Refrigerators

by Patrick Ford
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Hey guys, we've talked a lot about heat engines in the last couple of videos and in this video, I'm going to introduce you to another type of device called a refrigerator and what we're going to see is that there's a lot of similarities between refrigerators and heat engines. So let's go ahead and check this out here. Now. Before we get started, I want to talk about about an idea which we've kind of taken for granted up until now, which is the idea that he always flows from hotter to colder and never the other way around. We talked a lot about this when we studied kalorama tree. The idea here is that if you have a really hot coffee cup and you hold it in your hand, heat will always flow from the hotter coffee to the colder hand, you would never expect that by holding a hot coffee cup that your hand would get colder and the coffee cup would get warmer. That would just be insane. In fact, this is so true. This is actually one of the other statements of the second law of thermodynamics. This is sometimes referred to as the Claudius or the refrigerator statement, which is that in a cycle it's impossible for heat to flow from colder to hotter without an input of work. And that's actually the most important sort of part of that sentence there, without an input of work. So sometimes you might see this written as spontaneously from colder to hotter. The way I kind of like to think about this is like a ball that's falling from higher to lower heights, if you have a table like this, a ball always fall downwards because it's going from higher to lower potential, you would never see the ball spontaneously go upwards against gravity because that's just impossible right? It would have to gain energy to do that, so that's why you have to supply some work. So that leads me to what a refrigerator is, because the refrigerator is basically just a type of machine, kind of like a heat engine. And what it does is it takes in work in order to pump the heat energy from colder to hotter. So it doesn't violate the second law of thermodynamics because you're going to supply work in order to do that. So the way this kind of works here is a heat engine would take the natural flow of heat from hot to cold and you would extract some work out of it. But a refrigerator, like the one in your house, what it does is it takes heat from the food and liquid and air that's inside of this compartment right here, that's the cold reservoir and it takes work from electricity, this work is supplied from the power outlet and then it basically pumps heat out to the outside air and that is Q. H. That's the hot reservoir. So if you'll notice here a heat engine and a refrigerator are basically just backwards. They are backwards, processes. All the arrows are reversed and you're actually now pumping in work in order to extract heat out to the hot reservoir. Alright, that's basically the fundamental difference between a heat engine and a refrigerator. Now, the only really equation that you need to know here is that the uh the change in the internal energy for a heat engine was just equal to zero because it's a cyclic process. It's the same thing for a refrigerator. They're both cyclic processes again, just running in reverse. So what that means here is that this work is still just gonna be Q H minus Q. C. As long as everything is absolute values and positive numbers. This number here, this work is always gonna be the difference between these two. The other one is the efficiency of the heat engine. Now remember that the efficiency of a heat engine was basically just how good that heat engine was at doing work. And there's a similar sort of term for refrigerators, which is called the coefficient of performance. A cooperation of performance is basically how good a refrigerator is. It's given by the letter K. Here and in order to kind of like think about this, What I would like to think about is that the efficiency was always work over Q. H. So the efficiency of a heat engine. This work here is kind of like what you got out of it, right, you got out some useful work from this heat engine, but you don't get that work for free. you have to pay the engine something, which is the heat that's taken from the hot reservoir in order to get it. So this efficiency is like what you got out of it, The work divided by what you paid to get it. And that was this qh here, the co finisher, official performance is kind of the same idea, except that some of the letters are different. What you get out of it, what you really want to get out of the refrigerator. If you want to get all the heat extracted from this cold reservoir, write a really good refrigerator is going to make things really, really cold on the inside and what you pay to get. It is actually just the work that is supplied from electricity, the power outlet. So this is the equation for the coefficient of performance and just how we can get from this equation and rewrite this in terms of this, then we can actually take this equation and we can rewrite this in terms of other variables as well. So, really, these are just the two equations that you need to know for the refrigerators, that's really all there is to it. So, let's go ahead and take a look at the problems here, because there are types of problems that you'll see are gonna be very similar to heat engine problems. So here we have a refrigerator and what it does is it's taking in 600 kg jewels of heat from the food inside. Remember that food inside is gonna be the cold reservoir. So this Q. C. Here is equal to 600 this is going to be killed jules. And what it does is it releases 720 kg jewels to the much warmer room. So that's the hot reservoir. So that's Q. H. This Q. H. here is equal to 720. Notice how this number is bigger than this one and that totally makes sense. So what happens now we want to calculate in part a the work that's required to run the refrigerator basically we're going to calculate what is W. And in order to do that, we're just gonna use these equations over here. Now we don't not told anything about the coefficient of performance yet. So we can actually just use this equation right here which is the work is always the difference between the hot and cold the Q. H. And Q. C. So this w here is just always the absolute value of Q. H minus Q. C. And so that's just gonna be 7 20 kg joules minus 600 kg jewels. And this equals 120. So this w here is just equal to 120 killer jewels. And that's the answer. Alright so let's move on now to part B. Part B. Now asks what is the coefficient of performance for the refrigerator. Now we're just gonna straight up just use this equation right here, we can use um Casey oh sorry, this is gonna be okay. Que is either QC divided by w or its Qc divided by a q h minus q C. So do we have enough information to use any of these equations? We actually have all of the numbers, right? We just filled out this energy flow diagram here. We've got all the numbers so it actually doesn't matter which equation we use, we're gonna get the right answer. So your coefficient of performance here is going to be Kay Qc which is the 600 that's what you got out of it, what you paid to get? It was the 120 kg jewels of work. So it doesn't matter if you actually convert this into jewels because the ratio is gonna be the same, this is gonna be a coefficient of performance of five. Now these coefficients of performances are always just gonna be numbers like this. Usually there'll be numbers from like 3-10 or something like that. Alright, so that's it for this one guys, let me know if you have any questions