Consider a Carnot engine cycle operating between a maximum temperature of T₃ = T₄ = 400 ^◦F and a minimum temperature of T₁ = T₂ = 60 ^◦F. Assume that the lowest pressure attained is p₁ = 1 atm, the highest pressure is p₃ = 9 atm, and the minimum volume of the working gas space is V₃ = 1 L. Take γ = 1.4. Compute the pressure and volume at each point in the cycle, as well as the heat in, heat out, and work out. Compute the overall efficiency from these numbers and check that this agrees with theoretical Carnot efficiency.