$4.($a$)$ A single cylinder four$-$stroke internal combustion engine operates at $2500$ RPM$.$ The engine works on an air$-$standard OTTO cycle in which the compression ratio is $10.$ At the beginning of compression, $\backslash ($ T$\_\{1\}=298\backslash$mathrm$\{$~K$\}\backslash )$ and $\backslash ($ P$\_\{1\}=1\backslash )$ bar. During the cycle there is a heat addition of $1300$ kJ per kg of fluwing air. Determine:

i$.$ the nett power developed by the engine in kW per kg of air,

ii$.$ the thermal efficiency of the cycle,

iii. the mean cfective preasure, in bars

iv$.$ the maximum temperature attained during the cycle, in K $.$

$(10$ marks$)$