First Law of Thermodynamics

All right. So far in the thermodynamics class or series of segments we have been waiting for this very moment. This is the first big concept that we have, okay. First law of thermodynamics. We also refer to it as conservation of energy because at the end we talk about energy can be conserved, etc., okay. And in the fluid mechanics class, for instance, we take this, we call this a conservation of energy and apply it to fluidic system. So it's very related to the thermodynamics. Okay. But I mentioned this at the beginning of these segments, saying that energy can neither be created nor destroyed, right, but it can change forms. Okay. But before I go ahead and write some equations that will help me with that, I want to take a more fundamental view and talk about this. Let's say that I have an income. It doesn't have to be dollars. I said dollar, but it's some type of a number, okay. 1,000 units. It doesn't have to be dollars. So, and let's say that this is my monthly income, and every month I'm spending, let's say, eleven hundred dollars. So everything that I, you know, spend adds up to eleven hundred dollars. Some to the rent, some to the car payments, some to the educational loans that you have, food, etc., right, entertainment, whatever. So, okay. If this is an income to me and this is kind of like, let's say, this is my system, so this is coming in, there's a thousand, and this is leaving as 1,100. What's happening every month? So I have a deficit of this amount, right? 100. What I just explained is from a finance point of view, but it is still the same thing that I will be discussing in here, except about these, you know, dollar signs or any unit that you want. I'm going to look at the change in the energy, okay. And if I want to write this this way, first law, here is what it says, okay? Total energy transfer into the system, total energy in it, total energy transfer. We talked about total energy transfer. What are the methods of it? I'll revisit it, but I have already discussed that. Total energy transfer basically is leaving the system, right. This is into the system, and total energy transfer out of the system, right? So now, okay, so far so good. What this inner total energy transfer into the system is like is this income, right. Income is this, and my system, I'm leaving this. So, for instance, the right-hand side will be minus 100 in this particular case, correct? And then we are going to say the change in total energy or total money in that particular example, okay. And I can do even better than that, because I don't want to deal with these terminologies. I can call this in energy, in energy, out is equal to delta E of the system. Delta is highlighting that this is a change, okay. Okay. So this really is the first law. This is the fundamental first law that I'm talking about. The only thing is, in here I explained this is, you know, this number is this in, right. Right now this heat transfer, work, mass can be all part of the energy transfer, right? So I want to, you know, discuss that. But before that, let me actually go ahead and discuss, you know, let's put some numbers. So I'm going to say like, you know, two minus three is equal to one kind of deal, right. Well, not mathematically, but you see where I’m going, right. In terms of the terminologies that I use. So let's look at one. The one is E system. So let's discuss that for a minute. I had a, you know, I had discussed that if this is a simple compressible system, then I'm going to have the kinetic energy, I will have the potential energy, as well as the internal energy. These two are the macroscopic forms of energy. This is a microscopic form of the energy, okay. And this will be one half m V square plus m g z plus m specific internal energy times the mass, okay. But now I'm looking at this delta E system, okay. So that what it means is I'm going to look at delta kinetic energy plus delta potential energy plus delta internal energy, okay. And then I can write this this way. Kinetic energy at the 2 minus kinetic energy at the 1, right, plus I can have potential energy at the 2 minus potential energy at the 1, plus internal energy at the 2 minus internal energy at the 1. So that's pretty much it, okay. For, you know, so there are actually three terms in here. I say that the total change of energy, but these are going to be it, okay. So let me ask you a question. If my system is stationary, what would be the change in the system energy? It's a stationary system. Okay. Stationary means that, looking over here, the velocity will be zero. Stationary. So this, this term drops out. What about the potential energy? Yes, the system will have the potential energy. I have a segment on this as well. I had the ball here. Depending on the datum, I will be able to call the energy of the system as different values because I will select different datum values, etc. But look what I'm doing in here. I'm looking at the energy difference. As long as I selected the same datum, right, one datum like in here versus there, then the potential energy change will be zero. So what I'm saying is that if my system is stationary, we use this often, okay, then delta E system actually will just be delta U, okay. That will be just delta U. So that will come in handy at some point in time, okay. And that's all I want to talk about the item number one. And now I'm gonna look at the item number two and three, and I will basically discuss them together, because one is out, one is in. And so basically, one has a positive, one has a negative in front of it, and you have it in the equation over there. Okay, but let me repeat, basically because I said that for closed the systems, right, if the system is closed and I call this control mass, right, what I will have is this two and three will have two components, okay? I will have heat transfer, and I will have work. Okay? That's the two forms that I have.If I have an open system, for open systems, which they also refer to as control volume, right, now I will have heat, no question about it. Same thing as work. But now the mass leaving or entering the system will bring its energy into the system or out of the system as well. Okay, so if I write this mathematically, what I just said, because I have some letters abbreviated for each term, let's say E in minus E out. So this is term number two minus term number three will be Q in, Q is the heat transfer, right? Q out, plus work in minus work out. Let's write the most general one: E mass in minus E mass out. Okay, and let's put a note over here. So this particular term, zero for control mass, right, because the mass, there’s no mass transfer, so it cannot carry its energy out or into the system. Okay, and if I'm looking at the units, so that's pretty much it, you know, in terms of what I want to cover. Once I cover all the stuff that I did, the rest covering the first law is piece of cake, kind of, you know, like adding a couple terms and equating to some other. So it's really a high school or lower-level mathematics is required for this particular case. Okay, the big elephant in the room at this point is the U though. Okay, so this I said delta U. How am I going to calculate the delta U? I'll address that in Module 3. So for now, so far we're not really dealing with that. Okay, so what's the unit so far? Right, so I have dealt with the energy and energy units. If I have like a pair, let's call it the SI, British gravitational pair, you're going to have joule or Btu. And most of the time it's going to be kilojoules because joules is kind of small. Okay, and I can also write this in rate form, right? This particular equation then it's going to be E dot in, energy rate entering, minus energy leaving will be Q dot in, which is heat transfer rate. This is power in minus power out and mass transfer rate in minus mass transfer rate out. Okay, so what will be the units in that particular combo that I write over here? This is going to be watts. Right, W will be sufficient. And Btu per hour will be another one, or if you want to be consistent with this type of writing, this can be said joule per second as well. Okay, I can also write this, you know, I'm running out of energy, pun intended, over here. Is that I can also write this in, you know, this equation in unit mass, right? Because you see going up here, I said, I didn't write it, but probably I will at the end of the day. But you see over here, so I can divide everything by mass. This goes away, this goes away, this goes away, right? So why don't I, you know, write it? Because I might as well, right? e in minus e out will be delta e of the system. Okay, so this e in will be basically everything that you see in lowercase. Lowercase, but not here actually, here but lowercase q, lowercase q, lowercase w, lowercase w, lowercase e, lowercase e. And the right-hand side, delta e system. And I want to write that because that's going to be V square over 2 plus gz plus the internal energy, or rather more, specific internal energy. Okay, and the unit this time around in terms of the pair is joule per kilogram. This was joule per second, right? And I'm going to have Btu per pound mass. That will be my unit pairs. Okay, so the only thing that I want to cover, and sometimes we, you know, some resources are finishing over here, but if you remember I had a convention, sign conventions, right? So just give me one second. Let me copy paste it over here and I'll be right back. Okay, it will be more convenient. I don't want to rewrite the same thing I did. Okay, so I'm back. So this is from the previous segment. I'll put the link over here as well at the right-hand side top. But the point is this. I have, if as long as the heat is coming into my system, I positive. If it's leaving, it's negative. Fine. Good. Here's the problem we talked about. If I have the work out, I'm going to put a positive. And here's, I'm going to work in, it's going to be the negative. Right, so then, okay, so I can still, for a closed system, because it's a closed system, at the end of the day, it doesn't matter. E in minus E out can easily be written this way. And as long as you know what you're doing, this is just perfectly fine. Okay, W in minus W out. Right, because when I have a work input to my system, work done on the system, what I will have is I will have increased energy, right? When I have the work done by the system, this will decrease the energy of my system. Okay, so this is fine. But you can see in here, this we have an issue. So this is positive, so it's supposed to be negative. So then I need a negative in between those two. Okay, so if I write this this way, and we use this in fluid mechanics this way as well, Q Net minus W Net. Okay, you can see over here what is happening. So this W Net is defined as basically work out minus work in. Isn't it? You know, because if you put a negative sign this, you get that equation. And Q, on the other hand, Q Net is defined as Q in minus Q out. Okay, you may not like it. You might not have to use it. As long as you know what you're doing, I'm okay with that. Some resources and professors call the plus sign over here, and they just define this as this, which is fine. There's nothing wrong with that. Only the problem with that approach is the FE exam follows this format. Okay, and let's also talk about a cycle. We talked about what a cycle is. So basically I start from the state, I go to state number two, then I go to state number three, and then I come right back to state number one, right? So in this kind of case, you can see as my, looking over here, I'm looking at the energy change, right? The energy change. So looking in here, so the right here, the change will be zero because the end state and the initial state is the same. So three is equal to, rather four is equal to one in this particular case. So if you want to call this one as four, like one to two, two to three, three to four, but the four is equal to one. So then delta E will be zero. So what does this mean about that equation that I write over here? This is another convenience. By putting a negative sign is that you're going to get Q Net minus W Net will be equal to zero. And if I move one of them to the other side, I will get Q Net will be equal to W Net. Right, the net, basically the net heat transfer coming into my system, will be coming out as the work output from the system. Okay, so this is, you know, we use this often as well. Okay, right. So that's all I have about the first law. Not a lot. It's kind of simple after we discuss all these. So now I'll be back with an example to illustrate how these all come together. Okay, thank you for watching this.