Q$\mathrm{.}3)20$ points

Air is enclosed in a variable$-$load piston$-$cylinder apparatus that features a paddle wheel. Initially, the air conditions are $400$ kPa and $17C.$ An external motor powers the paddle wheel, delivering $75k\frac{J}{k}g$ of work to the air. Throughout this process, heat is supplied to maintain the air temperature at a constant level, even as the gas volume expands to three times its initial size. Determine the required heat transfer per unit mass of air, in $k\frac{J}{k}g.$