Q$6.$ A six$-$cylinder $4\mathrm{.}5-$litre $4-$stroke supercharged engine operating at $4000$ rpm has an overall volumetric efficiency of $150\%.$ The compressor has an 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 $1\mathrm{.}8$ bar. The ambient conditions are $17C$ and $1$ bar. Calculate: $($a$)$ The rate of heat rejection from the after$-$cooler $($b$)$ The power absorbed by the supercharger from the engine.

$($Ans: $($a$)5\mathrm{.}156k\frac{J}{s},($b$)18\mathrm{.}82$ kW $)$