Thermochemistry: Work, Heat, & First Law of Thermodynamics
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Transcript: English(auto-generated)
00:17
Right, first an announcement, there's bad news and good news, which you want first.
00:31
The bad news is we made a mistake grading the exam.
00:42
So do you want the good news? 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.
01:07
Next exam, I assure you we are not going to make any mistakes. I think the mistake was only on form D. First two problems are all backwards.
01:22
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.
01:49
Okay, let's continue. Today we're going to talk about thermochemistry,
02:02
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 observe things,
02:21
not 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.
02:43
However, it's interesting. It's very difficult to define energy. It's everywhere. It can manifest itself in different forms.
03:01
Ever present, it 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,
03:22
this is very broad brush strokes, but it'll do, into two forms, work and heat. And work is much more useful.
03:41
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
04:01
can be converted 100% to lifting a weight in the surroundings. If what you can do can do that, that's going to constitute work. And if we want to get the energy back,
04:21
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.
04:43
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
05:01
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,
05:23
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.
05:44
That's how all energy ends up in the end as heat. Every joule of energy ends up as heat. You eat and you're hot. You're producing heat as you run.
06:01
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.
06:26
It just depends. So work is a coherent, directed form of energy. An object that's moving, if it's a macroscopic object,
06:40
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.
07:02
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.
07:22
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. So they camouflage themselves by playing dead
07:41
and just sitting there. So 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.
08:03
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.
08:21
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 useful yet.
08:47
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
09:01
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.
09:21
But if I just try to use heat alone, 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
09:41
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
10:02
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,
10:23
a scientist I knew decided to monitor his power, his electric power consumption. So 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
10:41
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. Then after a while, you throw it away.
11:02
Then you have space for books. One morning, he was looking at his Google phone there, and suddenly the electric power consumption went rah! And he's looking around, what on earth has happened?
11:23
His son was making a piece of toast. The next day, the toaster disappeared. Sorry, it's busted. Converting work into heat like that should be a crime. If you want to heat up your office,
11:42
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.
12:05
So 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.
12:25
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.
12:43
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,
13:01
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.
13:22
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.
13:42
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
14:02
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
14:24
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.
14:49
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?
15:01
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.
15:21
An isolated system, we'll give the definition a little bit later, but an isolated system is one that cannot exchange mass or heat or work with the environment. And we could consider the universe, however big it is,
15:41
to be an isolated system. 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.
16:00
And when stars burn, they're converting mass into energy into heat, so 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.
16:25
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. We reserve capital letters for good things, which we'll call state functions, capital letters,
16:43
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.
17:00
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,
17:23
and the atoms in this guy are moving slower. If I bring them into contact, thermal contact, so they touch, then the atoms in this guy are like Muhammad Ali. Boom, boom, boom, boom at the edge, right?
17:41
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. So we talk about heat flowing from one place to another as we watch just the excitement move,
18:04
just like watching a wave at a stadium. Just everybody stands up, and the impression is that you've got something moving. So as this excitement propagates, we talk about heat flowing from one place to another.
18:23
There are other forms. Of course, we talked about work, and I told you what work is. Electrical energy is also ordered energy. We can do work with it. And energy can also be stored in different kinds of chemical compounds,
18:42
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?
19:01
Anybody? Yes, exactly right. And how are the organic materials built up since it takes work to build up molecules like that? No, from the sun.
19:23
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.
19:44
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.
20:00
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
20:21
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 a hundred years. The optimists say, well, we've only gone through half the oil but you've gone through a hundred million years of oil in a hundred years.
20:42
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.
21:00
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,
21:21
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
21:40
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.
22:00
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
22:21
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
22:41
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.
23:04
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.
23:21
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.
23:45
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
24:02
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.
24:22
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
24:41
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
25:03
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.
25:20
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
25:46
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.
26:03
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.
26:25
A state function, these will 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.
26:41
Well, 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
27:04
with vapor here and to specify the state of the system, we have to specify the temperature, the pressure,
27:20
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.
27:42
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
28:02
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.
28:22
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 rearrange.
28:43
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.
29:00
They grow the corn. They feed a calf, and round and round they go. And 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.
29:23
If f went up, then this is bigger. The final value of f is bigger than the initial value. Then the change in f is positive. If it is lower, then the change in f is negative. And the value, the important thing is that the value
29:44
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.
30:00
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,
30:20
because we don't have to do every kind of experiment in the lab. We can do a few simple experiments, and then we can add and subtract things and get what we want. We don't want to have to do a complicated experiment. Gravitational energy, the gravitational potential energy is
30:42
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.
31:00
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 lowercase k for a kinetic variable,
31:23
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.
31:40
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, and then we measure the difference. How much heat did it produce in a calorimeter,
32:00
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.
32:21
Operationally, then, we can define a state as a situation in which there's slow 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 crosshairs on it, and it's not moving too fast.
32:41
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, and then we measure it again. If we have a temperature, that means, as we saw with gases,
33:05
they have a characteristic curve, the Maxwell-Boltzmann distribution. And if the gas is at a constant temperature, then the molecules have to be following that distribution.
33:22
And that means they're moving in certain ways, and other things that 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,
33:43
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, but the total number has not changed. They've sat there. And if the energy level occupations stay constant,
34:02
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 things are all over the place,
34:21
and so it's very difficult 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,
34:44
and I want to know which of these have the same change in potential energy. Anybody want to have a go?
35:05
No? Well, 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
35:21
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?
35:41
If that 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.
36:03
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.
36:22
For example, in a piston in a car in an internal combustion engine, I'd like to burn this stuff. This stuff here is isooctane. That's 100-octane gas.
36:42
So 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. And I think there's one place in Malibu that sells gas called Trick Gas, 104-octane. And all the Ferraris and Lamborghinis
37:02
and high-performance cars are pulling up to fill up there. Of course, if you have a car that's that expensive, then the six bucks a gallon you're paying for Trick Gas is chump change. But anyway, if you had isooctane,
37:20
it's got eight carbons, but notice that 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.
37:45
Okay? And the balanced chemical equation then is this guy and 25 or 12-and-a-half moles of molecular oxygen gives eight moles of CO2. There's the climate change.
38:01
And nine moles of H2O. We know the balanced reaction, and we can measure how much heat comes. We can take isooctane, a mole of it, put it in an insulated container,
38:21
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,
38:42
certainly it isn't 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.
39:04
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,
39:21
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. Okay, so here's an example. The heat that you get by combustion of isooctane
39:41
is minus 5,461 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.
40:01
It's producing heat and the heat's going to the surroundings. It means you put your hand there, it feels warm. For heptane, n-heptane, a linear chain of seven carbon atoms, C7H16,
40:24
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?
40:40
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
41:01
and then go from there. So just in round numbers, 8 times 12 is 96 plus 18 is 114. Now we got 84 plus 16 is 100. So they have a slight difference because seven carbons versus eight.
41:22
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 moved the decimal point. But in terms of octane rating,
41:43
isooctane is called 100-octane gas. And n-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,
42:01
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
42:25
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
42:43
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,
43:01
but it's not producing any forward motion of the car. And this stuff, the 100-octane stuff, is smooth as silk. The power just 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,
43:23
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, but they have much lower energy content.
43:41
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.
44:02
But in terms of energy content, they're lower, much lower. Diesel is only 35 octane, but a diesel engine has a completely different design because in a diesel engine, there's no spark plug.
44:25
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.
44:40
It 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,
45:04
you'll know what I'm talking about. You feel like you're being fumigated. And so it's very hard to get the air quality 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.
45:22
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?
45:41
With the gases, we measured the pressure and volume, 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
46:01
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.
46:20
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.
46:43
Now, 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.
47:02
Now, 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. Trade secret. We'll see what it is in a minute.
47:20
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,
47:42
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.
48:01
So it was a good investment. OK, let's construct an argument to demolish this device and prove that it cannot exist.
48:21
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.
48:41
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 produce twice as much, we could feed four power enhancers off that. And then we could feed eight and 16, and we could keep going.
49:02
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 electricity, no nothing, just black boxes
49:21
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.
49:42
You can use feedback. Since it produces twice as much, what you do is you route a certain one amp and 12 volts around at the input. And then you just bleed off one amp and 12 volts forever with not putting in any fuel, not connecting it up
50:03
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.
50:25
Nobody has ever been able to do that. And that's because a device like that is absurd. It can't possibly work because it violates the first law of thermodynamics. What was in the black box?
50:41
Some people did buy them. It was just a car battery. It runs for a couple hours, and then it runs out. Car battery needs to be recharged, right? But by then, the guy's out of town. Hey, my power and answer doesn't work.
51:02
Where is that guy? He's got your $500 for a $100 battery. All right, let's talk about internal energy. This is not quite so familiar as enthalpy. Enthalpy we encounter all the time.
51:21
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.
51:41
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
52:03
and down and down as we bleed off the energy. And so whatever heat and work are involved, the total has to add up to the change in internal energy.
52:20
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 plus work. The question is, can we use a delta Q?
52:40
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?
53:01
And the answer is, that doesn't 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 got.
53:25
And if all you do is move money from checking to savings, you're no richer, no poorer. But individually, the account numbers move up and down. And so it's only the total amount of money that you've got
53:40
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. And so we just cannot know how much of either is involved
54:02
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
54:22
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.
54:43
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.
55:00
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,
55:23
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,
55:42
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 at some temperature T star in a piston.
56:05
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.
56:20
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. Okay. So we're going to do some work by lifting a mass or masses,
56:44
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
57:04
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.
57:21
That's the best. Twenty-four hours is about the right time. But for scheduling reasons, we rarely do that. The reversible change, we'll define what it is in a second, but what it means is that if you change anything by just slightly,
57:46
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.
58:00
In fact, in theory, they're infinitely 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
58:28
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,
58:42
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.
59:01
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,
59:25
and I said, why is that guy dumping bleach all over the ground? And then there was the most incredible explosion. 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
59:45
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...
01:00:00
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.
01:00:21
So the first law 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.
01:00:41
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 one inch at a time and it takes all day because he's got solar panels powering it,
01:01:01
he gets fired. Say, look, we've got to get this foundation done 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
01:01:21
comes out of the smokestack 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.
01:01:41
And they are not going to be operating on batteries anytime soon. You put an earth mover on batteries, it does this. Battery's dead. So we don't want to run out of diesel.
01:02:02
OK, here's our situation. Here's our heat reservoir. Here's our piston, and we've got four masses on it. And obviously, if we don't move any of the masses off,
01:02:20
nothing changes. We can't get any work. We have to move some masses off, and then the other two move up because now the pressure's 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.
01:02:44
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, and we got some work there. Let's figure out how much work we can make the gas do
01:03:03
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.
01:03:24
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.
01:03:42
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 G times the height. Good. Well, let's figure out what happens to the height.
01:04:06
The initial state is P1V1 is 4mgh1, because the total mass is four of these little m's. G is there, and the height is h1. And the final state is P2V2 is equal
01:04:24
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
01:04:44
and the g's, and we find that h2 is equal to 2h1. So we take off half the mass, and the thing went up twice as high. That's what Boyle would have told us, basically, is going to happen. No surprise.
01:05:01
How much work did we get? Well, the work is where those masses started and where they ended. And the work we get, we lifted up two masses. The other two we didn't lift. And the difference in height is h2 minus h1.
01:05:20
So the total work we get is 2 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.
01:05:43
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, the other three go up. We take one off, the other two go up.
01:06:02
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.
01:06:21
How far did they move up? Well, to cut to the chase, the other three move up to h2 equals 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,
01:06:40
we get that mass sitting there. At h2 minus 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.
01:07:00
And conveniently, the threes go away. We find h3 is two h1. Well, we called h3 h2 before. We concluded it was two h1. We slide off the third mass here, and the work we get then is mgh1. And the final mass, then the other two go up.
01:07:25
And the final mass moves up to a height h4, where h4 is two h3. And that turns out to be four h1. And the work we get then is that final mass and the difference, which is three. And therefore, the total work that we got is 13-thirds mgh1,
01:07:47
which is much bigger than two. And our conclusion then is that by doing it more slowly, we get more work. The important thing here is that only the pressure
01:08:02
difference between the inside of the container and the outside can be used. If the inside's at one atmosphere and the outside's at one atmosphere, nothing's going anywhere when you do this. We have to have a pressure difference. The gas has to be at higher pressure initially
01:08:22
than the external pressure. Otherwise, we don't, we can't do anything. We kind of 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
01:08:42
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 to solve the intermittent problem of wind and solar energy.
01:09:01
When the wind's blowing, they're going to compress gas. And when the wind's not blowing, they're going to let it come out and get the energy back. And this is called off-peak storage. Here's one scheme. You take cool air, and when your wind
01:09:24
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
01:09:40
or old gas mine or something, and you hope it doesn't have any leaks. If it has leaks, you're going to get, take it back. And then, when you need the energy back, nothing's coming here now. You let the air come out, and it's under pressure, and you drive a turbine, and you drive a generator,
01:10:02
and you generate electricity at night or when you're be calm. You can go to these guys. I don't know if they're 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
01:10:21
to make the efficiency better. And my comment on this is it probably won't work well. In other words, it's easy to think of all kinds of schemes. You'll see millions of them on the web. The question is, if you want to power the state
01:10:43
of California overnight or for a week when there's 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 it's so huge
01:11:03
that it's just totally out of the question. Because you're 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. And where did you get that energy? When you've burned up all your fossil fuels
01:11:22
and you have no other energy source. If you try to make solar panels, by only using solar panels to power the solar panel factory, you're going to get one panel per year or something. And then you're going to see how long it's going to take if you want to be truly sustainable.
01:11:41
Going forward, we're 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's not good enough, then you need to think of something else. But we'll continue on this then on next Tuesday.