*David Wood*Show bio

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

Lesson Transcript

Instructor:
*David Wood*
Show bio

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

Radiation is a form of heat transfer that can be calculated using the Stefan-Boltzmann Law. Learn what radiation is, explore the vacuum flask example of radiation, then learn to explain the Stefan-Boltzmann law before applying it to a calculation example.
Updated: 10/28/2021

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 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.

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.

**Radiation** is a type of heat transfer that travels through electromagnetic (mostly infrared) 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. It's also why it's so hot next to a campfire. Radiation bounces off mirrored or reflective surfaces, which is why a vacuum, or thermos flasks have a mirrored surface - to stop heat energy escaping by radiation.

The Stefan-Boltzmann Law helps us calculate the heat transferred by radiation per second, measured in joules per second, or watts. It tells us that it's equal to the Stefan-Boltzmann constant sigma, which is always 5.67 * 10^-8, multiplied by the emissivity of the object (*e*), 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 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.

Without radiation we would get no heat from the Sun and wouldn't be able to survive on Earth. While some types of radiation are dangerous, when it comes to heat transfer, unless you're flying too close to the Sun like Icarus, you should have absolutely nothing to worry about.

After you've reviewed this video lesson, you will be able to:

- Define radiation
- Explain how the Sun's heat gets to Earth, how you can feel the heat from a campfire, and why thermoses have reflective surfaces
- Identify the Stefan-Boltzmann Law
- Calculate the heat transferred by radiation using this law

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