Problem $2.$ A four$-$cylinder, $2\mathrm{.}5-$liter, SI automobile engine operates at WOT on a four$-$stroke airstandard Otto cycle at $3000$ RPM$.$ The engine has a compression ratio of $8$:$1,$ a mechanical efficiency of $86\%,$ and a stroke$-$to$-$bore ratio $\frac{S}{B}=1\mathrm{.}025.$ Fuel is isooctane with $AF=15,$ a heating value of $44,300k\frac{J}{k}g,$ and combustion efficiency ${}_c=100\%,$ At the start of the compression stroke, conditions in the cylinder combustion chamber are $100$ kPa and $60C.$ It can be assumed that there is a $4\%$ exhaust residual left over from the previous cycle. The engine is converted to operate on an air$-$standard Miller cycle with early valve closing $($cycle $6-7-1-7-2-3-4-5-6$ in Fig. $16).$ It has a compression ratio of $8$:$1$ and an expansion ratio of $10$:$1.$ A supercharger is added that gives a cylinder pressure of $160$ kPa when the intake valve closes, as shown in the figure below. The temperature is again $60C$ at this point. The same fuel and AF are used with combustion efficiency.

Calculate:

temperature and pressure at all points in the cycle

indicated thermal efficiency

indicated mean effective pressure

exhaust temperature