by Patrick Ford

Hey guys, so now that we understand how refrigerators work in this video, I'm gonna show you another type of advice that you might run across, which is called a heat pump, and what I'm gonna show you is that they work very similarly to refrigerators. We'll even see a similar equation for the coefficient of performance. The trickiest thing here is understanding conceptually the differences between a heat engine, a refrigerator and a heat pump. So that's what I want to show you in this video. Let's get started. A heat pump, like I said, is just like a refrigerator, It pumps heat from colder to hotter. So let's kind of recap everything we've learned so far, a heat engine, remember, takes the natural flow of heat from hot to cold, it takes some energy from the whole hot reservoir and it extracts some usable work and it produces some usable work here and then it takes whatever works whatever energy it didn't convert to work and expels as waste heat to the cold reservoir. A real life example of this would be like an engine, like a real engine in your car, or like a generator that you might have in your house. A generator, which which uses gasoline, basically can power your home just in case you lose power or something like that. Alright, now a refrigerator is like a heat engine, but it works in reverse. What it does is it extracts heat from the cold reservoir and it requires an input of work like the electrical outlet that your fridges plugged into, and then it expels heat out to the already hot reservoir. Alright, so the key thing here is that a refrigerator doesn't produce work. It requires some work to be done. Alright, a real life example would be like the fridge in your house or even like an air conditioner. Right? You want the inside of your home to be cold. So you have to take that heat and you have to pump it to the outside. Now, let's talk about a heat pump, right? It still pumps heat from colder to hotter. However, what happens is that the reservoirs are switched and that's the sort of main idea of a heat pump. So, if you live somewhere really, really cold, what happens is the cold reservoir is the outside air, right? If you live somewhere north, basically what a heat pump does, is it takes heat from the already cold air outside into sort of like a generator or something like something like that, and then it requires some work. And what it does is it heats that air and then pumps that into your house. So, here's the difference in a fridge, the cold reservoir was inside the hot reservoir was outside in a heat pump. It's sort of inverted the colon reservoir is outside, but now the hot reservoir is inside and that's the main difference. Now, a heat pump still just like a refrigerator requires some work to run. So that's why it's not really like a heat engine, it's more like a fridge, but it's sort of running inside out. All right, so, a real life example is, you know, if you live somewhere cold, you might have something like a space heater or something like that. That's a perfect example. Alright, So what does that mean for the equations? Well, for a refrigerator, the coefficient of performance was QC over w right. The heat extracted from the cold reservoir, that's what you get out of it, divided by the work. Which is what you pay to get it for a heat pump. It's a little bit different because what you're really getting out of it is actually this you're actually getting this heat that gets pumped into your house or the hot reservoir. So, here what happens is that we replace the QC with a Q. H. That's all there is to it. Now, it's just a Q H. In the numerator. Alright, so that's all there is to it guys, that's sort of a conceptual difference. Let's go ahead and take a look at our example. Alright, so here we have a heat pump. It has a coefficient performance of 3.6. Now, one thing I forgot to mention here is that the coefficient performance for heat pumps. We did note as K hp is just sort of like, you know, so you don't get confused between them. So, we have here is that K H p is equal to 3.6? We also have as a power supply of seven times 10 to the third watts. So remember that power is p this is equal to seven times 10 to the third watts. Now be careful here because this means that it's seven times 10 to the third jewels per second. That's what I want is what we want to do in this problem is calculate the heat energy that's delivered into a home over four hours of use. So really want to heat energy. Remember that's Q. Except we want it delivered into a home. So remember, according to this diagram, we're using this diagram, that's qh from, that's what you get out of the equation. So we're really looking for Q. H delivered over four hours. Alright, so how do I calculate that? But we only have one equation for heat pumps. It's just this one right over here. So we've got here is that K hp is equal to the heat delivered to the hot reservoir divided by the work. Now, remember this isn't qh over four hours. This is just Q. H. Over W. This is just the equation for one cycle, but we can actually modify it so that it works for any amount of time. So, remember that the relationship between work and power is that power is W over delta T. So what happens is I can rewrite this and say w is equal to power times time. So what happens is we can basically take this cage P. Equation in these terms, we can rewrite them. This is gonna be K. Qh and this is the work done, this is gonna be power times the delta T. Over four hours. Right? So I'm writing this over four hours of use, I just have the power and I just need to multiply by delta T. For four hours. Now what I do that basically what I get here is that this qh isn't just for one cycle, This QH becomes the heat energy delivered over four hours. So this is how I get to my target variable over here. It just comes straight from this equation here. Alright. So basically if I move this to the other side and start plugging in numbers right times P times delta T. For four hours. So my K. H. P. Is equal to 3.6. Actually gonna go ahead and start that another line. So we have 3.6 times the power which is seven times 10 to the third. And then we have the delta T. For four hours. We want it in seconds. Because remember this is jules per second. So we have here is I have four hours times 60 minutes per hour times 60 seconds per minutes. You'll see that the hours and minutes cancels, leave you only with seconds. And if you go ahead and work this out, what you're gonna get is you're gonna get 3.63 times 10 to the eighth. And that's in jewels. So thats how much heat energy gets pumped into your home over four hours. Alright, so that's it for this one guys, let me know if you have any questions.

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