$[$Q$3]$ An ideal Otto cycle has a compression ratio of $8.$ At the beginning of the compression process, air is at $100$ kPa and $27C,$ and $800k\frac{J}{k}g$ of heat is transferred to air during the constantvolume heat$-$addition process. Accounting for the variation of specific heats of air with temperature, determine $($a$)$ the maximum temperature and pressure that occur during the cycle, $($b$)$ the network output, $($c$)$ the thermal efficiency, and $($d$)$ the mean effective pressure for the cycle. $15$ points