 Right. First, an announcement. There's bad news and good news, which you want first. The bad news is we made a mistake grading the exam. So do you want the good news? Yes. The good news is we are too lazy to dig through all those scanned files, so we're going to give everybody 20 points as if they got it right. Next exam, we are not going to make any mistakes. I think the mistake was only on Form D. The first two problems are all backwards. But we don't want to dig through them all, so we're just going to make sure everybody got that right. So there you go. I think some of you needed those points. Okay, let's continue. Today we're going to talk about the problems of thermochemistry, heat work, and the first law of thermodynamics. Remember, scientific laws are generalizations of observations. And the law only applies in the limits where you've observed things, not outside those limits. But we've pretty much done that. Outside those limits. But we've pretty much observed things like heat and work for eons. And we feel that we understand what's going on fairly well. However, it's interesting. It's very difficult to define energy. Everywhere it can manifest itself in different forms. Ever present can never be destroyed or created. In a way, energy is the scientist's God. Difficult to understand, but everywhere. We can broadly classify energy. This is very broad brush strokes, but it'll do. We're going into two forms. Work and heat. And work is much more useful. Nobody says I'm going to go to heat and earn some money. So work is going to be the useful kind of energy. And useful for us is going to mean that whatever you're going to call work has been converted 100% to lifting a weight in the surroundings. If what you can do can do that, that's going to constitute work. Then if we want to get the energy back, we let the weight drop. And we do something with it. So an elevator that has to go up is doing work because you're pulling the big compartment up plus all the tonnage of the people on board. And that's why you take the stairs and leave the elevator off so as to not waste energy. We'll figure out what the term waste energy means a little bit later. Since energy is conserved, you can't possibly waste it because it's constant. Heat is the amount of energy that can be used to raise the temperature of something like water. If I take a gas flame, I can heat water with it, but I can't lift a barbell up in the air with a gas torch. No matter how much I put the flames on it from below, heat it up like crazy, I notice that it doesn't go anywhere. And that's because heat is disordered energy. That's how all energy ends up in the end as heat. Every jewel of energy ends up as heat. You eat and you're hot. You're producing heat as you run. Your body. And that's controlled because if you get too hot, your sweat pours open and you start evaporating water. And that was the big worry about the runners, but of course they overdid it. And some energy can have both work and heat. It just depends. So work is a coherent, directed form of energy. An object that's moving, if it's a macroscopic object, then if it's moving, then all the atoms and molecules in the object are moving together. They're held together by their intermolecular forces and by chemical bonds. And then the whole thing, so all the atoms are moving together. That can't happen by accident. That's somebody doing something, throwing something. I think rocks don't just start jumping up out of the ground. And your eye picks this up. Your eye is a derivative detector. That's why animals, when we walk around, they just hold still and you walk straight by them. But if they move, you know that something's alive. You look, you see it. They camouflage themselves by playing dead and just sitting there. If you see coherent something coming, moving, it could be dangerous. If it's bigger than you, you run. If it's a rock, you duck. If it's a car, you get out of the way. But you notice it right away. And that's why you don't want a device that has moving things on it that distract your eye when you're doing something else. You just walk off and fall down the stairs because you're fiddling around with something. Batteries are electric chemical devices. We'll talk about them a bit. And they can be used to do work, obviously. You can have an electric car or an electric train and so forth. And it could run on batteries, although, as it turns out, batteries are so wimpy that they aren't very, very useful yet. Heat, on the other hand, is an incoherent, undirected form of energy. In the case of heat, what happens is the atoms are basically moving faster if we heat them up. But they aren't moving together. And that's a huge difference. I can have a lot of energy supplied as heat, and it's useless to get something done unless I design a heat engine or some kind of engine to convert some of the heat to work. But if I just try to use heat alone, and I take a ball here and I put it here and I put a flame under it, there's plenty of energy if I figure out how many joules. But because it's all random, I don't get any coherent motion from the ball. I have to do something special, like have a cannon with a barrel, and then I blow something up and then the compressed gas pushes it, and I only get a fraction of the energy into the projectile. The rest heats up the barrel and everything else. So I have to put in more gunpowder than I actually would figure to get one-half mv squared for the projectile. Work can be 100% converted into heat. For example, by operating an electric toaster, a scientist I knew decided to monitor his power, his electric power consumption. He connected himself up with the Google meter where he could see instantaneously his electric power consumption on his phone. The first thing he did is he started unplugging all the vampire devices, the electric toothbrush charger, the shaver, and every time he unplugged something, the TV, you don't need a TV that's ready to go on instantaneously because you're never going to turn it on, so you just unplug it. For a while, you throw it away, and you have space for books. One morning, he was looking at his Google phone there, and suddenly the electric power consumption went, and he's looking around, what on earth has happened? His son was making a piece of toast. The next day the toaster disappeared. Sorry, it was busted. Converting work into heat like that should be a crime. If you want to heat up your office, you can either have an electric heater, you just turn it on, nothing happens, it just heats up your office because you're a little cold and you're too lazy to do some jumping jacks, or you can do a calculation on your computer, and it'll produce a ton of heat, and you get the calculation for free. When I'm cold in my office, I just do a little bit of work in Mathematica, and it heats up enough, and that's it. We can't, unfortunately, convert heat back into work, 100% efficient. Converting heat to work would be like herding cats. We just can't get all the atoms and molecules to start moving in unison together when they're just going every which way because we can't get in there with little tweezers and say, look, start behaving. We can't control it. And therefore, when we degrade energy finally into heat, we've lost it. If we drop a rubber ball on the floor, it has potential energy MGH when I start out, and then I let it go and it bounces. And it doesn't come quite back up even if it's a really good one to the same height. And if I just watch it, it goes dong, dong, dong, and then it's gone. And the question is, where did the energy go? And the answer is both the ball and the floor are a little bit warmer. But because of the conversion between heat and work, it takes quite a bit of work to make a lot of heat that you would notice. And that's why if you go camping, you forget your matches and you think, hey, I'm going to get two sticks and start doing this stuff. You'll find out how extremely difficult it is to get a fire going by that method. You have to be incredibly determined and you have to have forearms as big as hams too so that you don't get too tired and stop and then it cools off. It's a very inefficient way. It does, in fact, work, but I wouldn't rely on it. If there's a little rain, forget it. You'll never get it going. And this observation that dates back to Joule and perhaps even before Joule, that energy can change forms but is always conserved is the first law of thermodynamics in a nutshell. Energy is conserved. When Southern California Edison sends me a flyer to say conserve energy, I want to call them up and say, well, what else could I possibly do? Have you heard of the first law? Of course, what they really mean is don't convert a useful form of energy into a useless form of energy. That's a little more subtle. More accurately, the energy of an isolated system is constant. An isolated system will give the definition a little bit later but an isolated system is one that cannot exchange mass or a heat or work with the environment. And we could consider the universe, however big it is, to be an isolated system. If we've included everything in it, then however much energy it had when it was created is how much it has today. It's a constant number of Joules, an astronomically big number, but that's it. And when stars burn, they're converting mass into energy into heat and they're degrading the energy. They're taking useful form of energy and turning it into heat and they will all burn out eventually and then everything will be gone at that point. Okay, heat, usually we give it the letter Q. I have no idea where the letter Q came from but it's conventional, small letter. There are capital letters for good things which we'll call state functions, capital letters, and small letters that are wimpy things that aren't as important. We reserve for things like heat. Heat will flow between two objects in thermal contact if they have a different temperature. That may sound a little bit circular but that's essentially how we imagine heat. If we have two objects at different temperatures then if we zoom in on them, the atoms in this guy, even though he hasn't melted, are just moving faster and the atoms in this guy are moving slower. If I bring them into contact, thermal contact, so they touch, the atoms in this guy are like Muhammad Ali, boom, boom, boom, boom at the edge, right? And what happens is they get these guys moving faster and then as they move faster they hit the next guy and so forth and we get a flow of energy which is just like a flow of water downhill that we talk about heat flowing from one place to another as we watch just the excitement move just like watching a wave at a stadium just everybody stands up and the impression is that you've got something moving. As this excitement propagates, we talk about heat flowing from one place to another. There are other forms. Of course, we talked about work and I told you what work is. Electrical energy is also ordered energy. You can do work with it. And energy can also be stored in different kinds of chemical compounds. Coal, natural gas, oil, tar sands, you name it. Where did all the chemical energy that we're pilfering now from these fossil fuels, where did it come from? Anybody? Yeah, exactly right. Organic materials built up since it takes work to build up molecules like that. No, from the sun. It all came from the sun. And the sun is nuclear. So everything is nuclear because all the heat in the earth, geothermal, is nuclear. Without nuclear, you've got nothing. Remember that as time goes forward. The plants die after they've built themselves up, built up cellulose and other things. They die and they go down and they get compressed under incredible pressure and there's a phase diagram. You squeeze the oxygen out of them and you start making long oily things that can compress more. Because as things go down, they may get compressed like crazy. The pressure may be huge. And they sit there a long time. So they've got millions of years to change phase. And we put all that energy in from the sun every day, all those plants, millions of years. And then we burn it all up in 100 years. The optimists say, well we've only gone through half the oil, but you've gone through 100 million years of oil in 100 years. That's not good. Plus, we did that when none of you were here. When I was a kid, none of you were here. Now you're all driving around. What do you suppose is going to happen to the sustainability of that model? It's a big worry. Mass itself, this is the method the sun uses and nuclear power plants, mass itself can be partially converted into energy. And the beauty of this is that c squared is a huge number. 9 times 10 to the 16. That's a lot of energy that you get from a little mass. And that's why the sun can keep on burning incredible power output. Just what impinges on the earth at 93 million miles is a minuscule fraction of the total power output through the whole sphere. It's unbelievable power. The problem is we just can't harvest it very efficiently. There's even more energy in some distant quasar millions of times more than the sun, but that's also useless for us, unfortunately. So there's plenty of energy around, but it may not be where you can get at it. And the fossil fuels have turned out to be the easiest to get at. Any kind of form of energy can be measured in joules, and that's how we usually do it. And whatever you do with work, it's eventually converted into heat. Always. And that's where it ends up. And then, if it's heat all at the same temperature, it's useless because you can't get anything to flow if things are at the same temperature. So you can't get anything done. Eventually, the whole universe cools off to the same temperature, and that's that. Okay, some conventions. For convenience, we divide the universe up into the system. That's what we're interested in. And the surroundings is everything else. We usually focus on the system when we're talking about thermodynamics. But we have to keep in mind that the surroundings are there. And usually the surroundings take a beating. The surroundings get degraded. Systems may be open. That means they can exchange both mass and energy. Or they can be closed. That means they can exchange energy. They could be like a closed flask where I have a chemical reaction and heat could come out into the lab. But no chemicals come out. No mass is exchanged anywhere. That's a closed system. Or it could be isolated. It could be unable to exchange anything with the surroundings. An approximation for that is a very good thermos or a very good doer where we don't let any heat creep in from the surroundings and we don't let any cold come out either. We just keep everything insulated. And we keep the lid on. We don't ever look in either. Isolated systems, of course, are an idealization. Just like an idealized gas, a true isolated system doesn't exist except maybe if you consider the entire universe. And that's kind of a trick because then there's nothing outside it. So, of course, it's isolated because it can't exchange something with something that's not there. Thermodynamics refers to systems that are not changing too fast. They're at equilibrium or they appear to be have settled down. Thermodynamics is the science of after the smoke has cleared. What is it like? Kinetics is exactly how did the bomb go off. And that's much more difficult. Thermodynamics is extremely advanced because it doesn't care how you got from A to B. It just says, where did you start? Where did you finish? Great. Now I'll give you the theory of that. Kinetics says, hey, exactly how did that thing happen when the spark plug fires? Which atom starts reacting? Which hydrogen comes off? How does that propagate? That's much more complicated. And that's incompletely understood even today. A state function, so be the capital letters, is any quantity that depends only on the state of the system. Not how you got there. It depends only on the state of the system. For example, I could have water in equilibrium with ice. I guess that's a scotch. Or I hope it is. Something from the doctor's office perhaps. Or I could have water in equilibrium liquid with vapor here. And to specify the state of the system, we have to specify the temperature, the pressure, the phase, and the composition. If we have more than one kind of stuff in there, we have to say what the mole fraction of each thing is. And once we've specified all those things, then thermodynamics says I don't care how you did that. I don't care if you froze the ice first and let some of it thaw or how you did it. You tell me how it is now and I'll start giving you certain kinds of properties that are conserved. Certain things you can rely on once you specify the state of the system. We're interested in changes in state because a chemical reaction is nothing other than a change in state. We start with particles over here, electrons, protons, neutrons. In most chemical reactions, the protons and neutrons just sit there and then the electrons buzz around and rearrange and they give us a product. And as a chemist, what we want to do is we want to take worthless reactants, do some work and come out with very, very expensive products that we can sell which are made out of the same atoms but just rearranged. We want to take cow manure and end up with steak. Things like that. We can make money doing that because one's much more valuable than the other. And of course that's what a farmer does. They put the cow manure on the corn, they grow the corn, they feed a calf, and round and round they go. Here's a state function I've just called it F for function. And we have an initial state and a final state and the change is the final minus the initial. If F went up, then this is bigger. The final value of F is bigger than the initial value than the change in F is positive if it is lower than the change in F is negative. And the value, the important thing is that the value of delta F depends only on where you start and where you end and not how you did it. You can do it any way. Including and this is important imaginary ways you can imagine a way to go from here to here, that's fine. Still work because you don't have to know how it's done so it doesn't even have to be something you actually did. It could be something you imagine might be possible. And that's the power of this approach because we don't have to do every kind of experiment in the lab. We can do a few simple experiments to track things and get what we want. We don't want to have to do a complicated experiment. Gravitational energy the gravitational potential energy is a state function. It just depends on how high the mass is not how you got it there. And enthalpy capital H is a state function we're going to talk about more. Internal energy capital U, free energy capital G, entropy capital S, Helmholtz energy capital A, and so on. So whenever you see these capital letters you think aha that's a state function and we use a capital K for an equilibrium constant and we always use a lower case K for a kinetic variable because that's going to depend on how you do it. Strictly speaking a state should not change in time which is kind of a contradiction because we're talking about changes in state. But what we mean is we start somewhere and we make good and sure that nothing's changing now and then we let something happen and then we make good and sure nothing further is changing at the end of the difference. How much heat did it produce in a calorimeter or what have you and then we've measured the change in state. But we don't want them to move around too much while we're actually trying to measure them because then we have a lot of difficulty defining what the state is. Operationally then we can define a state as a situation in which there's no enough change or small enough change over time that we can make an accurate measurement that we can home in on it and say, okay we've got the cross hairs on it and it's not moving too fast we can see what we want to measure we can measure the temperature the pressure the composition good ready let the reaction go and then it settles down if we have a temperature that means as we saw with gases they have a characteristic curve Maxwell-Boltzmann distribution and if the gas is at a constant temperature then the molecules have to be following that distribution and that means they're moving in certain ways they can vibrate can be vibrating slow or fast and the number of each molecule that's doing its thing shouldn't be changing a lot sometimes they switch you've got a fast guy vibrating and you've got a slow guy and they collide and now this guy's the fast guy and this guy's the slow guy there and if the energy level occupations stay constant then we have such a thing as a temperature in many situations like in an explosion we don't know what the temperature is because things are changing too fast to measure anything and the things are all over the place to talk about a state okay here's a problem I've got a mass and I moved it up in a uniform gravitational field little g and I want to know which of these have the same change in potential energy anybody want to have a go? no? now let's look we only care about the initial and final points and therefore the ones that have the same initial and final points have the same change in potential energy A, B, C and E have the same change D went higher so there's a different change in potential energy for D but notice we don't care what happened in between just the initial point and the final point what's the difference the length is the same that's the same change in state function well why do we care about state functions? the reason why we focus on state functions is we usually don't know what happened it's very difficult to know in detail what exactly happened I know what reactants I started with I know what products I ended up with but I don't know everything that happened in between exactly which thing did this and which intermediate came and so forth for example in a piston in a car in an internal combustion engine I'd like to burn this stuff this stuff here iso-octane that's 100 octane gas that's the stuff you can't buy at the pump a little bit too expensive you can actually buy even better gas than that I think there's one place in Malibu that sells gas called trick gas 104 octane and all the Ferraris and Lamborghinis and high performance cars are pulling up to fill up there first if you have a car that's that expensive then the 6 bucks a gallon you're paying for trick gases but anyway if you had iso-octane it's got 8 carbons but notice it's not a linear n octane it's branched and it's very important for fuel to be branched the oil companies spent millions of dollars figuring out how to take oil and get branched chain hydrocarbons out of it and the balanced chemical equation then is this guy in 25 or 12 and a half moles of molecular oxygen gives 8 moles of CO2 there's the climate change and 9 moles of H2O we know the balanced reaction and we can measure how much heat comes we can take iso-octane a mole of it put it in an insulated container and burn it all with oxygen completely and we can measure the temperature change and we can figure out how many joules of heat it produced no problem and we can do that for any kind of fuel but we don't know exactly which carbon when the oxygen comes in in the case that 12 and a half first of all where's the half of the oxygen comes in and which of these falls off first what happens in detail well you get all kinds of things when the thing goes boom and the beauty is we don't care for thermodynamics all we care about is how much heat we get when we're done we want to make sure we burn it completely and the car engine doesn't always do that that's part of the reason you have a catalytic converter but we don't need to know the step by step exactly what's happening and that's important because we usually don't know that if we knew all that we could probably design much much better systems ok so here's an example the heat that you get by combustion of iso-octane is minus 5461 kilojoules per mole the negative sign is important because that means the heat is coming out negative delta H means the heat is coming out of the reaction it's producing heat and the heat's going to the surroundings means you put your hand there it feels warm and you have a a linear chain of 7 carbon atoms C7H16 the heat of combustion delta H the enthalpy of combustion is minus 48 47 kilojoules per mole so here's the question which fuel is more efficient per dram because if you're going to truck this stuff around you don't really care per mole you care per gram because when you truck stuff around the heavier it is the more it costs you to move it around well let's figure out what the molar mass is and then go from there so just in round numbers 8 times 12 is 96 plus 18 is 114 then we got 84 plus 16 is 100 they have a slight difference because 7 carbons versus 8 and octane then if you divide this by 114 gives 47.9 kilojoules per gram and heptane is better it gives 48.47 kilojoules per gram because you just move the decimal point but in terms of octane rating iso octane is called 100 octane gas and then heptane is actually called zero octane that means if you go to the stock room and get a big bottle of n heptane and you just walk by somebody's car and pour it in they're going to have a bumpy ride home and they're going to be taking their car to the dealer or perhaps to a mechanic they don't want to get fleeced and that's because the octane rating has nothing to do with the energy the octane rating has to do with the resistance to premature detonation what happens when you squeeze on heptane is that before the piston reaches the bottom of the stroke where you want to spark it it actually starts blowing up and so the engine gets all out of sync and the pistons are supposed to run like you run your legs it's supposed to be a coherent thing they fire this one fires and so on and it's orchestrated and if it starts just firing at random you just lose all the power so it's producing energy but it's not producing any forward motion of the car and this stuff the 100 octane stuff is smooth as silk and this comes right out because it never detonates before you want it to so you've got complete control on it so it has nothing to do with the energy content of the fuel but rather how easy it is to convert the energy into kinetic energy of the car and that depends on engine design other fuels have even higher octane rating or energy content that means they may run very smooth but you need a much bigger tank to go the same distance with the fuel E85 is 105 octane methanol is 113 and ethanol just burning ethanol itself is 116 octane but in terms of energy content they're lower much lower there's only 35 octane but a diesel engine has a completely different design because in a diesel engine there's no spark plug in diesel you first compress the air like crazy big compression ratio from where you start to where you're in then you inject the fuel and it just blows up on itself on its own ignites and blows and because of the compression ratio being very high a diesel engine can have very good efficiency but because of the way it works historically emissions have been a problem if you've ever ridden a bike behind an old diesel car you'll know what I'm talking about you feel like you're being fumigated and so it's very hard to get to where you want to have it with diesel engines you can do it but then there's extra costs to controlling the emissions and you have to pay for those and diesel fuel used to be cheaper than gasoline but now it's not necessarily cheaper than gasoline and so you have to take that into account okay why should we trust the first law with the gases we measured the pressure the temperature volume we got Boyle's law Charles Law and so forth but what about this how can we say that energy is in fact conserved and the best way to show that it has to be true is to assume it's not true and in fact when I was a postdoc at Cal there was a guy hawking a device called a power enhancer I think he was out on Telegraph Avenue and what it would do is you'd put in some current and voltage and you'd get out twice as much current at the same voltage and this thing wasn't connected to anything it wasn't connected to the wall so it just enhanced power he claimed he had a lot of people who were just hanging around listening to him but none of the faculty in the sciences at Berkeley stopped for even a nanosecond to listen to this this proprietary device takes in DC current when you ask him what's in the box man he says I can't tell you got a black box I can't tell you what's in it we'll see what it is in a minute you take in DC current at 12 volts and it produces twice as much DC current at 12 volts that sounds good but that's creating energy there and energy has to come from somewhere if you believe the first law and you pay a small one-time fee and then you connect this thing up and he says you can just run twice as many things so your power bill is much lower I'll sell you four of them and then you can run everything in your house for just a little bit of current in they were quite expensive like $500 but supposedly they worked forever so it was a good investment okay let's construct an argument to demolish this device and prove that it cannot exist the question is how are we going to do it well let's suppose that it does what it says it produces more power and doesn't need to be connected to anything and it keeps doing it forever well then the first thing we could do is we could use one power enhancer since it produces twice as much we could feed two power enhancers off that and since they don't have that and since they produce twice as much we could feed four power enhancers off that and then we could feed eight and sixteen and we could keep going and then we could put in just a little bit of current and we could power the whole state of California out of our large number of power enhancers sitting there and since they don't take anything in no fuel no nothing just black boxes sitting there we have a free source of energy that's one argument but an even more convincing argument is to do it this way you don't need to have thousands of devices and connect them up you can do it this way you can use feedback since it produces twice as much what you do is you route a certain one amp and twelve volts around the input and then you just bleed off one amp and twelve volts forever with not putting in any fuel not connecting it up to a socket nothing forever so now you have a black box that is producing power from nowhere with no source well if such a device existed I assure you we would be selling them nobody has ever been able to do that and that's because a device like that is absurd can't possibly work because it violates the first law of thermodynamics what was in the black box some people did buy them it's just a car battery it runs for couple hours and then it runs out car battery needs to be recharged but by then the guys out of town hey my power and answer doesn't work where is that guy he's got your five hundred bucks for a hundred dollar battery alright let's talk about internal energy this is not quite so familiar as enthalpy enthalpy we encounter all the time but internal energy is just the energy contained within the system and it's a state function and we're going to see that it consists of two parts for any system that can produce heat and work whatever heat and work it produces must add up to the change in the internal energy as the real power and answer runs and the battery discharges the internal energy of the battery is going down and down and down and down as we bleed off the energy and so whatever heat and work are involved they have to add up the total has to add up to the change in internal energy and this is another formulation of the first law if I have a system and it changes internal energy it has to add up to heat and that's how this works the question is can we use a delta q can we say for any system undergoing a change from some initial to final state could the change in heat and work also be written delta q is the heat of the final minus the heat of the initial and delta w is the work of the final minus the work of the initial and the work because heat and work can exchange so work is like your savings account and heat is like your checking account and the two added together tell you how much money you've got and if all you do is move money from checking the savings you're no richer no poorer but individually the account numbers move up and down it's only the total amount of money you've got that's any good to keep track of not what's in individual accounts and we can't do this we aren't allowed to do that because they aren't conserved neither heat nor work alone is conserved we just cannot know how much of either is involved only from the initial and final states we don't know how much heat and how much work it took to get there only the total for example by friction we can dissipate a lot of work into heat when you run your car your tires get hot and the tires are rated if you have a very powerful car you may have z rated tires so they're thinner they're wider they dissipate heat more effectively the terminal temperature of the tire goes like the square of the velocity and you can actually have a blowout if you don't know what you're doing and it's a hot day and you're going downhill and you've got an economy car and you've got low temperature rated tires and they just overheat get weak they may get mushy so you may lose control and then you may have a blowout which is not a good thing to do okay for an ideal gas we have an equation of state now that we know what a state is an equation of state boy that's a powerful phrase because that means we can specify the state of the gas once we know these and we know how all the variables are hooked together for an ideal gas so we can take this and we can assume one mole of gas let's say for just for the sake of simplicity and we're going to keep the gas in contact with a heat reservoir or a thermostat or a T star in a piston and then we're going to put masses on top to adjust the pressure and what we're going to try to do is we're going to try to lift as much mass into the surroundings as we can with this gas and we're going to try several ways and see which way ends up with the most mass the highest that's done the most work that's what we want to do typically is do a lot of work so we're going to do some work by lifting a mass or masses in this case in the surroundings and what we're going to see is that the best way to do it is unfortunately the slowest way that's also the best way to learn the worst way to learn is to take an eight hour course and then that's the end of the course you get exhausted you can't pay attention if you don't follow something it's over and it's of limited utility the best way is to have a little bit every day that's the best 24 hours is about the right time but for scheduling reasons we rarely do that the reversible change will define what it is in a second but what it means is that if you change anything by just slightly you can reverse where you went you can go backwards so you can literally go back to where you were just by changing something slightly so that means you didn't do anything very sudden they're very slow quiet processes like digestion although I guess some people's stomachs rumble from time to time quiet processes tend to be more reversible and our digestive system is very good at extracting as much energy as possible from what you eat up to certain limits we aren't cows so if we eat cellulose the cellulose just goes through a cow eats cellulose and they have all these bacteria and the bacteria break it all down and then the cow eats the bacteria and that's kind of a good trick that's why cows have so many stomachs because they have one stomach for these guys one stomach for these guys and so forth if you've got a loud, sudden process like an explosion or the roar of a race car engine then that's very far from reversible if you go out to the Bonneville Salt Flats and you see the huge, powerful cars I had no idea how loud they were until I was mistakenly standing there and I said why is that guy dumping bleach all over the all over the ground and then there was the most incredible explosions I thought I was going to die and all the guy was doing was revving his top fueler to spin the tires in the bleach and get them red hot so that when the race started they would just stick to the ground and he could go like that and I never went back there again after that because the smell of bleach going up and the roar and being a little kid it wasn't that entertaining and at that time I didn't drink beer so there wasn't any of that which everyone else I noticed seemed to be doing unfortunately we can't wait forever so the first law has to do with energy it has to do with energy but society has to do with power if you want to get something done you need power not energy power is energy plus do it now you watch an earth mover come and grab a ton of dirt and move it up and dump it over here that's power and if the guy does it it takes a lot of time and it takes all day because he's got solar panels powering it he gets fired so look we got to get this foundation dug today we've got the cement pouring tomorrow et cetera et cetera so you need power and you see that because when one of those caterpillar earth movers digs into the ground this huge plume of black smoke stack because they don't have the same emissions controls yet and you can just see the diesel going down in real time because it takes a lot of power to lift up tons of material in the air and then move it over here and dump it and they are not going to be operating on batteries anytime soon if you put an earth mover on batteries it does this the battery is dead so we don't want to run out of diesel okay here's our situation here's our heat reservoir here's our piston we've got four masses on it and obviously if we don't move any of the masses off nothing changes we can't get any work we have to move some masses off and then the other two move up and now the pressure is less and the gas pushes it up we don't need to know how fast it goes or anything like that we just need to know where it ends up that's going to tell us how much work we did and if we slide off two of the masses here on this imaginary shelf they didn't change height so there's no work there but these two did go up we got some work there let's figure out how much work we can make the gas do in this case well, the temperature doesn't change so p1v1 is nrt star and that has to be equal to p2v2 the pressure is just the weight per unit area so the pressure is the total mass sitting on that plate times the force of gravity divided by the area of the plate and because it's a piston assume that the walls are straight the volume is just whatever the area is times the height it doesn't need to be a circular cross section and that means that p times v if I put these in is just equal to the mass times the height good well, let's figure out what happens to the height the initial state is p1v1 is 4mgh1 because the total mass is 4 of these little m's g is there and the height is h1 and the final state is p2v2 is equal to only two masses times g times h2 and since these two are equal that means that h2 and h1 have to be related to each other and if we set them equal we can cancel out the m's and the g's and we find that h2 is equal to 2h1 so that we take off half the mass and the thing went up twice as high as the oil would have told us basically is going to happen no surprise how much work did we get well the work is where those masses started and where they ended the work we get we lifted up two masses the other two we didn't lift and the difference in height is h2-h1 so the total work we get is times m times the force of gravity acceleration of gravity and then h1 and that's how much work we got okay suppose we take them off one at a time going to be slower but the question is if we take them off one at a time if we're more patient are we going to get more work or less work we take one off we take one off the other two go up take one off the final one goes up we take the final one off then goes to infinity presumably but doesn't have any mass doesn't do any work okay we slide the first mass off we get no work because it didn't change height the other three move up how far did they move up well to cut to the chase the other three move up to h2 four thirds h1 this is again what Boyle would have told us at this place h2 we slide off the second mass and so when we slide the second mass off we get that mass sitting there at h2-h1 we get one third mgh1 from that first one the remaining two go up to a new height which turns out to be three halves h2 but we know what h2 is it's four thirds h1 and conveniently the threes go away we find h3 is 2h1 well we called h3h2 before we concluded it was 2h1 we slide off the third mass here and the work we get then is mgh1 and the final mass the other two go up the final mass moves up to a height h4 where h4 is 2h3 and that turns out to be 4h1 and the work we get then is that final mass and the difference which is 3 and therefore the total work that we got is 13 thirds mgh1 which is much bigger than 2 and our conclusion then is that by doing it more slowly we can work the important thing here is that only the pressure difference between the inside of the container and the outside can be used if the inside is at one atmosphere and the outside is at one atmosphere nothing is going anywhere when you do this we have to have a pressure difference the gas has to be at higher pressure initially than the external pressure otherwise we don't do anything we blithely assumed the external pressure was zero here but the external pressure is usually atmospheric pressure and this difference sets an upper limit on the amount of work that we can get in a real system people are scheming to use exactly this gas in a cylinder on a grand scale there is a problem of wind and solar energy when the wind is blowing they are going to compress gas and when the wind is not blowing they are going to let it come out and get the energy back this is called off peak storage here is one scheme you take cool air and when your wind and solar are running you run a compressor that takes work but you have electrical energy from your wind and solar you compress the air into this huge old coal mine or old gas mine or something and you hope it doesn't have any leaks if it has leaks you are going to take a bath and then when you need the energy back nothing is coming here now and you drive a turbine and you drive a generator and you generate electricity at night or when you are calm you can go to these guys I don't know if they are out of business yet and you can also use the waste motor heat to heat the air on the way out so there are schemes to actually try to make the efficiency better and my comment on this is it probably won't work well in other words it is easy to think of all kinds of schemes you will see millions of them on the web the question is if you want to power the state of California overnight or for a week when there is no wind how big does this thing this motor and this thing and this thing have to be how many of them do you need and the answer there is usually so huge that it is just totally out of the question because you are going to have to pay for all these things they don't come for free and you need an energy source to manufacture all of them where did you get that energy when you burned up all your fossil fuels and you have no other energy source if you try to make solar panels by only using solar panels using solar panel factory you are going to get one panel per year or something and then you are going to see how long it is going to take if you want to be truly sustainable going forward we are going to have to face these kinds of issues thermodynamics always gives us the bottom line it says you cannot possibly do better than this and if that is not good enough we will continue on this then on next Tuesday