Problem $2$: Diesel Cycle $(30$ points$)$

A diesel engine in a passenger vehicle has four cylinders, each with a bore of $86$ mm and a stroke of $86$ mm $.$ At the start of the compression stroke, the cylinder contains air at a pressure of $100$ kPa and $25C.$ At the start of heat addition, the cylinder temperature is $477C$ and at the end of heat addition, the cylinder temperature is $1527C.$

a$)$ Determine the displacement volume, in L $,$ of each cylinder in the engine.

b$)$ Populate a scorecard of $p,T,v,u,h,$ and $s$ for each state in the cycle.

c$)$ Determine the compression ratio and cut$-$off ratio.

d$)$ Determine the net power developed by the entire engine, in kW$,$ if the engine is operating at $2100$ rpm under the given conditions.

e$)$ Determine the specific entropy generated during each process of the cycle, in $k\frac{J}{k}g-K.$ Which process is least reversible? You may take the boundary temperature to be the highest temperature in the process if heat is being added and the lowest if heat is being rejected.

f$)$ Determine the cycle efficiency. How does this compare to reversible cycle efficiency for a cycle operating between the high and low temperatures in the cycle?