$1.$ A $3-$L V$6$ engine operates at $2400$ RPM with a mechanical efficiency of $\backslash (84\backslash \%\backslash ).$ Cylinder conditions at the start of compression in an SI engine operating at WOT on an air$-$standard Otto cycle are $\backslash (60^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $98$ kPa $.$ The engine has a compression ratio of $\backslash (9\mathrm{.}5$: $1\backslash )$ and uses gasoline with AF $\backslash (=15\mathrm{.}5\backslash )$ and a heating value of $\backslash (43,000\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ).$ Combustion efficiency is $\backslash (96\backslash \%\backslash ),$ and the exhaust pressure of the engine is $100$ kPa $.$ Calculate: $($a$)$ Temperature at all states in the cycle, $\backslash (\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),($b$)$ Pressure at all states in the cycle, kPa, $($c$)$ Specific work done during power stroke, kJ$/$kg$,($d$)$ Heat added during combustion, kJ$/$kg$,($e$)$ Net specific work done, kJ$/$kg$,($f$)$ Indicated thermal efficiency, $\backslash \%,($g$)$ Brake power, kW$,($h$)$ Torque, Nm$,($i$)$ Brake mean effective pressure, kPa, $($j$)$ Friction power lost, kW$,($k$)$ Brake specific fuel consumption, g$/$kW$-$hr$,($I$)$ volumetric efficiency, $\backslash \%,($m$)$ Output per displacement, kW$/$L$,($n$)$ Exhaust temperature, $\backslash (\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),($o$)$ Actual exhaust residual, $\backslash \%,$ and $($p$)$ Temperature of air entering cylinders from intake manifold. Hint: Solve a$-$m assuming that there is no exhaust residual.