$($b$)$ Evaluate the rake face temperatures during orthogonal turning with a zero rake angle tool when $V=2$

$\frac{m}{s},$ depth of cut $=2mm$ and feed $=0\mathrm{.}2m\frac{m}{r}ev.$ The chip thickness ratio and chip tool contact length

obtained at these conditions were $0\mathrm{.}2$ and $0\mathrm{.}45$ mm $,$ respectively. The dynamometer measurement gave

tangential cutting force $760$ N and normal cutting force $390$ N $.$ Other data are: $=7200k\frac{g}{m^3},C=502\frac{J}{k}g$

$C,k=50\frac{W}{m}C,{}_0=25C$ and fraction of heat going into chip is $0\mathrm{.}85.$