Hey guys. In this video, we want to talk more in detail about radiation as a method of heat transfer. Alright? Let's get to it. Remember that certain hot objects can expend heat. They can emit heat in the form of electromagnetic radiation, which is another word for electromagnetic waves. Okay? These substances that can do it are known as black bodies or blackbody-like. Okay? A blackbody is an object that can emit the maximum amount of thermal radiation at a given temperature. A blackbody-like object will always emit less energy in the form of thermal radiation than a true blackbody. Okay?

As with all waves, a particular wave or a particular electromagnetic wave in this case is defined by its frequency. Okay? It can also be defined by its wavelength but the frequency remains constant no matter what medium the wave is in whereas the wavelength changes between media so it's better to define it by frequency. Electromagnetic waves, as I said, are just a fancy way of saying light. So for light a particular frequency will be referred to as its color. Visible light, which is what we can see, only occupies a very very small amount of the electromagnetic waves. There are other types, radio waves, x-rays, gamma rays, microwaves, etc. Okay. But for visible light, the color is absolutely dependent on the frequency. And so we just extend that convention to everything. Even talking about x-rays we'll talk about the color of an x-ray as the frequency of the light. Okay? Black bodies do not emit light at a single color. Okay. This remember this verbiage, this wordage that I'm using, it doesn't have to be visible light for me to say it's a single color. It could be entirely x-rays and all that means is it just doesn't emit x-rays at a single frequency. Okay. Black bodies don't emit light at a single color. They emit light across a spectrum of colors. A spectrum is just a whole bunch of different colors each coming at a different probability. So let me minimize myself. This picture is a spectrum, a black body spectrum, of light. We have in the vertical axis the brightness of the light, and in the horizontal axis the frequency, so the color of the light. And as you can see at low temperature, the most probable light, sorry, the brightest light is at a lower frequency than at a higher temperature. Okay? In the visible light spectrum and light that we can see, low frequency light is red, moderate frequency light is yellow, and high frequency light is blue. That's why I showed the hotter black body as having a blue curve because the color of light is going to be closer to blue and the cold black body emitting light as a red curve because its brightest color is gonna be closer to red. Okay? The particular shape of the spectrum, what the brightest color is, how wide it is, etcetera, is going to be determined by the temperature, okay, of the black body. The color of the light that is seen, what you will actually see is going to be the brightest color. That's going to be the one that survives and that's going to be the one that you can see. Okay? As temperature increases, the light shifts from red to blue. Okay? So maybe you've heard that blue flames are hotter than red flames. Okay? That's typically true because for black bodies when you're emitting blue light it's because they're at a higher temperature than a black body that emits red light okay. But there could also be a chemical process going on where the chemical that you're heating up specifically emits blue light or red light and that has nothing to do with black body radiation. Now at very, very high temperatures this spectrum shifts away from the visible light. Now it's so high in frequency it's no longer visible. What ends up happening is the colors that you see are only the tail end of this right here. This tail end that happens to be in the visible range and the combination of the colors you see is white light. So at very very high temperatures when this spectrum shifts out of the visible range this light shifts from blue, which was hot black bodies, to white, which are black bodies that are so hot that they're emitting like ultraviolet light or x-rays even, low energy x-rays, so that all that you can see, because all we can see is visible light, is the tail end of this spectrum right here. And all of those lights are emitted at very similar brightnesses, brightnesses. There's no clear peak brightness. And a combination of colors produces white light. Okay so that's why really really hot metals glow white. Okay? Like we saw in the blacksmith picture when I introduced heat transfer. Alright?

Now, the radiance, which is something I'll talk about in a second, of thermal radiation emitted by a blackbody-like object is given by the Stefan-Boltzmann law. And the Stefan-Boltzmann law, the radiance is given by j. The Stefan Boltzmann law says it's equal to εσT4. Okay? ε is known as the emissivity. It's how closely to a true blackbody a blackbody-like object is. A true blackbody has an emissivity of 1. All blackbody-like objects have to have an emissivity less than 1 because they emit less light, less thermal radiation, than true black bodies for a given temperature. Okay? σ is known as the Stefan-Boltzmann constant and it has some value object emitting the power per unit surface area of the object emitting the thermal radiation. Okay? Radiance is very very similar in its definition and has identical units to intensity but it's different than intensity. Okay. They both have the same units, watts per meter squared. And the best way to explain the difference is like this. Imagine the sun. Okay? The sun is emitting light. Okay? We're over here on earth and some of that light travels all the way to earth to reach us. Okay? What can we measure? Okay. We always measure intensities of light. The watts per meter squared. What is the sun actually emitting that's inherent to the sun? It's emitting power which is in watts. Okay radiance is not power. Intensity is power per unit area. This light is being emitted what's called isotropically, the same in all directions. So the light creates a sphere of some radius r where r is the distance between the sun and the earth. That's how big the sphere is where all the light passes through. So the intensity that we measure is the power of emitted light over the surface area of that sphere which is 4pi r squared, right, where r is the distance between the earth and the sun. Now what's the radiance? The radiance is the power emitted by the sun which is remember a unique quality of the sun. The sun emits power. That's determined by internal things about the sun whereas the intensity is determined by how far away from the sun you're measuring. Okay? What the radiance is is it's the intensity at the surface of the sun. Okay? It is the power per unit surface area of the object emitting the light. So it's however much power that object is emitting divided by the surface area of that object. So it's that same power but this time it's divided by the surface area of the sun. And the radiance doesn't change with distance because the radiance is only measured at one point. It's only measured at the surface of the object emitting the light. Intensity could be measured anywhere, but radiance is always measured at the surface. Okay?

Now, the brightest color in the emission spectrum of black body radiation or thermal radiation is given by Wien's displacement law, and it's just b/T. Where b is Wien's displacement constant and it's some value. Okay? That'll be the color that you see if it's in the visible light region. If it's past the visible light region you're gonna see white light instead. Okay? Let's do a problem. A spherical object of 0.01 meter radius with an emissivity of 0.8 is heated to a temperature of 1000 kelvin. How much heat is radiated by this object in 5 milliseconds? What is the brightest color of this emission? So I'm gonna call this a and I'm gonna call this b. Okay? So part a. We're talking about thermal emission so we're going to have to use the Stefan-Boltzmann law first. First. So the Stefan-Boltzmann law is the radiance equals the emissivity times the Stefan-Boltzmann constant times the temperature to the 4th power. Okay the emissivity is 0.8, the temperature is 1000 kelvin and the Stefan-Boltzmann constant is just a constant. So it's 0.8. The Stefan-Boltzmann constant is 5.67 times 10 to the negative 8 and the temperature is 1000 kelvin. If it was given in Celsius you'd have to convert it to kelvin. This is an absolute temperature, this is not a difference in temperatures. So degrees Celsius and kelvin not the same unit. And this is to the 4th power. Okay? So the radiance is going to be 45,360 watts per square meter. Okay? Now we want to know how much heat is radiated by this object in 5 meters per second. Well what does the radiance tell us? The radiance tells us the power emitted by the object at the surface of the object. Okay? So the power is gonna be the radiance sorry. It's gonna be the radiance times the surface area of the object. Okay? Remember the power is the radiance at the surface of the object. So we already have the radiance 45,360 in our SI units. This is a spherical object so the surface area of the sphere is 4pi r squared. The radius is 0.01 meters squared, so the power is 57 watts. Now what we want to know is how much heat is radiated in 5 milliseconds. Well now that we know the power, which is the amount of heat per second, we can simply say that the heat is the power times the amount of time, which is 57 watts times 0.005, that's 5 milliseconds, and that is going to be 0.285 joules. Okay that wraps up our discussion on thermal emission and radiation as a form of heat transfer. Thanks for watching guys.