The temperature and pressure values at the beginning of compression in a V$6$ gasoline engine with a three$-$liter stroke volume running at $2400$ rpm according to the ideal cycle at full throttle are $60\backslash$deg C and $98$ kPa. The compression ratio of the engine is $9\mathrm{.}5$:$1,$ the H$/$Y ratio is $15\mathrm{.}5$:$1$ and the fuel used is gasoline. Assuming that the combustion efficiency is $96\%$ and the mechanical efficiency is $84\%$; Answer the following questions based on the information given. $($Note: There is no residual gas in the cylinder at the end of the cycle.$)$

a$)$ Show the cycle steps by drawing p$-$v and T$-$s graphs. $(5$p$)$

b$)$ Calculate the temperature $(\backslash$deg C$)$ and pressure values $($kPa$)$ at each point of the cycle. $(35$p$)$

c$)$ Find the specific work $($kJ$/$kg$)$ produced during the expansion time. $(5$p$)$

d$)$ Calculate the amount of heat energy $($kJ$/$kg$)$ that enters the cycle during combustion. $(5$p$)$

d$)$ Find the net work $($kJ$/$kg$)$ produced during the cycle. $(5$p$)$

e$)$ Calculate the thermal efficiency $(\%)$ of the cycle. $(5$p$)$

f$)$ Calculate the indicated engine power $($kW$).(5$p$)$

g$)$ Calculate the effective engine power $($kW$).(5$p$)$

g$)$ Find the power $($kW$)$ spent on friction. $(5$p$)$

h$)$ Calculate the torque $($N$.$m$)$ for the given engine speed. $(5$p$)$

i$)$ Calculate the average effective pressure $($kPa$).(5$p$)$

i$)$ Calculate the effective specific fuel consumption $($g$/$kW$.$h$).(5$p$)$

j$)$ Calculate the volumetric efficiency $(\%).($Take the density of air as $1\mathrm{.}181$ kg$/$m$3.)(5$p$)$

k$)$ Calculate the power per liter of stroke volume $($kW$/$lt$).(5$p$)$