Two engine options are being compared for a new car. Engine $1$ is naturally aspirated with CR of $10\mathrm{.}5$:$1$ and inlet conditions of $60C$ and $96$ kPa $.$ Engine $2$ is supercharged with aftercooling and has cylinder inlet conditions of $80C$ and $130$ kPa $.$ To avoid knock, it is desirable to have the Air and Fuel temperature at the start of combustion in Engine $2$ the same as in engine $1.($assume $k=1\mathrm{.}4)$

a$.$ Calculate the temperature at the start of combustion in engine $1$

b$.$ Compression ratio of engine $2$ that would give the same temperature at the start of combustion

c$.$ Temperature reduction in the aftercooler of engine $2$ if the compressor has an isentropic efficiency of $82\%$ and inlet conditions are the same as engine $1.$