1. The problem statement, all variables and given/known data Prove that the work done by an ideal gas with constant heat capacities during a quasi-static adiabatic expansion is equal to W= (PfVf)/(Y-1)[1 - (Pi/Pf)^((Y-1)/Y)] where Y = gamma, which is heat capacity at constant pressure over heat capacity at constant volume 2. Relevant equations 3. The attempt at a solution Alright so this is my attempt and im not sure where to go from here... In an adiabatic quasi-static process we can write the formula PV^Y = constant constant = K for simplification Since its adiabatic no heat change so Q=0 Using the first law of thermo Q= ΔU -W We know that W = -PdV and P= K/V^Y so... W = ΔU W = -PdV W = -(K/V^Y)*dV W = -K∫(1/V^Y)*dV W = -K[V^(1-Y)/(1-Y)]*∫dV W = -(K/(1-Y))[Vf^(1-Y) - Vi^(1-Y)] W = -(K/(1-Y))[Vf^(-Y)*Vf - Vi^(-Y)*Vi] W = -(1/(1-Y))[((Vf*K)/(Vf^Y)) - ((Vi*K)/(Vi^Y))] since Pi = K/Vi^Y and Pf = K/Vf^Y sub those in W = -(1/(1-Y))(Vf*Pf - Vi*Pi) Times this by (-1/-1) and we get W = (PfVf - PiVi)/(Y-1) This is where I get to not sure where to go from here to make this into W= (PfVf)/(Y-1)[1 - (Pi/Pf)^((Y-1)/Y)] Any suggestions and help would be greatly appreciative.