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Introduction to Heat Engines

Patrick Ford
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Hey guys. So by now we've talked a lot about the first law of thermodynamics and the next couple of videos, we'll start to talk about the second law of thermo and what we'll see is that it's not so much an equation as it is. A bunch of statements. And these statements have to do with these things called heat engines. So before we get there in this video, I want to introduce you what a heat engine is and hopefully I'll give you a really good analogy for sort of understanding these things. I'll also show you the equations and diagrams that you'll need. So let's go ahead and check it out here. Basically, a heat engine is it's kind of a machine or a device or something like that, and what it does is it converts heat energy into useful work. Now the analogy that I always love to use is that it's just like the engine that's in your car. A car engine is a perfect example of a heat engine. So, I always want you to think about it whenever we talk about these things or just in case you forget now without getting into the specifics, basically where your car works is it takes some gasoline, some fuel source and your car ignites that gas, it creates a ton of heat and thermal energy. And basically what your engine does is it takes that heat energy and then it uses it and converts it into useful work by turning the wheels of your car and that's what makes you go forward in your car. So it converts heat into useful work and it doesn't do this perfectly. So, what ends up happening is that some comes out the back end as exhaust. So, this is just the exhaust heat that comes out the back of your car. All right. So, that's really how any heat engine works. It takes in heat and then converts it into useful work and then it spits out whatever it doesn't use. All right. So, instead of having a bunch of different diagrams for a bunch of different types of machines, physicists a long time ago developed what's called an energy flow diagram. You're gonna see these things a lot in your books and classes. And basically what this thing is, is it represents the heat transfers that are happening and any kind of heat engine, regardless of whether it's a boat or a plane or a car, whatever. Alright, so there's a couple of important things you need to know about them. The first one is that this energy flow diagram has what's called a hot reservoir. Now, what's that mean reservoir? It's kind of like a weird word, but it's basically just a source of heat energy that's going into the engine. In my car engine analogy, the source of the heat energy was the burning gasoline that we ignited. Right? So the hot reservoir is just the gasoline that you're igniting. That's what the engine uses in order to produce work. So the second thing you need to know is the work is the usable energy that's produced by the engine that's turning the wheels of the car. And our analogy, right? So your car takes the gas, sets it on fire and then uses that to spin the wheels of your car and move you forward. All right now, lastly, we have what's called a cold reservoir and that's kind of like the opposite of a hot reservoir. It's basically where all the wasted heat energy goes once it's expelled out from the engine. And in my example here, that was basically just the exhaust pipe. That's where the rest of the not used. Heat energy goes. All right. So that's the basics of how a heat engine works, sort of conceptually. Let's take a look at some of the equations that you'll need. Now remember we talked about the first law of thermodynamics, which was this equation here, Delta E equals Q minus W. We also did in a previous video took a look at cyclic processes and cyclic process had a special condition that the change in internal energy, delta E was zero. So, directly from this equation, if delta is equal to zero and that means that Q has to equal W. So we saw, is that for cycles, the W for the cycle equaled the que the work done in the cycle equals the heat added during a cycle. Now, heat engines are always going to be cyclic. Now, this process here of burning gasoline and this and that doesn't just happen one time it happens over and over and over and over again. As long as you can feed your engine more gas. Right? So heat engines always happen in cyclic processes that repeat over and over again. We also have that heat is flowing in and out over a cycle. So basically just directly from this equation, the work that's done by the engine is equal to the heat that gets added over the cycle. Now, what happens is again, we have two heats, we have one that's going in one that's going out. So what is this Q. Net here? It's actually both of them. It's actually the heat that's going in, that's Q. H. And it's positive because it's getting added to your system and then this Q. C. Is leaving your system, so it gets a negative sign. So that's basically the equation that you're gonna see. One way you can kind of think about this is that the work that's done is equal to whatever heat that goes in minus whatever heat that goes out. But I just highlighted this one because this is the one that you're most likely going to see in your problems. So that's really all there is to it guys, let's go ahead and take a look at our example here. So we have a heat engine that's taking in 500 joules of heat, it's doing 300 joules of work, and we want to calculate how much waste heat is expelled from the engine. So, which variable is that? Well, if we want to sulfur some kind of a heat that's going to be a Q. We're solving for how much waste heat is expelled. So, I'm going to label this as Q waste. All right. So, before we actually get into any equations, let's sort of draw out in our energy flow Diagram, what's going on here? So, remember, we have a hot reservoir, we have a cold reservoir. What we're told in this problem is that 500 jewels of heat is being taken into the heat engine. So, which variable is that? Remember your heat engine takes in heat from the hot reservoir. So, that just means that this QH or Q in is equal to the 500 jules. Now, what your heat engine is doing is it's taking some of that heat energy and it's doing 300 jewels of work. So, that's pretty straightforward. The work is always just gonna come out of your heat engine like this. So, you're w here is just gonna be the 300 jewels. So, if we're asked to find out the heat, the waste heat, it's basically the one heat that we don't have in this debt in this diagram here, which is the heat that gets expelled out to the cold reservoir. So this is Q seed or in other words Q out. And that's basically what this waste heat represents. All right. So the trick to these kinds of problems here is kind of translating which variable they're asking you to solve? So Q waste is equal to Q. C. In other words it's equal to Q out. I need any of these. They all mean the same thing. All right. So that just means if we're looking for Q. C. Now we can just use this equation over here. So let's get started. The work done by the engine is equal to the nets. Heat transfer to the cycle which is gonna be qh minus Q. C. Alright, so, we have the work that's done by the system by the engine. That's the 300 jewels. And we also have the heat that gets added to the system. So we can solve this Q. C. Over here, just by rearranging. So basically what happens is you just flip you move this to the other side, this becomes Q. C. Equals Q. H minus the work done by the engine. So, it's just gonna be 500 jewels -300 jewels. And you end up with 200 jewels. All right. So, it's as simple as that basically what's going on here, is that there's 500 jewels that gets added to your system and then the engine sort of splits that up. Right? It does 300 joules of work and it spits out the rest which it doesn't use, which is the 200 jewels that's left over. So this w here there's 300 is always going to be the difference between what comes in and what goes out. Right. So, anyway, that's uh an introduction to heat engines. Let me know if you have any questions.