It was found from experiments where the chips produced during shap$-$ ing were caught in a calorimeter that the mean chip$-$temperature rise was $500$C$.$ The cutting conditions were as follows: Cutting speed $=1$ m$/$s Undeformed chip thickness $=0\mathrm{.}5$ mm Width of chip $=5$ mm Working normal rake $=45$ degrees Cutting force $=6000$ N Thrust force $=0$ Chip thickness $=1\mathrm{.}2$ mm Length of workpiece $=300$ mm After $100$ strokes of the shaper, the insulated workpiece was immersed in a calorimeter and its additional heat content found to be $30$ kJ$.$ Neglecting the heat conducted into the cutting tool, calculate the pro$-$ portion of the shear$-$zone heat conducted into the workpiece.