1. In this problem we consider a heat engine functioning via a four-step thermody cycle known as the Otto cycle. This cycle is an idealization of the operation of a gasoline engine or any other engine with spark plugs (note that the steps of the four-step cycle here should not be confused with the strokes of a four-stroke engine). = 0.500 L, PA = - - In Step 1 the gas in a cylinder undergoes a feversible adiabatic compression from an initial state with VA 1 bar, TA 300 K to volume VB (compression ratio = VA/VB = 10.8). In Step 2, the gas is reversibly heated at constant volume Vc = VB to To = 3000 K (this step approximates the heating of the gas due to the spark-initiated combustion of fuel injected prior to Step 1, with To being a reasonable guess at the temperature of the flame). In Step 3 the gas performs work by reversible adiabatic ex- pansion back to the original volume V₁. In the final step, the gas returns to the original pressure and temperature at constant volume (this step represents expunging the heat from the engine by refilling it with fresh cold air-fuel mixture). Assume that we have a diatomic ideal gas with temperature-independent heat capacity Cv = nR. (a) Sketch the steps of the process on a p V diagram and calculate volume (L) and pressure (bar) for every state in the process. Assume that the amount of gas stays con- stant throughout the cycle. (b) Calculate the work (w), heat (g) and change in internal energy (AU) in each step of the cycle. (c) Calculate the thermal efficiency of this engine as the ratio of the total work done by the engine through the complete cycle to the amount of heat received from combustion in Step 2. (d) The parameters in this problem are taken from the published technical specs of the 4- cylinder 2L engine (2./4=0.5) of 2016 Honda Civic LX rated to generate 158 horsepower @ 6500 rpm (= 6500 rotations of engine crankshaft per minute). Compute the total power produced by our model of this engine (power = work / time) and compare to the actual data from Honda. Assume that a complete cycle occurs every 2 crankshaft