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12 Dec 2019

All materials emit blackbody radiation as long as they are at a temperature greater than 0 K even though we cannot perceive most of it. Our eyes are not sufficiently sensitive to the low levels of visible light that are emitted at room temperature (and we do not visually process electromagnetic radiation beyond the visible range), but light energy in the visible range is emitted at rate that lets us see blackbody radiation at higher temperatures. Power is the rate at which energy is transferred (1 W = 1 Js), and power densityis the amount of power per unit volume. The y-axis of the simulation is expressed in units of power density.

There are instances when we can observe the transition of temperature that leads to a noticeable shift in blackbody radiation, and the object at that temperature begins to glow. For example, the sudden supply of electricity to an incandescent light bulb causes the temperature of the filament to quickly reach a temperature high enough that radiation from the entire visible spectrum is emitted (producing white light). When the supply of electricity is removed, the filament dissipates heat and gradually returns to room temperature, which is why we can see a red line in the bulb as the light dims.

Imagine an electric stove where a setting of 6 heats the coil, but it still appears black. When the dial is turned to 7, the coil begins to noticeably glow red, which means that the power density of the radiation at 700 nm surpassed a threshold. At what approximate temperature is the coil when it begins to glow red? Assume the human eye noticeably perceives a glow when the power density of light reaches 30 W⋠m−2⋠μm−1 (units appear in simulation as (MW/m2/μm).

Express the temperature in degrees Celsius to two significant figures.

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