A $2$ stage single acting reciprocating air compressor has a low pressure cylinder of $200$ mm bore and $280$ mm stroke. The clearance volume is $7\mathrm{.}5\%.$ Intake pressure and temperature are $1$ bar and $18$C$.$ The final pressure is $10\mathrm{.}5$ bar. The intermediate pressures are correct for minimal work and the intercooling is perfect. The compressor runs at $300$ RPM and the polytropic constant is $1\mathrm{.}3.$

$$ Sketch the pV diagram

$$ Find the intermediate pressures

$$ Find the effective swept volume of the low pressure cylinder.

$$ Find the temperature and volume of air delivered per stroke at $7$ bar

$$ Find the power required to run the compressor