Incandescent light bulbs work by electrically heating a metallic filament to a high temperature so that it emits thermal radiation in the visible range. Assume a 50 W incandescent bulb uses a tungsten filament with a diameter of 0.2 mm and a length of 30 mm (ignore emission from the ends of the filament), the consumed electrical power (50 W) is all radiated out by the filament, and the filament can be modeled as a blackbody. (a) What is the temperature of the filament when the bulb works at 50 W? (b) What is the wavelength of radiation with the highest emissive power? (c) The radiation with wavelength between 400 nm and 700 nm is visible and thus is the "useful" output from the light bulb. The ratio of emitted power within this wavelength range to the total emitted power is defined as the efficiency of the bulb. Calculate the efficiency of the incandescent bulb in this case. What is the "efficiency" of the sun by this definition?