A gas is compressed from V$1=0\mathrm{.}3$ m$3,$ p$1=1$ bar to V$2=0\mathrm{.}1$ m$3,$ p$2=3\mathrm{.}5$ bar. Pressure and

volume are related linearly during the process.

$1)$ Derive the equation that relates pressure to volume.

$2)$ Sketch the p$-$V diagram for the process.

$3)$ Calculate the work, in kJ$.$