Question

All things radiate light as a blackbody, though some things are closer to being "perfect" blackbodies than others.

It turns out that light emission and light absorption depend on the same microscopic interactions, so the difference between a perfect blackbody and an imperfect blackbody has to do with light absorption. A perfect blackbody perfectly absorbs all light that falls on it (so it would appear pitch black). A piece of charcoal, for example, is very close to a perfect blackbody. If an object absorbs very little of the light that falls on it, like a shiny piece of metal, that object is very far from being a perfect blackbody.

The Stefan-Boltzmann Law for light emission, P=σAT4, gives the power emitted by a perfect blackbody. If an object is not a perfect blackbody, it emits less power. The emissivity ϵϵ of a material describes how similar it is to a perfect blackbody: ϵ=1 for a perfect blackbody, while ϵ=0 for an object that doesn't emit any light whatsoever.

Including emissivity in the Stefan-Boltzmann Law is simple: P=ϵσAT4.

Let's explore some of the implications of emissivity using an important example: the light radiated from a human being.

Consider a person standing naked in an empty room. The average surface area of a human is around 1.75m.

Part E

It turns out that human skin is very nearly a perfect blackbody with an emissivity of about ϵ=0.98 (at least for infrared light, where most of a person's radiation happen), so your calculation in Part D is pretty close to the actual net power radiated by a person under the circumstances we've been considering.

In such circumstances, this person is losing a lot of the energy generated by their basal metabolism. As a result, they would feel cold. That's one reason we wear clothes - the fabrics in our clothes generally have a much lower emissivity than our skin.

Recalculate the net power radiated by this person if they are wearing cotton clothing, noting that cotton has an emissivity of ϵ=0.77. For the sake of simplicity, assume that cotton covers all the exposed skin of this person.

(Hint: the emissivity of a material affects not just the light it radiates but also the light it absorbs.)

Part D Ans - 105 W = net power radiated by the person

Answer 1