Let's engage the first law of thermodynamics. Classical Thermodynamics. So, thermodynamics has at its foundation three fundamental laws. And with considerable lack of imagination, they are named the first law, the second law and the Third Law. There are no known exceptions to these laws. You might recall in the first week I discussed an attempt by an American inventor to manufacture an exception to the First Law, it was unsuccessful. We're going to study the First Law, which is remarkably simple and yet remarkable powerful. And you can answer important questions, such as does a gas cool upon expansion? What are energy changes associated with chemical reactions? Exclusively from knowledge of the first law of thermodynamics. The first law can be expressed in a variety of ways. A colloquial one that's reasonably simple to remember and reasonably accurate is to say that energy can be neither created nor destroyed, but it may be distributed in different ways. And put even more succinctly, we could say: energy is conserved. So, let me spend a little time talking about the history of the first law before we dive into any equations. And shown on this slide is Antoine Lavoisier. So, a father of modern chemistry. It turns out if you trace research advisors back, I trace back to Lavoisier. So, I just love looking at my great great great dissertation grandfather, perhaps. And he's shown here with Madame Lavoisier, who helped him in his scientific studies. So, they were a team, and it looks like they have some interesting piece of apparatus there, along with a feather quill. One did science in different ways back in those times. So, this was not one of Lavoisier's glorious moments. in fact, when it comes to thermodynamics, and in particular, what I want to talk about is heat. So going back to the ancients, there has been considerable philosophic and philosophical, and scientific discussion of what is heat? And so, Lavoisier who did wonderful things for chemistry. He eliminated the phlogiston theory of chemistry, which said that when you burned things, stuff left those things, as opposed to actually oxygen adds to those things we know now. But at that time, people thought phlogiston was being liberated when you burn something. So, score one for the Lavoisier there. But when it came to heat, actually he had an incorrect view of things. He said that heat was an invisible fluid and it was called caloric, and it flowed from warm bodies to cooler ones, that's how heat was transferred. There was this flow of heat, and you know given the opportunities to do experimental science at the time, that was an assumption that people bought into. Lavoisier, as long as we're doing history, he had sort of an unfortunate end, he was guillotined in the terror of the French revolution. It turns out, it was hard to make your living as a scientist in those days. instead he was also a tax collector for the royal family. And as, as a farmer generally it was known as these tax collectors, that did not endear him to the French people when the revolution came along. So, it was said that Europe's best head was severed from its shoulders when he was guillotined. But he did make wonderful contributions to chemistry, and we remember them even if caloric wasn't one of them. So, let's move to another person in the history of the first law. And that would be Benjamin Thompson or Count Rumford, as he became. So Count Rumford did quite a number of things. Amongst other things, he was a British soldier or spy during the American revolution in the colonies. But he survived that experience. And at some point, when he was in Germany, he was boring out canons. And notice that the canon became hot as you were drilling into a solid piece of brass for example, to make the tube for the canon. And immersed that cannon into a vat of water and discovered that the water could be made to boil. And this was not consistent with the caloric view of heat, because it seemed that you could indefinitely just keep creating this heat as you were boring. And he did other experiments that showed there was no mass associated with this heat transfer. And so, he presented a paper to philosophical transactions, volume 88. Where he said, based on his analysis of weights and temperatures, that there was an equivalence between work and heat. And that heat was a form of motion. And so that was quite controversial, but also quite interesting at the time. And it was really expanded upon and put on its soundest scientific footing by James Prescott Joule. And so Joule, for whom the unit of energy is named, the Joule. And Joule built this wonderful experimental apparatus that you see here. So, this is a weight running over a pulley, wound in a spool like fashion around this cylinder, which as the weight descends and it pulls on the string and it causes this cylinder to revolve, it spins some paddles in a vat of water. And it's done relatively slowly. The weight is falling relatively slowly. And the water is insulated from the surroundings, and just look at the temperature of the water. And what Joule showed was that the work associated with a weight moving in a gravity field was transformed into heat, and it would increase the temperature of the water. And he did very careful measurements, and established this equivalence between heat and work. In fact Joule made many contributions. it was really Joule's work together with Prescott which sort of developed the first way to do refrigeration through gas expansion and generating cooling power by expanding gases into volumes. So, a very practical problem obviously. Well, let's leave the personages of thermodynamic history and actually put a few definitions on the table that will help us to discuss the concepts associated with the First Law. So, there are two ways that energy can be transferred between a system and its surroundings. So, the first thing to do is, let's define system and surroundings. System, that's the part of the world under investigation. What we're interested in. Surroundings, everything else. So, unless the system we're interested is the entire Universe, which it could be, but most of the it won't be. then the surroundings will be the Universe, and the system will be any little subset of the Universe we're interested in. Well, the two ways we can transfer energy between those two things are work and heat. And so, let's talk about what those are. Work, often abbreviated with a little w, is the transfer of energy as a result of unbalanced forces. So, maybe a big weight on top of something and we remove a block, and foom, that weight's going to fall down because of gravity. We're going to adopt a convention. And that is, we're going to call work a positive quantity when it does work on the system. That is, it causes the energy of the system to increase. So, positive energy. Po, excuse me, positive work means the energy of the system increases. We say work is done on the system. The opposite case, negative work. That is where the system is doing work on the surroundings. And that's just a convention we need to adopt. What, what does the sign mean. Similarly, we need a convention for heat. And so, our convention will be that when heat is added to the system, that is positive heat. When heat is extracted from the system, that is negative heat. And so what is heat itself? It is a transfer of energy resulting from a temperature difference. So that is sometimes called the zeroth law of thermodynamics. It's not an assumption, it's a law. You can prove it, we won't. But and that law says: two bodies in contact at different temperatures will flow heat from the hotter one to the cooler one, until they are both the same temperature. Right? So that flow of heat is positive when the heat is being added to the system we're interested in. It's negative, if it's the other way around. So, let me talk a bit more then about what is the work done by gas on a surroundings, for example, with a specific example. So, let me do an expansion. So, it's work, that is, it is a result of unbalanced forces. And so, if I take a look at this experimental apparatus, I've got a gas inside this cylinder. There is a piston head on top of the cylinder with a mass on top. And right now, it's blocked with some pins. When I remove those pins, the pressure on the inside is unbalanced relative to this mass, and as a result it raises the mass until the pressures are equalized. So work is done in raising a mass a distance, and in this case I've emphasized the distance h. And the reason it's work is, it's in a gravity field. So, it must be the case that the initial pressure of this gas is greater than the external pressure. And what is the external pressure? It's mass times the gravitational constant divided by the area of the piston, and that defines pressure in classical physics. The final pressure of the gas is going to be equal to the external pressure, on the equilibrium, not rising and falling anymore. And so, the work then, is minus Mgh, that's classical physics again. If I introduce the area in the denominator and in the numerator, then I'll have pressure here on this side, force divided by area. I've got a volume one this side, area times a height. And so, work that can be done on the surroundings by gas is minus the external pressure. Minus because that's our sign convention, minus the external pressure times the change in the volume, and the volume got bigger. Alright? So, because delta v is positive and w must be negative, we must have this negative sign in our expression. That is the pressure volume work that a gas can do. So, let's take a moment here and I'll let you work with that equation briefly, and then we'll come back. Well lets wrap up by considering the, the converse of the gas expanding against the surroundings. What about the case where the gas is compressed by the surroundings? And so, that's a slightly different set of unbalanced forces that I've shown in this schematic for an experimental system. Now, my pins are in a different position, they are underneath the piston head. There is a mass on top of the piston head, which is exerting a pressure that is greater than the internal pressure of the gas. And as a result when I remove the pins, that piston head is going to compress. The gas pressure will increase as it's being compressed until it reaches a final pressure equal to the external pressure. We set up the equations in exactly the same way. We'll get exactly the same work expression. The difference of course, is that the change in volume is not positive here, it's negative. And so, that's consistent with our sign convention. We want the work to be a positive quantity, when work is done on the system. So, minus the external pressure times a negative volume change will give a positive work, and that's what we want. Alright, so we're going to take a look at PV work in considerably more detail. Because understanding what kind of work gases can do, or work can be done on gases is critical to appreciating the concepts that are associated with the first law. And so in the next lecture, we'll take a look at the different paths by which we might go about doing or extracting PV work.