An absorbing and emitting gas at a temperature of Tg$=1100$ K flows between two very long parallel plates. Both the plates have an emissivity of $0\mathrm{.}8$ and are maintained at a uniform temperature of T$1=$T$2=500$ K$.$ The spacing between the plates, L is $1$ m$.$ Determine the absorption coefficient of the gas if the amount of cooling required at each wall surface is q $=35$ kW$/$m$2($Please$,$ note that this is a classic inverse problem where one or more properties are estimated from measured heat fluxes or temperatures, as the case may be$).$