$2-$ A six$-$cylinder, four$-$stroke, $3\mathrm{.}2-$L compression$-$ignition engine operates on the ideal diesel cycle with a compression ratio of $19.$ The air is at $95$ kPa and $67C$ at the beginning of the compression process and the engine speed is $1750rpm.$ The engine uses light diesel fuel with a heating value of $42,500k\frac{J}{k}g,$ an air$-$fuel ratio of $28,$ and a combustion efficiency of $98\%.$ Using constant specific heats at $850K,$ determine:

$($a$)$ The maximum temperature in the cycle and the cutoff ratio.

$($b$)$ The net work output per cycle and the thermal efficiency.

$($c$)$ The mean effective pressure $($MEP$).$

$($d$)$ The net power output.

$($c$)$ The specific fuel consumption, in $\frac{g}{k}Wh,$ defined as the ratio of the mass of the fuel consumed to the net work produced.