ideal gas to solve for the work done after it expans in a polytropic process (n=1.2) 2. Relevant equations W = integral of P*dV PV = nRT PV = RT* PV = mRT PV^n = Constant 3. The attempt at a solution I get W = integral of PdV = (P2V2 - P1V1)/(1-n) After this part my solutions are completely different than how I solved for work Initially I thought, since PV = nRT I can just substitute it in and get W = (P2V2 - P1V1)/(1-n) = nR(T2-T1)/(1-n) but in the solution it solves for the volumes, using P1V1 =RT1 This is where I have a bunch of questions... I haven't been explained these equations too well in lectures so I've been reading my textbook but it doesn't explain anything on PV = RT. But I believe it's using molar volume I tried to solve for the initial volume using P1V1 = R*T1 which gave the correct value But then I tried P2V2 = RT2 to get V2 and substituting it into the work equation which didn't seem to work out because the volume is different if I were to use P1V1^n = P2V2^n I understand that this equation can be used for a polytropic process but I don't get why I can't use P2V2 = nRT2 to solve for the volume instead. The process still involves an ideal gas, so how come when I use these two different equations my volume is different?