A three cylinder, four stroke, SI engine has a bore of $90$ mm and a stroke of $95$ mm$.$ The

compression ratio is $9$:$1.$ The engine runs at $5000$ rpm$.$ The relative cycle efficiency based on

the Otto cycle is $56\%.$ The calorific value of the fuel used is $42$ MJ$/$kg and the volumetric

efficiency is $80\%.$ The ambient pressure and temperature are $1$ bar and $300$ K$.$ IMEP is $7\mathrm{.}2$ bar.

Brake specific fuel consumption is $280$ g$/$kW$-$h$.$ Calculate the following:

$($a$)$ Indicated specific fuel consumption $($g$/$kW$-$h$)($b$)$ BMEP $($c$)$ Air$-$fuel ratio

$($d$)$ Brake power output $($e$)$ Mechanical efficiency.