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Patrick Ford
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Hey, guys, in this video, we want to talk more in detail about radiation as a method of heat transfer. All right, let's get to it. Remember that certain hot objects can expend heat. They can emit heat in the form off electromagnetic radiation, which is another word for electromagnetic waves. Okay, these substances that can do it are known as black bodies or black body like Okay, a black body is an object that can admit the maximum amount off thermal radiation at a given temperature. A black body like object will always emit less energy in the form of thermal radiation than a true black body. Okay, as with all waves, ah, particular wave or particular electromagnetic wave in this case is defined by its frequency. 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, or just a fancy way of saying light. So for light, ah, particular frequency will be referred to as its color visible light, which is what we can see on Lee occupies a very, very small amount of the electromagnetic waves. There are other types radio waves, X rays, gamma rays, microwaves, etcetera. 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. This remember this verb, this wordage that I'm using? It doesn't have to be visible light for me to say. 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 that minimize myself. This picture is this a spectrum of black body spectrum off light we have in the vertical axis, the brightness of the light and in the horizontal access the frequencies. So the color of the light and as you could see at low temperature the most probable lite. Sorry, The brightest light is that a lower frequency than at a higher temperature? Okay, in the visible light spectrum and like 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 admitting light as a red curve because its brightest color is gonna be closer to read. 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, off 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 gonna 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. 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, um, it's red light. But there could also be a chemical process going on where the chemical that your heating up specifically amidst blue light or red light and it 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 and frequency it's no longer visible. What ends up happening is the colors that you see are on Lee the tail end of this right here. This tailing 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 the spectrum shifts out of the visible range, this light shifts from blue, which was hot black bodies toe white, which are black bodies that are so hot that they're omitting like ultraviolet light or X rays, even low energy X rays so that all that you can see because all we could see is visible light is the tail end of the spectrum right here, and all of those lights are omitted at very similar brightness is there's no clear peak brightness and a combination of colors produces white light. Okay, so that's why I really, really hot metals glow white. Okay, Like we saw in the blacksmith picture when I introduced heat transfer. All right, now the radiance, which is something I'll talk about in a second off thermal radiation emitted by a black body like object is given by the Stephan Bolton Law and the Stephan Bolton Law. The radiation the radiance is given by J the Stephan Bolton Law says it's legal. Tau epsilon sigma T to the fourth. Okay, F salon is known as the imbecility. It's how closely to a true black body a black body like object is a true black body has an epsilon of one. All black body like objects have haven't Absalon less than one because they emit less light less thermal radiation than true black bodies. Forgiven temperature. Okay, Sigma is noticed a Stefan Bolton constant. And it has some value right here in S I units. Now what is radiance? Radiance is 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 admitting 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 admitting? 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 is a tropically 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 omitted light over the surface area of that sphere, which is four pi r squared where r is the distance between the earth and 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 off the object, admitting the light. So it's how rush power that object is admitting, 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 Onley measured. At one point, it's on Lee, measured at the surface off the object, admitting the light intensity can be measured anywhere. But radiance has always measured at the surface. Okay, now the brightest color in the emission spectrum off black body radiation or thermal radiation is given by vines or beans. Displacement law and it's just be divided by T, where B is viens 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 passed the visible light region. You're going to see white light instead. Okay, let's do a problem. A spherical objects of 0.1 m radius with an impressive ity of 0.8 is heated to a temperature of 1000. Kelvin, how much heat is radiated by this object in five milliseconds? What is the brightest color of this emission? So I'm gonna call this a, and I'm gonna call this Be okay. So Part egg. We're talking about thermal emission. So we're gonna have to use the Stephan Bolton Law first. So the Stephan Goldsman Law is The radiance equals the imbecility times of seven Bolton. Constant times the temperature to the fourth power. The imbecility is 70.8. The temperature is 1000, Calvin and the Stephan Goldsman constant is just constant. So it's 08 The Stephan Bolton constant is 567 times 10 to the negative eights, and the temperature is 1000. Kelvin. If it was given in Celsius, you'd have to convert it to Calvin. This is an absolute temperature. This is not a difference in temperatures, so degrees Celsius and Calvin not the same unit. And this is to the fourth power. 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 m 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 R s, I units, This is a spiritual object. So the surface area of the spheres four pi r squared the radius 01 m squared. So the power is 57 watts. Now, what we want to know is how much heat is radiated in five milliseconds. Will not 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 570.5 That's five milliseconds, and that is going to be 0.285 Jules. Okay, That wraps up our discussion on thermal emission and radiation as a form of heat transfer. Thanks for watching guys.