$.$ In a single$-$stage air compressor the diameter of the cylinder is $250$ mm; the stroke of the

piston is $350$ mm$,$ and the clearance volume is $900$ cm$3$

$.$ Air is drawn in at a pressure of

$0\mathrm{.}986$ bar and delivered at $4\mathrm{.}1$ bar. If the law of compression is pV $1\mathrm{.}25=$ C where C is a

constant, calculate the distance travelled by the piston from the beginning of its compression

stroke when the delivery valves open.