 Chapter 2 is all about energy. We are starting to get into actual energy analysis. We are keeping track of energy and using our understanding of how it behaves to predict what's going to happen in the real world. This is where we actually get into thermodynamics. This is the actual point at which we are starting to use thermodynamic analysis. Note that the first law of thermodynamics is the law of conservation of energy and we are using that to predict behavior of energy. Because energy can't be created nor destroyed, any energy that enters a system either stays there or it doesn't. If you have a building and two people enter and if humans can't be created nor destroyed and you see one leave, there must be one human from that group still in the building. That is the analysis we are applying to our systems. And in an effort to start as simple as possible, we are removing as many variables as we possibly can. So we are analyzing either closed or isolated systems so that we don't have to worry about mass crossing the boundary yet and we are considering only ideal gases or some very specific types of solids. That limits actual substances from our analysis. We have a very convenient way to keep track of the properties of the substances we are analyzing. We don't have to get into how actual real substances behave. We are keeping things as simple as we can. Let's try out our first law reasoning by considering a special room. It's perfectly sealed so no air can go in or come out and it's well insulated. Meaning no heat transfer can cross the boundary of the room. If I were to plug in a fan in this room and turn it on and leave it over time what would happen to the temperature of the air in the room? Would it go up, go down, or stay the same? The correct answer is it would go up over time. But John, I hear you saying, fans make things cold. No they don't. A fan makes you feel cold if you're sitting in front of it because it is pushing air over your skin. The moving air over your skin is able to pull more heat out of your skin than stationary air would be or rather air driven by natural passive convection. You're losing more heat to the atmosphere which makes you feel cooler but the fan is just converting electrical energy into mechanical energy into kinetic energy of the air. We have energy entering our room in the form of electricity at the outlet and it is going through a series of conversions until it manifests as kinetic energy of air. Well, that kinetic energy of air is eventually going to go into friction and therefore into thermal energy of the room or rather the air in the room. So the temperature of the air in the room will increase over time. That type of consideration is what we are using the first law for. We look at where energy enters where it could leave and we use that difference to represent the energy change of a system. To try a slightly different example, what if instead of a fan it was a fridge? We have a refrigerator running in a room that is perfectly sealed and perfectly insulated and just to add another variable into the mix, what if I told you that that fridge was perfect? It was as ideal a fridge as you could possibly build. What would happen to the temperature of the air in the room? The temperature of the air in the room would still increase. We know that because we have energy entering and it can't leave. Even if the fridge is operating as perfectly as it possibly can you are still paying an investment of energy to move heat around. Just like how the fan converts electricity into moving air the refrigerator is converting electricity into moving heat around. That movement of heat is eventually going to manifest as an increase in temperature of the air in the room on average overall. I will point out that just like the fan the refrigerator doesn't create coal. For our purposes there is no such thing as coal, it is just the absence of heat. Just like a flashlight is not a darkness vacuum, it is a light emitter, right? The fridge makes things inside of it cooler by removing heat from them. It pulls the heat away from the stuff inside and pushes it out the back. That movement of energy around is what you are getting for your investment of energy in the form of electricity. The temperature of the air increases as a result of the fact that we have energy entering and it can't leave. When we talk about energy we are going to be talking about a whole bunch of different varieties of energy. And the analogy I like to use for this is that of Billy and his parent. You imagine Billy as a child in a bedroom who really loves his blocks and every night before Billy goes to bed his parent has to come in and convince Billy that all the blocks are accounted for. Every night Billy's parent counts the blocks and says to Billy hey we have 26 blocks we had 26 blocks yesterday we've had 26 blocks for all of eternity. Therefore we have all the blocks and Billy knowing this fact will go peacefully to sleep. Well what if one day Billy woke up and there were only 25 blocks? Billy screams his parent comes in and together they search for that extra block. Well the parent notices that a window is broken and that extra block was laying outside. Well we could say that the number of blocks seen might encompass the blocks inside the room plus any blocks that left the room. Similarly if the next day one of Billy's friends came over and left one of their blocks Billy's parent might count 27 blocks. That means all of Billy's blocks are accounted for plus the one that was added by the friend. So maybe Billy's parent overcomes this by locking the door preventing any visitors from seeing Billy and then making sure that the window is perfectly sealed and made out of a strong enough material that Billy cannot possibly push blocks through the window. Then we could say the number of blocks seen in the room must be 26 or rather the number of blocks in the room must be 26 because they can't leave. Also for the purposes of this discussion blocks can't be created nor destroyed. Well let's imagine that one day Billy panics he only finds 25 blocks and Billy's parent comes in and says ah yes you're right there are only 25 blocks but the parent notices that Billy's toy chest is sitting slightly lower in the carpet than it normally does. Ah Billy's parent thinks that extra block must be in the toy chest. The parent goes over tries to open the toy chest and Billy freaks out. Parent he says you cannot violate my fourth amendment rights you cannot search that chest without any reason behind it and Billy's parent respects Billy's rights and does not open the toy chest. But Billy's parent knows that that toy chest always weighs 30 pounds. So if it always weighs 30 pounds and if Billy's parent were to measure the weight of the toy chest and subtract 30 pounds that difference in weight must represent how many blocks are in the toy chest. So maybe we could say 26 is going to be the number of blocks seen plus weight of chest minus 30 pounds divided by the weight of a block. That allows us to say that the number of blocks seen plus the number of blocks that must be in the chest as a result of weighing the chest still adds up to 26. Okay well Billy is satisfied with this explanation and this reasoning and all is well for a couple more days until Billy notices that there are only 23 blocks and doing the math performing some weight analysis on the toy chest they observe that there are only two blocks in the toy chest where is that missing block Billy demands? Well Billy's parent looks around and observes that Billy's bathwater is awfully dirty. Furthermore it's sitting a little bit higher than it normally does and that bathwater has never changed it's always the same water and somehow it doesn't evaporate so it's the same water at all times. If it's a little higher that implies that there must be something else in there something like perhaps a toy block. So we can take the same approach to Billy's bathtub that we did to the toy chest. We could say maybe the volume of water inside the bathtub minus the volume of water normally divided by the volume occupied by a single block must represent how many blocks are in the bathtub. Now we could keep going with this and come up with different ways of accounting for blocks appearing in different places but the point of the matter is this, the blocks must be somewhere. This is perhaps a bizarre but accurate way to think about energy. We know that the energy can't be created nor destroyed therefore it must exist somewhere. The difference between this analogy and actual energy is that we can't see the energy. All we can do is account for it in different ways. When we consider different types of energy we are considering ways in which those blocks are manifesting that we can observe. And by understanding how that energy affects the situation we can deduce how much energy there must be. We can't see the energy, we can't count it directly, we can only account for it as it appears in other forms. Does that make sense? So we might account for mechanical energy by looking at perhaps a rotating shaft. We might account for kinetic energy by looking at something moving or something's velocity having changed. We might account for thermal energy by determining a temperature and figuring out how much energy is associated with a change in temperature, etc. I will also point out that most of this is the result of empirical analysis. You are performing experiments, you are observing how you convert energy from one form to another and you deduce something about how much energy there must have been as a result. Our units of energy are only as arbitrary as the conversions we used to determine them. For our purposes we are going to limit reality down to a couple of specific types of energy to start. We are going to consider macroscopic energy and microscopic energy. Those two categories will make up all of our total energy. Macroscopic energy is the energy inherent to the situation that the thing is in. Microscopic energy is the energy inherent to the thing. You can think of it like the energy of the thing and the energy inside the thing if you like. Furthermore, in our notational scheme we are going to call total energy uppercase E. That's the total energy of the thing that we're considering which is what we call a system. Uppercase E is the total energy of a system. Furthermore, within our notational scheme we will use a dot to indicate a rate of change with respect to time. So you could call that the rate of change of the energy of our system with respect to time. And we will use lowercase letters to indicate specific properties. So lowercase E is uppercase E divided by mass. That makes it an intensive property. This would be the specific energy of our system. And we are saying the total energy is going to be the combination of the macroscopic energy minus the microscopic energy. And by establishing this distinction we can consider macroscopic and microscopic energy sources a little bit more conveniently. Like for example, the only macroscopic energies we will consider are kinetic and potential energy. Note that uppercase KE indicates kinetic energy in the energy dimension as opposed to lowercase KE, which would represent specific kinetic energy, kinetic energy divided by mass. Similarly, lowercase PE is going to represent the total potential energy divided by mass. That makes it specific, therefore intensive. The total kinetic energy we will calculate by taking one half times the mass of our system multiplied by the velocity of our system squared. And that velocity is relative to the surroundings because we are talking about the macroscopic energy, the energy inherent to the situation. And the total potential energy will be calculated by taking the mass times gravity times height. And that height is relative to something else wherein we determine a relative difference in potential energy. So then if specific kinetic energy is total kinetic energy divided by mass, then in taking one half times mass times velocity squared divided by mass, we are left with just one half times velocity squared, which I can write as velocity squared over two. And I can write specific potential energy as being mass times gravity times height divided by mass, which would just be gravity times height. So back in this relationship, I can say macroscopic energy is total kinetic energy plus total potential energy. And if I wanted to, I could also write out lowercase e is equal to lowercase ke plus lowercase pe plus microscopic energy. Same page so far. Okay. When we consider microscopic energy, we are going to be considering four different types of energy. We call them sensible energy, which is the portion of the internal energy of a system associated with the kinetic energies of the molecules. That's a very fancy way of saying sensible energy is the energy associated with temperature. Latent energy is the internal energy associated with the phase of a system. Chemical energy is the internal energy associated with the atomic bonds of a molecule. Nuclear energy is the energy that holds the actual atoms together. So if I were to increase the temperature of my coffee from 60 degrees to 70 degrees Celsius, I am increasing the sensible energy of our coffee. By the way, it's named that because it was sensible to people. That sensible energy increase manifests as an increase in temperature. Latent energy is associated with phase changes. So an easiest way to consider that would be to consider the fact that you feel cold when you step out of a shower. You have a lot of liquid water on your skin that liquid water is evaporating. Going from a liquid to a vapor requires energy. That latent energy required for the phase transition has to come from somewhere, and the closest source of energy for that water to evaporate is you. So the water pulls energy out of you to accomplish its phase change. To accomplish that phase change, we require an investment of latent energy. Similarly, the reason that ice is so much better at cooling my coffee than cold water is because going from solid to liquid requires energy. It requires latent energy, and the source of energy around the ice is coffee. So the sensible energy of my coffee is going into the ice, increasing its latent energy, converting it from a solid to a liquid. Once it becomes liquid water, then the sensible energy of my coffee will decrease and the sensible energy of the water in the coffee will increase until they reach equilibrium. Chemical energy is the energy associated with chemical reactions. If you were to burn a hydrocarbon of your choice, set a big pool of gasoline on fire, you are converting chemical energy into eventually sensible energy. The chemical energy inherent to the gasoline, and I guess the oxygen in the air, is going to be emitted as heat, which is going into the air, which is increasing the air's sensible energy. When we talk about nuclear energy, we are talking about two different types of nuclear energy, nuclear fission and nuclear fusion. So breaking apart the nucleus of an atom, that fission process is going to emit energy and under certain circumstances, if you combine molecules together, you can emit energy, that fusion process creates energy. It's how the sun works. And also I will point out that you can change energies, you can convert energies into different forms, and depending on how you define your system, that energy may start as something else entirely. For example, if we were considering me cooking eggs on top of a skillet on top of a campfire, that energy going into our eggs, my eggs, is going to be coming from the high temperature cast iron in that skillet. The high thermal energy and the high sensible energy of the skillet is pushed through heat transfer into sensible energy of the eggs. Well, where did that energy come from? If we expand our scope a little bit and consider the fire, the chemical energy of the carbon atoms inside of the wood and the oxygen atoms in the air are coming together and they are releasing energy. And if you go back even further, that energy came from the sun. Some hydrogen atoms that rammed together that turned into helium or helium atoms that came together, et cetera, and that fusion process emitted energy. It emitted energy in the form of photons. And those photons just spread through space and then eventually, a couple of them were coming down next to a tree and we had some carbon dioxide in the air that got hit by a photon and that carbon dioxide was excited enough that the carbon split off from the oxygen and the tree nearby grabbed the carbon and the carbon said, I'm with the tree now and oxygen was like, it's fine. I don't care. You be with the tree. I'll go do my own thing. I'll go to grad school or whatever. And then those carbon atoms in the tree eventually combusted are broken apart. They pair again with oxygen and that reuniting process emits energy. It's lit, man. And that release of energy is the same energy that entered the carbon dioxide in the first place. The photon came in, split them apart, and by bringing them back together, we are getting that energy back out, which is kind of cool if you think about it. When you're sitting around a campfire, that energy that you're receiving is energy from the sun, right? That's neat. Anyway, that energy could be the nuclear energy in the sun. It could be the chemical energy in the wood and the air. It could be the sensible energy in the cast iron. It could be the sensible energy in the egg. Depending on how you draw your systems, the conversion process could include more or fewer steps. All of that aside, when we talk about microscopic energy, we use a shorthand to refer to all four of these. That shorthand is internal energy. Internal energy is sensible energy plus latent energy plus chemical energy plus nuclear energy. We use another shorthand for the combination of sensible and latent energy. That's thermal energy. These are just nicknames. The variable we use to represent internal energy is u. And just like the rest of our notational scheme, uppercase u represents total internal energy. Lowercase u represents specific internal energy, which would be total internal energy divided by mass. And internal energy is the combination of sensible energy and latent energy and chemical energy and nuclear energy. So coming back to this form, I can shorthand all of those microscopic energies as u. Therefore, I can say e is equal to ke plus pe plus u. Or I can say delta e, the change in energy of a system, is going to be the change in kinetic energy plus the change in potential energy plus the change in total internal energy. And similarly, I can say the change in specific energy of our system would be the change in specific kinetic energy plus the change in specific potential energy plus the change in specific internal energy. Okay, while we're here defining things, I want to review the fact that E dot represents the EDT. And if I'm talking about the rate of change of energy of our system with respect to time, then that is going to be the combination of how the kinetic energy is changing with respect to time, and the potential energy is changing with respect to time and how the internal energy is changing with respect to time. So it's D, DT of U plus KE plus P. The next observation I want to make is that as per the conservation of energy, energy cannot be created nor destroyed, energy that enters something either leaves or it doesn't. Those are the options. Again, if you put five kilojoules of energy into the box and three kilojoules come back out, then the change of energy of the box must have been two kilojoules. That accounting of energy is what we're here to do. That is first law analysis. We formalize that a little bit by writing out delta E, the change in energy of our system, is energy entering the system minus energy exiting the system. This is our first law of thermodynamics and this relationship is called the energy balance. Basically, every thermal problem boils down to applying an energy balance. We do that at some point. This is our first law analysis and it's what chapter two was all about. All we really have to do is figure out how energy is manifesting in these three forms. So, so far we've talked about that left-hand side. Next we can talk about the right-hand side. For our purposes, the energy on the left is the energy in the system and we call that static energy. That's not to say it isn't changing. That's just the energy that's inside the system. On the right we have what we call dynamic energy, which is energy that is crossing the boundary of our system. And just like with our static energy, which we break apart into other categories for convenience, we have categories for dynamic energy as well. For that, let's jump over a couple slides. Again, static energy is the energy that is contained or stored within the system. Dynamic energy is the energy interacting with surroundings. It's crossing the boundary of our system. For our purposes, we consider three possible forms of dynamic energy. Energy entering or exiting the system as work, energy entering or exiting the system as heat transfer, and energy entering or exiting our system as mass. Therefore, when we talk about a closed system where energy can enter and exit as heat or work, our energy balance can be written out with those work in and heat transfer in terms and work out and heat transfer out terms. For a closed system, energy can enter as heat transfer and work. We abbreviate heat transfer with the letter Q, we abbreviate work with the letter W. So the energy entering for a closed system is either heat transfer and or work. And the energy exiting is either heat transfer and or work. So if we write out delta E is equal to E in minus E out for a closed system specifically, that means that we're saying energy is either entering as heat transfer and or work, and energy is exiting as either heat transfer and or work. Those are substitutions that we can make within our energy balance. We can account for the energy entering as heat transfer or work or both. We can account for the energy exiting as heat transfer or work or both. And don't forget again those static energy terms that we just defined, internal energy, kinetic energy, potential energy. And in the event of an open system, we add mass into this mix and the energy associated with it. Following our notational scheme, specific heat transfer is total heat transfer divided by mass and would be expressed as a lowercase q and lowercase work would be specific work, lowercase w, I mean, would be specific work and that would be total work divided by mass. Let's try a couple example problems.