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Chapter 13: Problem 6

The outcome of Problem 5 indicates that a hot light bulb filament emits thousands of times more power per unit area than human skin. Yet both a human and a light bulb may emit a similar amount of light \(^{105}\) - both around \(100 \mathrm{~W}\). Explain how both things can be true?

Short Answer

Expert verified
Both the hot light bulb filament and human skin can emit a similar amount of light due to different factors that contribute to the total emitted energy. The filament has a much higher power per unit area, but its surface area is smaller compared to the human body. On the other hand, human skin has a lower power per unit area but a larger surface area. The combined effect of the temperature, emissive properties, and surface area of these two objects result in a similar amount of emitted energy, allowing them to emit a comparable amount of light.

Step by step solution

01

Understand Emission of Energy

The emission of energy depends on both the temperature and the emissive properties of an object. In this case, we are looking at a hot light bulb filament and human skin. The light bulb filament is at a much higher temperature, which is why it emits more power per unit area. On the other hand, human skin is at a relatively lower temperature, but it covers a larger surface area.
02

Consider the Surface Area

The total amount of emitted energy depends not only on the power per unit area but also on the overall surface area. A human body has a much larger surface area compared to that of a light bulb filament.
03

Calculate the Total Emitted Energy

To calculate the total emitted energy, we need to multiply the power per unit area by the surface area. Since the power per unit area of the filament is much higher, but the surface area is smaller, it's possible for the product of these two factors to be similar to that of human skin. Conversely, the power per unit area of human skin is lower but, due to having a larger surface area, it can result in a similar amount of emitted light.
04

Conclusion

Both the hot light bulb filament and human skin can emit a similar amount of light, even though a filament has a higher power per unit area. This is because the filament has a smaller surface area compared to the human body. The larger surface area of the human body compensates for the lower power per unit area, resulting in the same amount of emitted energy as the hot light bulb filament.

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