# Radiation, Heat Transfer & the Stefan-Boltzmann Law

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• 1:58 The Stefan-Boltzmann Law
• 2:54 Calculation Example
• 3:52 Lesson Summary

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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you will be able to explain how radiative heat transfer works, give some real-life examples of radiation, and use the Stefan-Boltzmann Law to complete radiation calculations. A short quiz will follow.

Ah, radiation! Run! That seems to be what people think of when you use the word radiation. But radiation has a few different meanings in physics. There is the dangerous radioactive type of radiation, made of alpha particles, beta particles and gamma rays - the kind of radiation that comic books tell us will turn you into the Hulk or some other equally cool superhero.

But the Sun also sends us radiation. The other, more general meaning of radiation is just a type of electromagnetic wave. Light is radiation, infrared is radiation, gamma rays are, too, it's true - but there's nothing inherently dangerous about radiation.

But in this lesson, we're talking about radiation as a type of heat transfer - the other two types of heat transfer being conduction and convection. Hot objects give off infrared radiation, which is just another part of the electromagnetic spectrum. But that infrared radiation also transfers heat away from that object. That's why it's hot when you stand next to a campfire. By the way, if you put your hand above a campfire, it's even hotter because then you not only have heating by radiation, but also by convection - another type of heat transfer.

So radiation is a type of heat transfer that travels through electromagnetic waves. Because of this, radiation doesn't need a medium (or material), and it can therefore go through a vacuum. This is how the heat of the Sun gets to us on Earth.

So we've already talked about campfires and the heat energy from the Sun. But there are many examples of radiation in the real world.

A vacuum flask, or thermos flask, uses our understanding of radiation (and heat transfer in general) to keep your soup warm. We all know that light bounces off mirrors, but all electromagnetic waves tend to bounce off reflective surfaces. So the mirrored surface of a vacuum flask does a great job of stopping heat loss by radiation. A vacuum flask also stops conduction by having a vacuum layer - conduction needs a material to travel through and convection by having an insulating lid.

## The Stefan-Boltzmann Law

The Stefan-Boltzmann Law gives us a way to put numbers to this concept of radiation. It helps us calculate the heat transferred by radiation per second, measured in joules per second, or watts. The Stefan-Boltzmann Law tells us that this is equal to the Stefan-Boltzmann constant sigma, which is always the same number, multiplied by the emissivity of the object (e), which is a number that represents how well an object radiates heat, multiplied by the surface area of the object (A) measured in meters squared, multiplied by the temperature of the object (T) to the power 4, where T is measured in Kelvin.

A few things to note about this equation. The Stefan-Boltzmann constant is always 5.67 * 10^-8. The emissivity of an object is a number between zero and one. A perfect radiator of energy has an emissivity of one, and a perfect reflector has an emissivity of zero. Stars like the Sun have an emissivity extremely close to one.

## Calculation Example

Okay, let's try an example. A light bulb emits heat by radiation and has an emissivity of 0.5. If the temperature of the filament of the light bulb is 2500 K, and the surface area of the filament is 0.0001 meters squared, how much heat is transferred by radiation from the filament of the light bulb per second? (Remember that the Stefan-Boltzmann constant is, as always, 5.67 * 10^-8.)

To solve this, all we have to do is plug numbers into the Stefan-Boltzmann Law. The heat transferred per second is equal to the Stefan-Boltzmann constant, 5.67 * 10^-8, multiplied by the emissivity of the bulb (0.5), multiplied by the surface area (0.0001), multiplied by the temperature (2500), to the power 4.

Type all of that into a calculator, and you get 110.7 joules per second, or in other words, 110.7 watts.

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