An air$-$standard Otto cycle has a compression ratio of $8\mathrm{.}5.$ At the beginning of compression, $p_1=100$kPa and $T_1=300K.$ The heat addition per unit mass of air is $1400k\frac{J}{k}g.$ Determine:

$($a$)$ the net work, in kJ per kg of air.

$($b$)$ the thermal efficiency of the cycle.

$($c$)$ the mean effective pressure, in kPa $.$

$($d$)$ the maximum temperature in the cycle, in K $.$