One method for reducing the pumping work in throttledspark-ignition engines is early intake valve closing(EIVC). With EIVC, the inlet manifold is held at a pressurepi, which is higher than the normalengine intake pressure pi*. The intakevalve closes during the intake stroke. The trapped freshcharge and residual is then expanded to the normal cycle(lower) intake pressure, pi*. You canassume that both cycles have the same mass of gas in the cylinder,temperature and pressure at state 1 of the cycle.
a) Sketch a p-V diagram including both the standard and EIVCcycle. On the p-V diagram, shade the area that corresponds to thedifference of pumping work between the standard and EIVCcycles.
b) What value of intake pressure pi and VEIVC will give themaximum reduction in pumping work for the EIVC cycle?
c) Derive an expression for this maximum difference in pumpingwork between the normal cycle and the EIVC cycle in terms of pe,pi*, Vc and Vm. Justify any assumptions you make.
