23. The Second Law of Thermodynamics

The Otto Cycle

# The Otto Cycle

Patrick Ford

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Hey, guys. In this video, we're gonna talk about the auto cycle, which is the theoretic cycle that the gas undergoes in a four stroke internal combustion engine. All right, let's get to it. Now, remember, guys that the common gasoline engine cars is a four stroke internal combustion engine. Okay, now those four strokes are the intake stroke, where fuel air mixtures pulled into the cylinder, the compression stroke where the piston compresses. That fuel air mixture makes it very, very dense. Very high pressure in between these compression and expansion strokes is ignition. Ignition fits right up in here. Ignition is the injection of heat by a spark plug into that very, very dense, compressed fueler mixture that ignites it, causes it to change chemically into carbon dioxide and water, and released a bunch of free energy. That free energy causes the expansion stroke where the piston is pushed away from that gas, allowing the exhaust to expand okay and release all that energy into the piston. And finally, there's the exhaust stroke, where the piston pushes all of that exhaust all that burnt gasoline and air through the exhaust valve and out of the piston, allowing the intake stroke to start again. Okay, Now, the auto cycle, as I said, is the theoretic cycle. Okay? It's a very ideal ized cycle that the gas is supposed to undergo. Okay, in a four stroke internal combustion engine. In reality, it doesn't happen quite like the auto cycle, but the auto cycles a close theoretic explanation of it. Okay, now the auto cycle is given on a PV diagram above me, and it occurs in six steps. The first step is the intake stroke. Okay, where gas is pulled in at a constant pressure. The second stroke is the compression stroke. Okay, which is compressed very, very rapidly. Okay. The piston is moving very quickly in the cylinder during these strokes. Okay, Step three is the ignition stroke. And this actually happens at a constant volume because ignitions intended theoretically to take place instantaneously instantly. All of that era, a few layers converted into exhaust, and the pressure dramatically rises before the piston can move. Okay, step four. Is that expansion stroke? Just like the compression stroke. So both of these, they both occur very, very rapidly. Okay, Now, step five is actually kind of like the second half of the expansion stroke. The expansion stroke isn't technically finished until step five is done. Step five allows a depressed aeration of the depressurization of the exhaust by heat leaving the cylinder. When the heat leaves the exhaust, the exhaust drops in pressure. And this also occurs at a constant volume, like the ignition stroke. And finally, Step six is the exhaust stroke, which also occurs at a constant pressure. Okay, so in the auto cycle, these ideal ized theoretic steps are step one being at a constant pressure. So it's an isil. Berrick expansion. Okay, step to remember the compression and the expansion strokes occur very, very rapidly. The piss is moving very quickly, much too quick for heat to enter or leave the cylinder. So this is an idea, Batic Compression. Okay, Step three is is a coric. It happens at this constant volume. Okay, It's an ISO coric pressurization. The pressures increase at constant volume. Okay, step for the expansion stroke. Just like I said about the compression stroke, both of them occur very, very rapidly. So this is also a DEA Batic. Okay. And step five, which is sort of like that second half of the expansion Stroke allows heat toe leave at a constant volume. So this is also ice. Oh, coric. As the heat leaves, the pressure drops. So it's a depressurization. Okay. And finally Step six the exhaust stroke where exhaust is leaving against no resistance. This is ISO barrack. It occurs at just this initial pressure. Okay, so these air the idealize step I so barrick idiomatic s a cork. Idiomatic s a cork I so barrick. Okay, let's do an example Estimate how much work is done by the gas in the auto cycle shown in the following figure Is this worked on on or by the gas estimate the work done by finding the area enclosed by the cycle Now, normally we would find the area enclosed by the cycle but the shape is weird for that. The shape is kind of like this. Okay, where this height is larger than this height. I don't know what the area of that shape is, but we can break this down into the two steps that contribute tau work. Notice that this step the ice, of course, step in this step the other I support step Don't do any work, okay? Because they are at a constant volume, and I support processes. Never do any work. Now. These two is a barbaric processes do contribute to the work, but they contribute the same amount of work. They're both horizontal lines, right on top of each other in opposite directions. They contribute the same magnitude of the work. But since they're opposite directions, the signs of the worker opposite. So they canceled. So really, the only thing that contributes to the work is this step and this step so we can find each of them independently and then add them together. Okay, so the red step can be thought of like a triangle. It could be approximated as a triangle, sitting on top of a rectangle. Okay, so you can see it looks like a triangle sitting on top of a rectangle. That is a shape that we can absolutely find the area for. Okay. And it starts at 00005 and ends up 0005 Okay. And the triangle starts here at seven and goes up to 170 the base of the rectangles at zero. Just the bottom and we can approximate the green process going to the left as that same shape. Okay. A triangle sitting on top. A rectangle. Okay, now the volume numbers, they're going to be the same. But the pressure numbers are going to be different up here. At the top of the triangle is 25. Here at the bottom of the triangle is one. And obviously it also starts at zero. Okay, so all we have to do is add the area of the triangle in the rectangle for both of these figures to find the two works done by each of these processes. So the area is going to be that of a triangle, plus that of a rectangle. Now, they both have the same base, but they have different heights. So I'm gonna put a little prime on the rectangle height. Just toe. Indicate that it's different if you take the distance or sorry, the difference here on a calculator, you'll find that 00045 So this becomes one half 00045 The height of the triangle is 163 1 70 minus seven. But don't forget that this is times 10 to the five Pascal's. We need that the volume is just cubic meters, so there's no times 10 to the anything here right plus 0.45 The same base for the rectangle and the triangle. But the height is seven, right? Obviously times 10 to the five past scouts Plugging this into a calculator, we get 3982 5 jewels for the area of the red loop. Okay, that red process. Minimize myself for the second for the green process. It's going to be the same exact equation, right? The area of the triangle, plus the area of the rectangle. The only thing that's going to change our the pressure numbers because the volume numbers are identical. This is a change in pressure of 24. Okay, right, that's the height. The volume number is the same, and this is a change clearly of one. Plugging this into a calculator. We get 585 jewels. So now the work is going to be the some of each of these, but with their appropriate sign, that's very, very important. The sign is very important. Now let's look at the red process, the red processes to the right so that work is negative. Okay, so we get a negative sign in front of the first thing. The work that sorry, the green processes to the left, so that work is positive. Okay, so we get a positive sign here in between those works now plugging this into a calculator, we get minus 3397.5 jewels. So that is how much work is done. Bye. Sorry is done in this auto cycle. Now, since it's negative, this is by the gas, right? That's very important. This is by the gas because it's negative. And obviously the work done by the gas should be negative. Because this is an engine. The gas should under go a cycle that allows it to release work that allows the engine to release energy into the system. Alright, guys, that wraps up the idealize auto cycle as the cycle of the gas undergoes any four pissed Sorry for stroke piston engine. Thanks for watching guys

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