The approximation of a constant-volume combustion process for a gasoline engine is not accurate. A more realistic model of the standard Otto cycle is called the "dual cycle" where the combustion or heat addition occurs partially at constant volume and partially at constant pressure. For a particular dual cycle, air is first compressed isentropically from T = 300 K and P = 100 kPa with a compression ratio of 8. Heat is then added at constant volume until the pressure reaches 3 MPa. An additional 1000 kJ/kg of heat is then added at constant pressure. The gas is then expanded polytropically (Pvn = constant with n = 1.5) to the initial volume. For this cycle: a) Sketch the process on a P-v and T-s diagram. Label each process. (1 points) b) Determine the temperature at each point in the cycle. (2 points) c) Determine the heat transfer during the expansion process. (2 points) d) Determine the entropy change of the gas during the expansion process. (2 points) e) Determine the mean effective pressure. (1 points) f) Determine the cycle efficiency. (2 points) Assume air to be ideal with constant specific heats.