Size of a Light-Bulb Filament. The operating temperature of...

Size of a Light-Bulb Filament. The operating temperature of a tungsten filament in an incandescent light bulb is $2500 \mathrm{~K},$ and its emissivity is 0.350 . Find the surface area of the filament of a $200-\mathrm{W}$ bulb if all the electrical energy consumed by the bulb is radiated by the filament as electromagnetic waves. (Only a fraction of the radiation appears as visible light.)

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Key Concepts

Energy Conservation in Radiative Systems

In radiative energy transfer problems, the assumption that the electrical energy input equals the energy radiated away is used to establish a balance between power consumption and emission. This conservation principle allows for the determination of unknown quantities, such as surface area, by equating input power with the power radiated as electromagnetic waves.

Emissivity

Emissivity is a measure of a surface’s ability to emit thermal radiation compared to a perfect blackbody. It is a dimensionless coefficient ranging from 0 to 1, where lower values indicate less efficient radiation. This concept is essential in real-world applications since most materials do not radiate with the ideal efficiency of a blackbody.

Stefan-Boltzmann Law

This law states that the power radiated per unit area of a blackbody is directly proportional to the fourth power of its absolute temperature. It mathematically relates the energy radiated by a surface to both its temperature and surface area, making it a crucial concept for calculating radiative heat transfer in thermal systems.

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