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Heat Transfer - Overview

Heat transfer is the exchange of thermal energy between physical systems. The rate of transfer is dependent on the temperature difference (thermal gradient) between the systems, and conductive, convective, and radiative properties of the material. Conduction is the transfer of energy between objects that are in direct physical contact. Convection is the transfer of energy between objects that are not in direct contact through the movement of fluids. Radiative heat transfer is the transfer of energy by radiation, which occurs due to a temperature difference between the systems.

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Video Transcript

welcome to the next section in our unit on the first law of thermodynamics. In this video, we're going to talk about How is it that heat transfers? What are the mechanisms by which it does that, and how can we model it mathematically? Now there is a rather old model proposed by Newton, which says that the rate at which he is transferred is going to be proportional to the difference in temperature between the two bodies that air transferring heat. So in the example of we dropped ice into a bucket of water, we've got some cold temperature reservoir and some hot temperature reservoir. And then the rate at which the ice cube gets hotter and the water gets cooler is proportional to the difference. If we have a large difference in temperature, then we'll have a large transfer of heat over time. If we have a small difference in temperature, then we'll have a small transfer Pete And again, this is right of transfer of heat, So a small rate of heat transfer or a large rate of heat transfer. It turned out that Newton was a little right, but not entirely because there's more than one way to transfer heat. One way that we talked about a lot is conduction, where two objects air touching each other or somehow thermally connected. And in this case, it does follow Newton's law of cooling. We have D. Q. T t equals some constants multiplied by the difference in temperature. In this case, Delta team means t hot minus t cold, not t final minus t initial. That wouldn't make any sense here. So in this case, we have our picture where we have a hot reservoir in a cold reservoir. And in between, it is a piece of material along which the heat is traveling. It has a length l which shows up in the equation. So that's the distance across which the heat must travel to go from the hot to the cold reservoir. And you have a surface area A Okay, So if I were to take this middle piece and rotate around, I would find a to be the cross sectional area through which the heat is traveling. So how large area means a large rate of heat transfer? A large length means a slow leak rate of heat transfer and then this other constant K has to do with what the material is made of. So whatever this centerpieces made of, we referred to it as thermal conductivity. A lot of times, if you go out shopping for a insulate er it for your house or something like that, then you're going to find it all characterized in terms of something called our value, where R is equal to L over case. So that's the thickness of the material divided by its thermal conductivity Noticed. This means that if we have a high thermal conductivity that we will have a low our value. If we have a low thermal conductivity, we will have a high our value. Hi, our value materials are insulate er's and we want to put them in our house to keep them hot in the winter and cold during the summer. So the way we do that is by buying something that has a lot of thickness and a pretty decent thermal conductivity. Large thermal conductivity again means that heat transfers quickly through the material. A low thermal conductivity means that it takes a long time for heat to transfer through the material. Next up we have conviction, so conviction which you've probably heard of is, well, it means that we have particles of air or some gas that are moving really fast because they're very hot and they collide with particles that are moving really slow because they're cold, and in the end we end up with particles that are moving at pretty much the same rate and have approximately the same temperature. It turns out that in order to model, conviction requires a lot of complicated mathematics, and it is beyond the scope of this course and your math ability to be able to handle that. I have never seen an introductory physics course that gave an equation for conviction, though they will show up if you continue on to more advanced courses. So all you really need to know that it involves particles in a gas or in a liquid, even something that's free flowing where you have a hot part and a cold part, and the mixing of these particles causes them to come to an equilibrium temperature over time. Next up is radiation, so here we're talking about the son that's radiating light out. There's literally not much in between, so we can't really do conviction. We definitely can't do conduction. But between us and the sun, we do get a lot of radiation. So the way we calculate that is that the radio radiation coming out of the sun is equal to something called the M acidity, which is just a measure of how well radiation leaves the body multiplied by the Stefan Goldsman content constant which is given over here. It's just a constant number. You can look up multiplied by the surface area of the material of the object, so that would be the surface area of the sun. Remember, For a spherical object, a would be equal to four pi r squared and then multiplied by the temperature of the object to the fourth power. So, uh, we could calculate the rate at which heat is coming from the sun towards us and then back. Try to backtrack that back to find what the temperature of the sun is. However, this turns out to be a little incorrect because at the same rate at which things are radiating power out, they also are absorbing radiation like that depending on the temperature of the surrounding materials. So it turns out that a better model is to say that the rate of heat transfer for a radiating object is equal to the same constancy. Missive, ity, times the Stefan Goldsman, constant times the area multiplied by the difference between its own temperature to the fourth power and the temperature of its surroundings to the fourth power. So if it had a very high temperature surrounding, then it would also be absorbing. So this first term is the rate at which it emits light. In the second term is the rate at which it absorbs light. So these are three techniques for transferring heat, and we're going to take a look at them in the coming videos.