Welcome back. So, we were looking at different forms of cycles last unit. We were talking about the power cycles, refrigeration, and heat pump cycles. And we had the generic description, a generic representation for those cycles. So, recall for our refrigeration cycle. We have a high temperature reservoir and a low temperature reservoir. We have our system, which right now is just a black box. And when we operate in a refrigeration or a heat pump mode, we have work that is into the system, or in this case power. The work transfer rate is into the system. And recall for refrigeration and heat pump, we reverse the direction of the heat transfers. So, our heat transfers now are into the system from the low temperature reservoir and out of the system into the high temperature reservoir. So, for the power cycle all of the directions of these arrows flip. But for the refrigeration cycle it looks like this. And this is my system, my refrigeration system. Okay so once we have this generic description where does the ice box or the really cold portion of our refrigerator fit within this generic schematic? And the answer to that is we simply say okay well where is the low temperature reservoir? That's what we're trying to essentially keep cool. So, this, so if we draw it like a little sketch here. I'll try and do an artistic rendering of a refrigerator for us here. so let's, this icebox portion the refrigerator actually corresponds to this portion of our diagram. Okay. The power into the cycle, of course, is our outlet which is using electrical power. So, there's that parallel. Okay. And if you ever looked at the back of your refrigerator, you'll see that there is a serpentine, where the cooling fluid, the refrigeration fluid is actually circulating. And that's on the outside of the refrigerator and that heat transfers out. The heat that's been removed from the ice box in order to keep the refrigerator cool is then rejected to the atmosphere in that region behind your refrigerator. So, this is the queue out, and it's rejected to the ambient. So, these are the refrigerator cooling coils. And again, that corresponds to this portion of our system. So, we can see how the different real components fit to this generic description. Now, we're going to come back to this generic description of heat pump and refrigeration, and power cycles. So, we have to be able to understand how to map from this conceptual space into actual practical space. So, this is a good exercise for us. you should try the same thing with an air conditioning unit, or a heat pump unit. Good, good thing to try and map what do, where do each of the components correlate or parallel to the generic description here. Okay. So now, we're going to talk very briefly about the 2nd law of thermodynamics. And we're not going to go into too much depth. But recall, last time I talked to you, we were saying how we need some information from the 2nd law of thermodynamics in order for us to understand limiting behavior. So, what's the best we can do? That's the type of limiting behavior that we're talking about. Now, the first law of thermodynamics tells us if a process is allowed, or does a process violate the conservation of energy? Recall, the conservation of energy applies for all materials, all systems, all fluids. All. It doesn't matter what the example is Could be phase change, whatever. As long as we can apply the criteria that it's you know, remember we have criteria about we have to have a simple, a simple substance. It has to be a quasi-equilibrated, it has to be equilibrated at the initial and final states, things like that. So, if we have a well defined system, the conservation of energy always applies. Now, remember we talked about, let's just get our equations in front of us, here, and that gives us something to talk around. So, recall for our closed system, this is a conservation of energy, which says the change in the energy within that control mass has to be balanced by the net heat transfer and the net work transfer. And we had a couple of example problems that we did where we said, well, can I have a system that has work transfer in, and heat transfer in? And the answer was yes. As long as we have an appropriate change in the energy within the control mass. Now, imagine that same system. And I'll ask you, okay, we have an initial state and a final state, and a final state. We've said in this kind of thought experiment that the heat transfer is in and the work transfer is in. Okay, so we know that that essentially makes this right hand side positive, greater than 0. Okay, because we have net heat transfer and net work transfer it. So we know that this final state, energy, has to be greater than the initial state of the energy. One of the things that we can ask is, in fact, take this entire system, this thought exercise, and turn it around. So I said, well, can you have a system that the work transfer and the heat transfer are out of the system? Sure. You just need to reverse the sign on the final and the initial states for the control mass. Okay. So I have two systems. Let's say the numbers are identically equal but they're opposite in signs. So, one, we have all the heat transfer and work transfer in, the other system we have all the heat transfer and work transfer out. The conservation of energy, again assuming that our we meet this criteria for our in, for our energy in the system. The conservation of energy says, either of those systems are possible, right? Both systems are within the constraint of a conservation of energy. The second law tells you which direction is allowed. So, let's keep working with this exercise here. So, we know, let's take our balloon that we talked about as one of our earlier examples. We're going to blow up the balloon, we're going to have some expansion work, in order to increase the size of the balloon. Okay. We know if that pressure inside the balloon is higher than the atmosphere, if we pop a hole in the balloon, the air will rush out. Okay. There are governing equations that can, that can that are representative of that process for the conservation of energy. The catch is the conservation of energy, doesn't tell you that, hey, the only appropriate direction for that process is to have the air come out of the balloon. Right? We can set up all the numbers, we can do all the analysis and it's all going to tell us, hey, the air has to come, the air can come into the balloon or out of the balloon. But we know intuitively. Air is not going to spontaneously go in to the balloon. And then, have the balloon end at some higher pressure. So, that's where the second law comes in. The second law tells us the allowed direction of a process. So, you can think of all sorts of good thought exercises. You could imagine take for example the change in potential energy associated with the hydraulic power plant. So, let's take a dam, and we're looking at the energy generation. We can setup again an observation equation for the system. And we could make it a control volume or control mass on a rate basis or whatever is appropriate. And we can say, we can in fact check the box that the conservation of energy is in fact the criteria for the conservation of energy is met. But we can't tell from this analysis whether or not the water should be going down or going up. And again, intuitively we know the water has to go down. So again, what does the second law do? The second law tells us what is the only allowed initial state and the only allowed final state. Okay, so that's some pretty advanced second law analysis. And we're not going to do that type of analysis in this class. But we do need some core information that the second law of thermodynamics provides. So, what are those pieces of information we need? Well, we're going to need this. The second law of thermodynamics also tells us limiting behavior, ideal exceptions. So, we can take for example, we have our turbine, right, which is our workhorse for our Power Point. So, we have some mass that goes into our turbine at state 1 and exits out turban at state 2. We spin a shaft and that allows us to generate some power. The second law tells us what's the maximum power we can derive from that turbine. So, this comes from the second law. Now again, we're not going to go ahead and evaluate the properties that are defined by the second law in order to determine the maximum work. In this class, we're going to recognize that we could if we took those courses, if we understood how to use those advanced concepts. We could in fact, determine the maximum work from fundamental principles in thermodynamics. But for now, all we really need to do is understand that the 2nd law is going to define maximum work out and minimum work in. And we're going to revisit this in just a few segments, because it's going to take us a little while to develop the tools to have this conversation. Okay. So, what else are we going to take from the 2nd law of thermodynamics? There are lots and lots of other, concepts that come from the 2nd Law. And that includes another conservation principle. And that conservation principle is based on entropy and entropy generation. And entropy is a thermodynamic property and again, it's an outcome of the second law when we write it in a mathematical expression. Again, for us, we're not going to look at state relations for entropy. We're not going to look at how to determine entropy from state parameters. We just want to use the definition of entropy in order to constrain some of our processes. And that may not make sense right now but it will soon. because I'll show you how we're going to use that understanding that there is a property entropy that is defined by the 2nd law. And it defines further ideal behavior for our thermal physical systems. Okay, the other thing that we get that we will use in this class from the 2nd law is the absolute temperature scale. So, the second law of thermodynamics tells us, not only limiting behavior and the directions of things, and ideal performance, but it also tells us how to link ideal performance to an absolute temperature scale. So, those are the key pieces of information we're going to take and move forward from the second law of thermodynamics. Okay. So, now, the second law of thermo dynamics and cycles. So, before we had discussed again power cycle and heat pump and refrigeration cycles. So, let's go ahead and draw again our generic picture of a power cycle and we'll label all of our relevant heat transfers and work transfers. And we know again, if it's a power cycle that's based on a heat engine. We have heat transfer from a high temperature reservoir into my power system. And I have to reject heat to my low temperature power system and they should all be on a great basis. Okay and we said, hey, we know that we can define an efficiency for the power cycles. We denoted that with a subscript P as being what we want which was the work out of that cycle. Divided by what we paid for to get it, which remember was essentially the heat transfer from combustion or from whatever the high temperature reservoir source was. The energy carrier for that high temperature reservoir. Which again, in most power plants, is going to be a combustion source. Okay, the 2nd law of thermodynamics tells us that there is a maximum performance associated with a heat engine. Okay, so that maximum cycle efficiency is defined as the Carnot cycle efficiency. So, that's MP max, or if you'd prefer, that's eight, I should say Carnot. And if we look at this definition here, this is the easiest way for us to memorize these formula. And you should know them, if you're working in this area, you should know them off, from memory, because they're that important. Remember, the heat transfer and the work transfer, net heat transfer and the net work, transfer for a cycle, have to be identically equal. Remember, that's a statement of the first law. That's a statement of the conservation of energy. And remember, we kind of set aside our side convention. And said, okay. Well, we're just going to write these variables. Understanding that it's going to be net heat transfer in, that's positive. This net heat transfer out is negative but we're going to take care of that with a sign convention here. So, these all should be considered absolute numbers, when we plug them in here. But if you look at this expression and again, everything on this side of the line, is valid for any power cycle, anywhere. Ideal or non-ideal. These are always valid. Right? This is just the definition of inefficiency. And then, when we do the substitution from work transfer to heat transfer, that's just the statement of the conservation of energy. Statement of the first law. So, these are always valid for ideal or non-ideal systems, and non-ideal systems is another way of saying real or actual systems. Okay, now we look at the column here on the right. Let's build this column on the right. The Carnot efficiency for a power cycle says, hey, the best you're ever going to get for power from a heat engine is limited by the temperatures of the reservoirs. So, you just look at the structure here for the heat transfer and you do an exact parallel structure. And that's the Carnot efficiency. The Carnot efficiency for a power cycle looks like this expression where you simply have the Carnot efficiency defined by the ratio of a low temperature in a high temperature reservoirs. This is really, really important. It sets the upper bound for what we can do. So, we're going to take that information and we're going use it right away, so let's take, this is an example that comes up time and time again. These are real world examples here. A heat engine only needs a temperature difference to create work. That's actually a part of the second law of corollaries. So, all we need is a temperature difference, and I can create work. Some people propose that the temperature difference between the water at the surface of the ocean, which is about 22 degrees Celsius. And the temperature at the ocean floor, which is about 4 degrees Celsius. So, if you're about 2,000 meters below sea level that that temperature difference, from the top of the ocean, to the bottom of the ocean, could be used to create a power plant, from this free and sustainable resource. So, what is the maximum thermodynamic efficiency of such a system? You're completely empowered to answer this question. The answer is, of course, the Carnot efficiency defined by those two limiting temperatures. So, you go ahead, write down your expression for the Carnot efficiency, recognize these temperatures are in Celsius. Every time you do anything in thermodynamic's analysis, you have to use absolute temperatures. So, we have to convert those to Kelvin. And so, we do that and we get 277 Kelvin divided by 295 Kelvin. And what we find is that the Carnot efficiency, which is the maximum efficiency we can ever get from this power plant is 6.1%. So, it's really, really low. So, while the resource is free and completely sustainable, we think, the efficiency of such a system is extraordinarily low. And, of course, the real world, we wouldn't even achieve the maximum efficiency. So 6%, while it's the best we can hope for, we wouldn't get anywhere close to that. Okay. So, I want you to keep thinking about this system. These are kind of our get rich quick schemes. Maybe we could use the ocean to power for the whole world. Okay, although it's a low efficiency, you've got a planet that is pretty much dominated by ocean. So, there's a lot of ocean to go around, so maybe we can overcome the low efficiency with scale, you got lots of ocean. What would be some of the practical challenges to such a power plant? I want you think of a list of like three challenges to implementing such a technology. And we'll start with that next time.
