An ideal Otto cycle is used to simulate a $4-$stroke Honda spark ignition engine $($SIE$)$ with a compression ratio, r $=10.$ The ideal cycle uses air as the working fluid and the state of the air at the beginning of the compression process is P$1=100$ kPa and T$1=27$C$.$ If $500$ kJ$/$kg of heat is transferred to the air during the heat addition process, determine

$($a$)$the temperatures at the end of the compression and heat addition processes,

$(5$ Marks$)$

$($b$)$ the net work output in kJ$,(5$ Marks$)$

$($c$)$ the power output in kW for an engine speed of $4000$ rpm $($rev$/$min$)$ and a displacement volume of $2\mathrm{.}0$ L$,(5$ Marks$)$

$($d$)$ the thermal efficiency of the cycle, $(3$ Marks$)$

$($e$)$ if the heat in this cycle $(500$ kJ$/$kg$)$ is added at constant pressure to simulate a diesel engine, what will be the cutoff ratio $($rc$)$ and the thermal efficiency of that simulated Diesel engine? $($assume the same T$1,$ P$1,$ and r $(4$ Marks$)$

$($f$)$ can we increase the compression ratio of the diesel engine to $20?$ Explain. $(3$ Marks$)$ Answer all of them dont leave anything out and explain each step and show diagrams for the Otto cycle and of the diesel cycle.

Assume constant specific heats for air at $300$ K$.$