Hey, guys, in this video, we're gonna talk about the different methods of heat transfer. Okay. When we started talking about thermodynamics, we talked about the idea of heat being transferred between two substances okay, that were in contact with each other. That's Onley, one type of heat transfer, though we even went so far as to talk about particles colliding at the boundary between two different substances and how that transferred heat between two different substances. But there are other kinds of heat transfer than direct conduction. Okay? And that's we're going to focus on in this video. All right, let's get to it. So far, we've discussed a lot about the quantity of heat transferred to do things. Okay, we talked about changing the phase right with latent heat. We talked about changing the temperature using our M cat equation way back when we talked about changing the size of things in thermal expansion. Now we need to talk about how he is transferred, okay? And like I said, we did spend some time in the beginning talking about two substances. Let's say A and B in direct contact where a had particles moving in random directions and every now and then A and B would have particles that would collide, and the collision between them would transfer heat from one substance to the other. In this case, from a to B, if a is hotter than be. But that's only one type of heat transfer. That's the heat transfer called conduction. There's also conviction, and lastly, there's radiation. Okay, okay. So as of right now, the Onley type of heat transfer that we've ever been talking about is conduction the direct transfer of heat between two objects that are in contact with one another. But there are still two other types to talk about. Okay. Each method of heat transfer has its own set of equations that govern how quickly or how much heat is transferred. Okay, but no matter how he does transferred, the equations of calorie amatrice still apply. So we still have are in cat equation and we still have our latent heat equation. Those still apply no matter how an object gets the heat. Whether that object gets it through conduction, whether it gets it through conviction or whether it gets it through radiation and vice versa for how it releases heat. If it releases heat through conduction through conviction or through radiation. Those two equations still apply. Okay, so let's talk briefly about the differences or not the differences. But what in fact, each of these methods entail. Okay, conduction is the transfer of heat from one substance in contact with another substance. Okay. And this is the type of heat. Transfer that up to this point, we've spent all of our time talking about the direct contact leads toa particle collisions along the boundary that exchange energy from one substance to the other. Right? That's conduction. We know all about it. Conviction is that indirect. So conduction is direct contact and directly transfer. Conviction is indirect. Transfer heat from one substance to another and this is accomplished by heating of fluid surrounding the hot substance. Okay, a classic example is a candle. So a candle with a flame on it heats the air in the immediate vicinity of that candle. Okay, that hot fluid then rises, so you can see I drew right this thing, implying that all of this hot fluid this hot air was rising up due to increased buoyancy. Okay, when a fluid gets hotter, the buoyancy of that fluid increases when it becomes more buoyant, it starts to rise in the fluid that it's in. So the air immediately around the candle starts to heat up, gets more buoyant than the air around it, and it starts to rise. That causes heat to go upwards. Okay, Now, the problem with conviction is that it's really, really, really complicated. Talk about it's a very complicated, fluid dynamics problem. And so we're not gonna talk about it any more than this. Just what conviction is. Okay, but conduction and now radiation, which I'm gonna talk about. Those have simple equations that we can learn how to use and how to apply to solve problems with them. That's not true for conviction. Okay, now, radiation is the release of heat emitted via Sorry of Let me start. Radiation is the release of heat via the emission off electro magnetic waves. Okay, electromagnetic waves carry and energy equal to the heat lost by the substance. Okay, So the substance is really, really hot. If it can radiate, it will radiate electromagnetic. I forgot the dick Electromagnetic waves and those electromagnetic waves will carry and energy equal to the heat lost by the substance. Like I said, not every substance can emit what we would call thermal radiation. Okay, I called it radiation here, but the technical name is thermal radiation. Because there are other types of radiation to Onley. Certain types of substances can emit thermal radiation. And we'll talk about that later. A common example of thermal radiation. Admission is ah, hot metal, glowing red or white as we can see here with this piece of whatever kind of metal it is in a blacksmith shop, the metal is heated so that it becomes pliable so that they can bend it and transform it into whatever they need. And when it's heated, it glows. Okay. And that glowing is the release of electromagnetic waves. Electromagnetic waves. I didn't say it is just a fancy name for light. Alright, guys, that wraps up our introduction to heat transfer and a brief overview of the three different types of heat transfer. Thanks for watching
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Hey, guys, in this video, we're gonna talk about conduction in more detail. While we've talked about conduction in the qualitative sense, the conceptual sense we haven't used any equations to describe conduction specifically, how quickly can he be conducted from one object to another? All right, that's what we're gonna focus on this video. Let's get to it. Remember that conduction is the transfer of heat through direct contact. Okay. Conduction is the most common type of heat transfer you're gonna encounter in your studies and your introductory physics courses. That's why it conduction. It was basically the only type of heat transfer that we've seen up to this point. Okay. When studying Kalorama tree, all he transfers where via conduction. Okay. And that was another point that I made when you put two objects in thermal isolation together in contact, the heat transfers always going to be conduction. Okay, well, we're interested in is how rapidly he could be conducted from ah, hot substance to a cold substance. Right? It always goes from hot to cold. And we're gonna get to that later on when we cover the second law of thermodynamics. But we want to know how quickly. This happens how long it takes the happen. Okay. Materials have a natural allowance for heat flow, known as the thermal conductivity given by Okay, okay. It's how easily they allow heat to be transferred quickly through them. Okay, The larger the thermal conductivity, the faster heat is conducted. Okay. So materials with a high thermal conductivity are called thermal conductors and material with low thermal conductivity are called thermal insulate er's. All right. Now, when dealing with heat, we talk often about a heat current. Okay, The current for the heat is just how rapidly the heat is moving per second. Okay, so it's just Q over Delta T. We've seen problems before That says heat was entering at 95 joules per second. That was the heat current. Okay, How much energy per second. Okay, so the conduction current is the heat current four conduction. Alright, let me minimize myself. We have to substances here. We have one at a hot temperature, one of the high temperature which we just call hot, and one at a low temperature, which was just called Colt. And a connection between the two. This is the conducting material. This is the conductor, okay, And the conductor is described by three things. It's got a cross sectional area. It's got a length and not written here. It has a conductivity, those air the three aspects that described the conductor. Besides that, you also have the temperature off the hot substance and the temperature of the cold substance, which have nothing to do with the conductor. Those air about these systems, the conduction current through the conductor is going to be given by K times a times the hot temperature minus the cold temperature over L. Okay, this is a very important equation, and the units are gonna be jewels per second because it's just the amount of heat transferred per second. All right, there are a few important consequences of this equation. First, the conduction current, like I said, is the rate at which heat is conducted through surface. There was substance. Okay, I explained that let's move past that. The heat conducted would then just be given by H Times Delta t. Okay, as long as H is a constant, If h is not a constant, then you couldn't just multiply it by the amount of time because H might change as that time goes on, if you knew the average conduction current, you could multiply it by the amount of time and find the total heat transfer. But this equation right here, typically Onley works if h is a constant. Okay, now notice H should not be a constant. Okay, The conduction current should absolutely change as the hot substance became colder because it's releasing heat and the cold substance becomes hotter. So naturally this is gonna drop, and this is gonna go up. That's what happens as he goes from the hot substance to the cold substance, so H should not be a constant. The conduction current will be constant if the hot and cold substances are what we call reservoirs. Like a reservoir of water. A reservoir of water is a giant source of water. Okay, what a reservoir is for anything, and we use it a lot in thermodynamics is a reservoir is an infinite source or sink of heat. That means that it can absorb and release an infinite amount of heat without changing its temperature one bit. Okay, that's what it means to be a reservoir. So if we look at our conduction current equation imagine now that the hot objects in the cold objects were reservoirs and the conductor and the conductor was connected between the two reservoirs. Then, no matter how much he went through the conductor, the temperature of the reservoirs would never change. That's the point of being a reservoir. It's an infinite source, so it can produce as much heat as it wants. It's an infinite sink so it can absorb as much heat as it wants, all without leading Thio any change in temperature. So if this substance and this substance here, where reservoirs in the conduction current through the conductor would in fact be a constant okay, and that's an important point to make because you'll probably see reservoirs quite a bit in thermodynamics. All right, let's do an example. Ah, hot reservoir at 100 degrees Celsius is connected to a cold reservoir at zero degrees Celsius by a 15 centimeter long piece of iron with the 150.5 square meter cross section. How much heat crosses the piece of iron and five seconds, and then it gives us the thermal conductivity of iron. Okay, so we're talking about how much heat in some amount of time, so we know that we need to use Q equals H Delta T. Okay. And we know that h the conduction current is K a th minus TC over l. We're told that the hot source and the cold source are actually reservoirs in this problem a hot reservoir and a cold reservoir. So the conduction current is gonna be constant. Let's calculate that the thermal conductivity of iron is 5 and the units of Watts per meter Kelvin R s I units, the cross sectional area is 0.5 The hot reservoir is 100 degrees Celsius minus zero degrees Celsius. Okay, Now, because this is a change in temperature, this is a difference in temperature, right? You have a hot minus a cold, even though there's no delta there because there's a change in temperature. We can simply leave this in degrees Celsius because that change in Celsius is equivalent to a change in Kelvin. And we do need Kelvin because if you notice the S I unit right here, is Kelvin okay? Divided by the length. And we're told that it's a 15 centimeter long piece of iron. So this is 150.15 m, plugging all of that in the heat. Current is 26 50 watts. Okay, Jules, per second is what I gave is the units for conduction current, but a jewel per second is just a watt. So most of the time conduction current is given in watts. Okay, Now, we confined the total heat transferred and were a perfectly allowed to use this equation because since the hot source in the cold source our reservoirs, their temperatures don't change and therefore h doesn't change. So this is 26 50 times. We were asked for it in five seconds. Okay. And so this is 13,250 jewels or 1.33 Kill the jewels. Like I said, typically, like thio give these units and kill a jewels. Because most of the problems with this is not it's 13.3, not 1.33 13.3 killing jewels. Because most of these heats are large enough to be represented as kill a jewels and to largely represented his jewels. Alright, that wraps up our discussion on the conduction current and conduction in specific. Alright, Thanks for watching guys
A cubic Styrofoam cooler containing ice on a hot day is shown in the following figure. The thickness of each wall of the cooler is 15 mm, with a side length of 1 m. If it is 40°C outside, how long will 2 kg of ice last in the cooler? Assume that during the melting process, the temperature inside the cooler remains at 0°C and that no heat enters from the bottom of the cooler. Note that the latent heat of fusion for water is 334 kJ/kg and the thermal conductivity of Styrofoam is 0.033 W/mK.
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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.
If the intensity of sunlight measured at the Earth’s surface is 1400 W/m2 , what is the surface temperature of the Sun? Treat the Sun like a true blackbody. Note that the distance from the Earth to the Sun is 1.5 x 1011 m and the radius of the Sun is 696 million meters.