In an Otto cycle, where the compression ratio is $7\mathrm{.}5,$ the heat input is $1500$ kJ$/$kg$.$ The pressure and temperature of the air at the beginning of the compression stroke $($point $1)$ are $100$ kPa and $20$C respectively. Cp$=(7/2)$R$,$ Cv$=(5/2)$R$.$ Determine

a$.$ The maximum temperature and pressure $($K and KPa$)$

b$.$ The thermal efficiency of the cycle $(\%)$

c $.$The MEP, mean effective pressure $($kPa$)$ d$.$ If the temperature at Point $1$ is changed to $50$C$,$ find maximum temperature, maximum pressure and MEP $($same units above$).$