$8.(\backslash (\backslash$mathbf$\{15\}\backslash$mathbf$\{$~ p t s $)\}\backslash )$ A copper sphere is covered by a wavelength selective coating, which can be modeled as a diffuse surface whose spectral emissivity is a function of wavelength as shown in the following figure. The sphere is in earth's orbit around the sun. Assume that the temperature of the sphere is uniform and neglect the radiation from the earth $($i$.$e$.,$ assume cold surroundings$),$ conduction, and convection. Estimate the equilibrium temperature of the sphere.