Light bulbs are sold using two primary performance characteristics. One is the power consumption of the bulb $($a surrogate for the brightness$)$ and the other is the color temperature. While times have changed, these temperatures are based on the filament temperature for an incandescent light bulb. Prof. Van Asselt$$s preferred color temperature is $2700$ K since it is so relaxing. Assume that the tungsten filament in the bulb can be treated as a blackbody and the visible spectrum extends from wavelengths of approximately $0\mathrm{.}4$ m to $0\mathrm{.}7$ m$.$ a$)$ Determine the percentage of radiation emitted in the visible spectrum for a $2700-$K incandescent bulb. b$)$ Determine the percentage of radiation emitted in the visible spectrum for the inferior $3000-$K and $5000-$K incandescent bulbs. c$)$ Calculate the wavelength that gives the maximum spectral emissive power for each of the three considered filament temperatures. d$)$ As the filament temperature increases, why do these bulbs move from appearing orange to appearing blue?