1. The problem statement, all variables and given/known data A cylinder with initial volume V contains a sample of gas at pressure p. The gas is heated in such a way that its pressure is directly proportional to its volume. After the gas reaches the volume 3V and pressure 3p, it is cooled isobarically to its original volume V. The gas is then cooled isochorically until it returns to the original volume and pressure. Find the work W done on the gas during the entire process. 2. Relevant equations W = 0 (for the isochoric cooling) W = -p(V_f - V_i) for the isobaric cooling W = -nRT * ln (V_f/V_i) <---- this is what I'm unsure about. 3. The attempt at a solution Total Work is going to equal the sum of the 3 work on the 3 processes: the expansion the cooling the further cooling Expansion process (isothermal?) W_1 = -nRT * ln (V_f/V_i) pV = nRT W_1 = -pV * ln (V_f/V_i) This is wrong but I don't know why. I don't know for sure that this an isothermal process. But it's not isochoric (because V changes from V to 3V). It's not isobaric because pressure increasing from p to 3p. It's not adiabatic because Q > 0, I think; it's being heated after all. So isothermal seems to be the right answer. For the second process W_2 = -p(V_f - V_i) = -3p(V - 3V) That I'm sure is right For the third process It's isochoric, so 0 work is being done.