Hey, guys. So now that we understand how refrigerators work, in this video, I'm going to show you another type of device that you might run across, which is called a heat pump. And what I'm going to 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 hot reservoir, and it extracts some usable work and it produces some usable work here. And then it takes whatever work 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 you would use as 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 fridge is 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 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 aren't switched. That's the sort of main idea of a heat pump. So if you lived 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 cold 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. Alright? So, a real-life example is, you know, if you live somewhere, you know, 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 Q_cW, right? It's the heat extracted from the cold reservoir, that's what you get out of it, divided by the work, which is what you paid 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 Qh. 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 of performance of 3.6. Now one thing I forgot to mention here is that the coefficient of performance for heat pumps, we denote as KHp, just sort of like you so you don't get confused between them. So what we have here is that KHp is equal to 3.6. We also have is a power supply of 7×103 watts. So remember that power is P this is equal to 7×103 watts. Now be careful here because this means that it's 7×103 joules per second, that's what a watt is. What we want to do in this problem is calculate the heat energy that's delivered into a home over 4 hours of use. So really want a 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 Qh delivered over 4 hours. Alright. So how do I calculate that? Well, we only have one equation for heat pumps. It's just this one right over here. So we've got here is that KHp is equal to the heat delivered to the hot reservoir divided by the work. Now remember, this isn't Qh over 4 hours, it's just Qh over W. This is just the equation for one cycle. 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 KHp equation in these terms, we can rewrite them. This is going to be K, Qh and this is the work done, this is going to be power times the delta t over 4 hours. Right? So running this over 4 hours of use, I just have the power and I just need to multiply it by delta t over 4 hours. Now when I do that, basically what I get here is that this Qh doesn't isn't just for one cycle, this Qh becomes the heat energy delivered over 4 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, I can start plugging in numbers. Right? It's times P times delta t for 4 hours. So my KHp is equal to 3.6. Actually, let me go ahead and start that another line. So we have 3.6 times, the power, which is 7×103, and then we have the delta t for 4 hours. We want it in seconds because, remember, this is joules per second. So we have here is, I have 4 hours times 60 minutes per hour times 60 seconds per minutes. You'll see that the hours and minutes cancels, leaving you only with seconds. And if you go ahead and work this out, what you're gonna get is you're gonna get 3.6×108 and that's in joules. So that's how much heat energy gets pumped into your home over 4 hours. Alright. So that's it for this one, guys. Let me know if you have any questions.