1. Otto and Atkinson Cycles An Otto cycle is a common combustion cycle used in automobiles. The py plot of the Otto cycle is provided below, starting from the initial point A and passing through B,C,D before returning to A. The processes AB,BC,CD,DA are described as well: AB: reversible adiabatic compression BC : isochoric power stroke CD; reversible adiabatic expansion DA : isochoric exhaust stroke Suppose the gas undergoing this cycle is an ideal gas of specific heat capacity at constant volume of c b and specific heat capacity at constant pressure of c p , and therefore the ratio y=c p​ /c p​ . Suppose both the compression ratio (i.e. the fractional change in volume during compression) and the expansion ratio (i.e. the fractional change in volume during expansion) are both 12:1. The cycle is started at A with a certain volume v 0 of the ideal gas at pressure P 0. At BC, heat of Q 0​ is imported into the 5ystem. a) Find the volume, pressure, and temperature at each of the points B,C,D in terms of v 0 ,P 0 ,Q 0 . b) Find the work output W by the otto cycle: c) Find the efficiency (i.e. the ratio W/Q 0 ) of the Otto cycle. An Atkinson cycle is similar to the Otto cycle, except that the expansion ratio is larger than the compression ratio, such that the pressure at the end of the expansion step is the same as the original pressure but at a larger volume than the original volume. The cycle then returns to A by an isobaric process. d) In the po-plot below, sketch the Atkinson cycle, starting from A (the corresponding Carnot cycle is shown by dotted lines). e) For this cycle, suppose the compression ratio is 8:1 and the expansion ratio is larger. Find the volume, pressure, and temperature at each of the points B,C,D in terms of v 0 ,P 0​ ,Q 0 . f) Find the work output W by the Atkinson cycle. g) Find the efficiency (i.e. the ratio W/Q 0) of the Atkinson cycle.