$2\mathrm{.}1$ A four$-$cylinder, two$-$stroke engine operating on the Otto cycle admits air at $70$ kPa and $250$ K$.$ The engine is required to produce $96$ kW of mechanical power using fuel with a heating value of $42560$ kJ$/$kg at $100$ kPa and $300$ K $($M$=145),$ and develop a thermal efficiency of $32\%.$ Considering a compression ratio of $8\mathrm{.}5,$ obtain:

a$)$ The diameter and stroke of the piston, in cm$,$ if the engine rotates at $1250$ rpm and the stroke$-$to$-$diameter ratio is $1.$

c$)$ The air mass flow.