A laser$-$materials$-$processing apparatus encloses a sample in the form of a disk of diameter D $=25$ mm and thickness w $=1$ mm$.$ The sample as a diffuse surface for which the spectral distribution of the emissivity, $($$),$ is prescribed. To reduce oxidation, an inert gas steam of temperature T $=500$ K and convection coefficient h $=50$ W$/$m $2$ K flows over the sample upper and lower surfaces. The apparatus enclosure is large, with isothermal walls Tenc $=300$ K$.$ To maintain the sample at a suitable operating temperature of Ts $=1600$ K$.$ A collimated laser beam with an operating wavelength of $=0\mathrm{.}5$ m irradiates its upper surface. $($a$)$ Determine the total emissivity of the sample. $($b$)$ Determine the total absorptivity of the sample for irradiation from the enclosure walls. $($c$)$ Perform an energy balance on the sample and determine the laser irradiation, Glaser, required to maintain the sample at Ts $=1600$ K