B$/$ A six$-$cylinder $4\mathrm{.}5$ liter $4-$stroke supercharged engine operating at $4000$ rpm has an overall volumetric efficiency of $150\%.$ The compressor has isentropic efficiency of $90\%$ and a mechanical efficiency of $85\%$ in its link with the engine. The compressed air is delivered to the engine cylinders at $57C$ and $1,8$ bar. Calculate: $($i$)$ the rate of heat rejection from the after$-$cooler. $($ii$)$ the power absorbed by the supercharger from the engine. Take $c_p=1\mathrm{.}005k\frac{J}{k}gK$ and $=1\mathrm{.}4.$