Understanding Thermodynamics in Metabolism

So in the previous lecture, we've opened up a can of worms that I can no longer dodge. This particular issue is absolutely central to all of metabolism, and that's this concept of thermodynamics and the laws of thermodynamics. When it comes right down to it, we have to understand as biologists a fair amount of physics because we are walking, talking biochemical reactors that are governed by the laws of physics. And so when we really want to understand metabolism, we have to understand at least the basis. of the laws of thermodynamics. And you may have studied these before. You will if you haven't yet. You'll study them in your physics courses. But the issue that we're dealing with in thermodynamics is really energy and the concept of energy. And I'll make that precise here, at least as precise as I can here shortly. These laws that govern energy are essentially inviolable except at very, very small, tiny, tiny scales that have absolutely nothing to do with biology as far as we can tell at this point. So we have to... really understand it because all of our metabolism is absolutely governed by these laws. And the first of those laws is this, is that the first law of thermodynamics says energy is conserved, meaning the total amount of energy in the universe is not changing, at least not at a scale that we experience. And what that basically means is that whatever energy is, we haven't defined it yet, whatever it is, the total amount of energy that exists now in the universe is the same as it was at the moment. moment the universe began in the Big Bang and the same as it's going to be throughout the rest of time. That means your body has to live within that universe and live within that law. So this one is a very interesting kind of problem that we have to face but the other one, the second one, is even worse. When energy is converted from one form to another within a system, less of the originally available energy is still available to do work within that system. And what that basically means is this... When a system changes state, if a system is in one state and goes to a different state, that means energy had to be transferred from one form to another. The first law says it can't disappear, it can't be created, it can't be destroyed. But this is saying that whenever a system has any kind of change within it, energy is being transferred from one form to another. When that happens, the total amount of energy that's available to change the system's state any further goes down. That's what the second law says. Now we can state that in terms of entropy and all this stuff. It's much more precise and much more direct if you say it in those terms. But we haven't defined those terms yet. So this is sort of where we are in our best guess or our best way of looking at it right now. So the issue is this, and this is absolutely critical. Congress has tried to repeal both these laws and they can't do it because there is not any thing that humans can do to change this. This is a This is basically a very, very deep property of our universe. And so we are in a situation where we can't have what's called a perpetual motion machine because of that second law in particular. Whenever a system changes state, meaning an engine, for example, starts spinning, and as it spins, it's changing state constantly and continuously. Whenever it changes state, it loses energy available to change its state any further, which means that you can't just take an engine fill it full of gas, run it, have that engine generate an electrical current, which you can do. You can certainly have an engine generate electrical currents, but then you can't take that electrical current, feed it back into the engine, and run the engine. And so we can't have a system that continually operates on its own. That means your body can't do the same, has got the same problem. It can't just eat once and then live off of the energy from that forever. So this is really central to our understanding of metabolism. So we've got to understand what this means, and the issue then is, well, what is energy? So we haven't defined this yet. We have these two laws that talk about energy, but we don't even know what energy is yet. So let's take a look at this. What exactly is energy? Well, energy is, from the elementary textbooks that you have in high schools and at least beginning courses in university level, they say that energy is the ability to do physical work. Now, physical work is not necessarily what you might think it is. Work is something that is, in this case, a very, very precise concept, and I want to make sure that we understand exactly what that concept means. Okay, so let me demonstrate what I mean by that. So here I have an ordinary stapler. I'm going to ask, am I doing work on this stapler? Hold it right here. Am I doing work on the stapler? And you might think I am because I have to expend some physical effort to keep it from falling. If I just let it go, it's going to fall. But in terms of physical work, what work actually is, I'm not doing work on it at the moment. There's no work being done on the stapler at the moment, at least not very much. I'm kind of tweaking it around a little bit. Now I'm doing work on it, though. No, I'm not. Now I'm doing work. I'm still doing work. Still doing work. But now I'm not. I've stopped doing work on the stapler. All right, so if you're looking at this, you might get a sense then that work has something to do with movement. And if that's true, then you'd be absolutely correct. Okay, so energy is this ability to do work. and work has something to do with movement. So what exactly is work? Again, if you look at the physical textbooks for introductory university courses, they'll tell you that work is the application of a force across a distance. And that's why it is that when I hold the stapler steady like this, there's no work being done because I am applying a force. You're absolutely right. There's effort involved in applying the force, but I'm not moving it across a distance. There's no displacement. So from this definition in this kind of system, that's what's required. Force has to be applied and there must be some sort of displacement. Okay, now these concepts then are often misinterpreted. And I want to talk a little bit about what energy isn't before we really start getting into what energy is. Here's what energy is not. Energy is not an aura. Energy is not some sort of thing that we all emit. Energy is not some kind of thing you can put your hands on and manipulate. Those things, whatever those concepts are, whatever those concepts may be, and whether or not they exist or not, I'm not going to debate. But what I will say is this. Those concepts of energy and having energy are not what a physicist means by energy. And the reason is this. Energy is not a thing. It's not a substance. It's not something you can see or feel or touch. Look at this word here. It is an ability. That's all it is, which means energy is an entirely abstract concept. It's not a real thing. It's not stuff that you can give to another person, although we talk about it in those terms, and I'm going to talk about it a lot. We transfer energy from one form to another. But really what that is, actually, if you get down to the more advanced textbook definitions or the graduate-level physics textbook definitions, you'll discover that they dispense with this idea of energy as the ability to do physical work, and what they do is they basically say energy is this quantity that you calculate in a particular way, in particular equations, that never changes. And that's... about the best we can do because it is entirely an abstract concept. Nevertheless, it's extraordinarily useful. It's a very, very useful concept. And so we can talk about it as if it were a thing. For example, we can talk about different forms of energy. And that's why I put this in quotes, because again, energy is not a stuff, but we can describe it as if it had different forms. And there are various forms of energy that you know of already. There's this concept of potential energy, the idea that if I do something, I can actually have an energy in a system that's not actually being... release. So for example, here I have a pen, and right now the pen has what we consider gravitational or positional potential energy. And the reason it's potential is that I can do this. I can drop it, and the moment I drop it, it starts to move, and it becomes then kinetic. And kinetic, in that particular case, it's mechanical kinetic because it's the energy of some object in the universe moving, actually moving. So... There are a couple of different forms of potential energy that we will deal with. There are more than just these forms on the slide, but the two that are important for us are gravitational and particularly chemical energy. And then we have this. Kinetic energy is mechanical. Like I said, any kind of motion, anything moving, if you throw a ball, that's mechanical kinetic energy, but there's also thermal energy in a system. And there's electrical energy, electrical potential energy, which we can put across a voltage, for example, across membranes, and that becomes a very important aspect of your physiology. And then there's electromagnetic energy. And electromagnetic, this is one of the greatest discoveries in human history. It was a guy named James Clark Maxwell who discovered that electromagnetism is all one thing. Electricity, magnetism, and even light are all just different manifestations of the same thing. And so here's the key point to metabolism. Metabolism is critical in this because metabolism really is all about converting chemical potential energy into one of these other forms and back. For example, we can take chemical potential energy and we can convert it to mechanical energy by walking or moving or speaking. We can take chemical potential energy and make it into electrical, electromagnetic energy in the form of, for example, electrical current across membranes of neurons. We can also, well, we can't, human beings can't, but other creatures can, for example, fireflies. They can take chemical potential energy in the form of ATP and form light, produce light. Plants go the opposite direction, take electromagnetic energy in the form of light and... make it into chemical potential energy. And for the rest of this semester, that's what we're going to be studying. We're going to be studying how it is that energy is transferred from one of these forms to another form. But remember, we can't violate the first or second laws. Whenever we transfer energy from one form to another, we can't destroy it and we can't create it. Also, though, whenever we transfer energy from one form to another within a given system, that system then has less of the available energy to do work within itself. And I'm going to, again, make those concepts more precise. I'm sure that there will be physicists who will be upset about the way I'm describing this, and they have every right to be because I'm simplifying things greatly. I'm going to try and make these things a lot more precise without using a lot of heavy mathematics here very shortly. So if we want to make these concepts more intuitive, it helps to have some concrete examples. And here's a picture that I want to ask, what are the forms of energy that you see here? And there are a couple of obvious ones, the most obvious being the dam right here, and then the water on this side of the dam higher than the water on this side of the dam. The river's way down here, you can't even see it. So what kind of energy is that? It's positional, and therefore it is potential. because this water on the left side of the dam, behind the dam, is much, much higher and can drop. So therefore, it's what we call potential or stored energy in the form of gravitational or positional. You can also see right here, the water going through the sluices here, and there's, I'm sure, in here driving some sort of a generator, but these water molecules moving through here and blasting out through the sluice are showing you mechanical kinetic energy. So we have very obvious forms here. But you can also see on the side of the hillside a bunch of light. So there's your electromagnetic energy that's currently being transduced by all these plants into chemical potential energy. Here's another example that will make those ideas a little bit more clear. We have two cats here. Now in this particular picture, I don't know why they did it this way, but this cat on the left is a leopard, the one on the right is a cheetah, but whatever, they're both spotted cats, so I guess that's fine. What kind of energy do we see in these pictures? Well, there's energy in this one. The cat's just laying there on the ground. There's that obvious energy in this one where the cheetah is running. So obviously the cheetah right here is exhibiting mechanical kinetic energy. It's moving and it's running and it's chasing something. What's it chasing? Well, it's chasing what this cat on the left side is demonstrating. What kind of energy does this cat have? Well, he's not moving. He's breathing. But if you look at this, this cat right here is demonstrating potential energy. Not positional, though. It's not like the water on the side of the dam. He's on the ground. This cat is not showing you any positional potential energy. What if it was up in a tree? And they do that. These leopards do that. But that's not what he's doing. What he's showing you is chemical potential energy. His body is made of chemicals that store energy, that can be released. And in fact, that's precisely what this cheetah is doing. It's chasing down a big blob of chemical potential energy that happens to have hooves and is running away from it at the moment. It wants to eat that blob of chemical potential energy, absorb all that energy, and then use it for kinetic purposes like chasing down more kinetic energy and so forth. But that's what metabolism really is. It's this dance between the chemical potential energy and the kinetic energy of all different forms that your body is controlling. And that is what metabolism actually is. Metabolism is controlling the energy states of the molecules inside your body. Okay, so now the goal is to take those intuitive ideas and make them more precise. And in particular, we're going to use this little picture here, this drawing, to give you a sense, a more precise sense of what exactly the first and second law are saying. Now, if you look here carefully, you'll see that there's a scale and there's a box on either side of the scale. What the box represents is some sort of system. It could be this cheetah. It could be your body, it could be a car, it could be anything. But it's a physical system that exists in this universe. And the issue with this system is that it's closed. In this particular case, we're assuming the system is closed. And what that means is a closed system cannot exchange matter or energy with any other system. So we're assuming then that there's no energy coming into this system, no energy going out of the system, no matter coming in or matter going out, because again we know matter and energy are actually intertwined. from Einstein's famous equation E equals mc squared, and this then is all of the energy that's in the system before the system changes state in some way. Something happens within the system, something moves. Afterwards, it's on this side. So this is the system energy state after the system has changed state. Okay, now if you look here, the total amount of energy before the system changed state and the total amount of energy after the system changed state is exactly the same, which is why the balance is set directly. directly on zero. So that's the first law. The first law says energy cannot be created or destroyed. But notice that the energy has changed inside. All of the energy on the left was blue, and that blue is representing a particular form of energy that is available to do work within that system. And that idea, the energy of a system that's available to change its state, is what we call the Gibbs free energy, named after a physicist named Gibbs. And so the free energy doesn't mean it's free in some way, you don't have to pay for it, it just means that it is available to do work within the system. Now after the system has changed state, some of that free energy... has dissipated. It's changed. The total amount of energy is exactly the same, but now the free energy has been converted into another form. It's been converted into entropy, right? So this entropy by this definition now, entropy of this definition is the energy within a system that is not capable of doing work. Now, it's not quite precisely what you're taught in your physics classes. In your physics classes, what I'm calling entropy here is what they call entropy times the temperature of the system. We'll get to that in a moment. But the point is that there is a change here. The total amount of free energy decreases and the entropy must increase. That is a statement of the second law. Okay, so what is entropy? Entropy is the energy within a system that is unusable by that system. Okay, and that's the most intuitive definition I can give you in the simplest possible way without using mathematics. Now, I'm going to give you another sort of more precise way of... seeing it without mathematics by using this demonstration here, by these pens. And the pens represent a system. So here are a set of three pens, and right now they're connected into a single object. And I want to measure the entropy of this system. Now one of the ways that I can do that is to measure the different ways that this system can change. Now there's a lot that I'm going to skip here, and again, physics profs will probably get upset with me about this. it's going to get to the main point. Now imagine this system can only change in the following ways. It can change in its attitude to the ground. Now if you're a pilot, you know what I'm talking about. The attitude of the aircraft, of an airplane, is how it is relative to the ground, whether the nose is going down or up or to the side or whatever. Now in this case, I want to know how many different ways can I change this object's attitude towards the ground. And again, if you're a pilot, you know that there are three inputs that you have to control if you want to control something in space. You want to control its position in space. One attitude controller controls the elevators on the back of the aircraft, and it controls the nose. So the nose goes up and down. That's called pitch. And then the other controller will control the ailerons, which are the things on the sides of the wings, which control roll, which will cause the thing to roll side to side like this. And then the last one is the rudder. the back of the vertical stabilizer, that rudder is the third input which will control the nose of the aircraft going side to side. That's called yaw. So again, any pilot will tell you that to control your aircraft, you only need three inputs. One input for pitch, one input for roll, and one input for yaw. If you have those controls, you can put your aircraft into any position you want relative to the ground. And that is telling us something. That tells us that this system, in this configuration... has three degrees of motion, okay, three degrees of freedom. And those degrees of freedom simply are the three elements that I have to put in in order to change this position to anything I want. Now, I could design the system so that there's more. The aircraft could have four or five inputs, and the pilot would have to have four or five inputs. But again, any pilot will tell you that that's a waste. There's no point in doing that. It just makes your life much more difficult. So what we're doing is we're measuring the degrees of freedom of motion. in the simplest possible way. So three we need. What about two? What if I was missing one of these three? Well, in that case, if I didn't have any yaw, then I'd be stuck. I could go up and down like this and I could roll, but I couldn't put the aircraft's nose in either direction this way or this way. So three is a requirement. Three is the minimal amount of inputs required to change the aircraft into any attitude you want. So that tells us then that the proper degrees of freedom of motion for the aircraft or for this pen configuration is three. There's three different ways I can do it. Okay, in the basic calculation of entropy, the entropy is proportional to the number of degrees of freedom of change or motion in the system. Okay, now I'm going to take the system and I'm going to change its configuration. I change it from this to this, and now notice that all three pens are independent of each other. Okay, it's the same system. It's made up of the same things, it's just in a different configuration. Now my question is this, does it have more or less entropy? Well, as I just said, entropy is proportional to the number of degrees of freedom that you have in the system. How many different degrees of freedom do I have now? Well, each pen has its own independent motion now. So that means each pen has its own number of degrees of freedom. And again, this pen, pitch, roll, yaw, this one, same thing, this one, same thing. Each one now has three degrees of freedom. Therefore, this configuration has nine degrees of freedom total. 1, 2, 3, 4, 5, 6, 7, 8, 9. Okay? So that means that the system in this configuration has more entropy than the system in this configuration where they're all connected. That's how we measure it. That's the way in which we can measure the amount of entropy in the system. And what the second law says is this. Whenever a system changes state, the total number of degrees of freedom of motion cannot go down if the system is closed. That's another way of saying it.

And so when we really want to understand metabolism, we have to understand at least the basis. of the laws of thermodynamics. And you may have studied these before.

You will if you haven't yet. You'll study them in your physics courses. But the issue that we're dealing with in thermodynamics is really energy and the concept of energy. And I'll make that precise here, at least as precise as I can here shortly. These laws that govern energy are essentially inviolable except at very, very small, tiny, tiny scales that have absolutely nothing to do with biology as far as we can tell at this point.

So we have to... really understand it because all of our metabolism is absolutely governed by these laws. And the first of those laws is this, is that the first law of thermodynamics says energy is conserved, meaning the total amount of energy in the universe is not changing, at least not at a scale that we experience. And what that basically means is that whatever energy is, we haven't defined it yet, whatever it is, the total amount of energy that exists now in the universe is the same as it was at the moment.

moment the universe began in the Big Bang and the same as it's going to be throughout the rest of time. That means your body has to live within that universe and live within that law. So this one is a very interesting kind of problem that we have to face but the other one, the second one, is even worse. When energy is converted from one form to another within a system, less of the originally available energy is still available to do work within that system.

And what that basically means is this... When a system changes state, if a system is in one state and goes to a different state, that means energy had to be transferred from one form to another. The first law says it can't disappear, it can't be created, it can't be destroyed. But this is saying that whenever a system has any kind of change within it, energy is being transferred from one form to another.

When that happens, the total amount of energy that's available to change the system's state any further goes down. That's what the second law says. Now we can state that in terms of entropy and all this stuff.

It's much more precise and much more direct if you say it in those terms. But we haven't defined those terms yet. So this is sort of where we are in our best guess or our best way of looking at it right now.

So the issue is this, and this is absolutely critical. Congress has tried to repeal both these laws and they can't do it because there is not any thing that humans can do to change this. This is a This is basically a very, very deep property of our universe. And so we are in a situation where we can't have what's called a perpetual motion machine because of that second law in particular. Whenever a system changes state, meaning an engine, for example, starts spinning, and as it spins, it's changing state constantly and continuously.

Whenever it changes state, it loses energy available to change its state any further, which means that you can't just take an engine fill it full of gas, run it, have that engine generate an electrical current, which you can do. You can certainly have an engine generate electrical currents, but then you can't take that electrical current, feed it back into the engine, and run the engine. And so we can't have a system that continually operates on its own. That means your body can't do the same, has got the same problem. It can't just eat once and then live off of the energy from that forever.

So this is really central to our understanding of metabolism. So we've got to understand what this means, and the issue then is, well, what is energy? So we haven't defined this yet. We have these two laws that talk about energy, but we don't even know what energy is yet. So let's take a look at this.

What exactly is energy? Well, energy is, from the elementary textbooks that you have in high schools and at least beginning courses in university level, they say that energy is the ability to do physical work. Now, physical work is not necessarily what you might think it is. Work is something that is, in this case, a very, very precise concept, and I want to make sure that we understand exactly what that concept means. Okay, so let me demonstrate what I mean by that.

So here I have an ordinary stapler. I'm going to ask, am I doing work on this stapler? Hold it right here.

Am I doing work on the stapler? And you might think I am because I have to expend some physical effort to keep it from falling. If I just let it go, it's going to fall.

But in terms of physical work, what work actually is, I'm not doing work on it at the moment. There's no work being done on the stapler at the moment, at least not very much. I'm kind of tweaking it around a little bit.

Now I'm doing work on it, though. No, I'm not. Now I'm doing work.

I'm still doing work. Still doing work. But now I'm not. I've stopped doing work on the stapler.

All right, so if you're looking at this, you might get a sense then that work has something to do with movement. And if that's true, then you'd be absolutely correct. Okay, so energy is this ability to do work. and work has something to do with movement. So what exactly is work?

Again, if you look at the physical textbooks for introductory university courses, they'll tell you that work is the application of a force across a distance. And that's why it is that when I hold the stapler steady like this, there's no work being done because I am applying a force. You're absolutely right.

There's effort involved in applying the force, but I'm not moving it across a distance. There's no displacement. So from this definition in this kind of system, that's what's required. Force has to be applied and there must be some sort of displacement. Okay, now these concepts then are often misinterpreted.

And I want to talk a little bit about what energy isn't before we really start getting into what energy is. Here's what energy is not. Energy is not an aura.

Energy is not some sort of thing that we all emit. Energy is not some kind of thing you can put your hands on and manipulate. Those things, whatever those concepts are, whatever those concepts may be, and whether or not they exist or not, I'm not going to debate. But what I will say is this. Those concepts of energy and having energy are not what a physicist means by energy.

And the reason is this. Energy is not a thing. It's not a substance.

It's not something you can see or feel or touch. Look at this word here. It is an ability.

That's all it is, which means energy is an entirely abstract concept. It's not a real thing. It's not stuff that you can give to another person, although we talk about it in those terms, and I'm going to talk about it a lot.

We transfer energy from one form to another. But really what that is, actually, if you get down to the more advanced textbook definitions or the graduate-level physics textbook definitions, you'll discover that they dispense with this idea of energy as the ability to do physical work, and what they do is they basically say energy is this quantity that you calculate in a particular way, in particular equations, that never changes. And that's... about the best we can do because it is entirely an abstract concept. Nevertheless, it's extraordinarily useful.

It's a very, very useful concept. And so we can talk about it as if it were a thing. For example, we can talk about different forms of energy.

And that's why I put this in quotes, because again, energy is not a stuff, but we can describe it as if it had different forms. And there are various forms of energy that you know of already. There's this concept of potential energy, the idea that if I do something, I can actually have an energy in a system that's not actually being... release. So for example, here I have a pen, and right now the pen has what we consider gravitational or positional potential energy.

And the reason it's potential is that I can do this. I can drop it, and the moment I drop it, it starts to move, and it becomes then kinetic. And kinetic, in that particular case, it's mechanical kinetic because it's the energy of some object in the universe moving, actually moving. So...

There are a couple of different forms of potential energy that we will deal with. There are more than just these forms on the slide, but the two that are important for us are gravitational and particularly chemical energy. And then we have this.

Kinetic energy is mechanical. Like I said, any kind of motion, anything moving, if you throw a ball, that's mechanical kinetic energy, but there's also thermal energy in a system. And there's electrical energy, electrical potential energy, which we can put across a voltage, for example, across membranes, and that becomes a very important aspect of your physiology.

And then there's electromagnetic energy. And electromagnetic, this is one of the greatest discoveries in human history. It was a guy named James Clark Maxwell who discovered that electromagnetism is all one thing. Electricity, magnetism, and even light are all just different manifestations of the same thing.

And so here's the key point to metabolism. Metabolism is critical in this because metabolism really is all about converting chemical potential energy into one of these other forms and back. For example, we can take chemical potential energy and we can convert it to mechanical energy by walking or moving or speaking.

We can take chemical potential energy and make it into electrical, electromagnetic energy in the form of, for example, electrical current across membranes of neurons. We can also, well, we can't, human beings can't, but other creatures can, for example, fireflies. They can take chemical potential energy in the form of ATP and form light, produce light.

Plants go the opposite direction, take electromagnetic energy in the form of light and... make it into chemical potential energy. And for the rest of this semester, that's what we're going to be studying.

We're going to be studying how it is that energy is transferred from one of these forms to another form. But remember, we can't violate the first or second laws. Whenever we transfer energy from one form to another, we can't destroy it and we can't create it. Also, though, whenever we transfer energy from one form to another within a given system, that system then has less of the available energy to do work within itself. And I'm going to, again, make those concepts more precise.

I'm sure that there will be physicists who will be upset about the way I'm describing this, and they have every right to be because I'm simplifying things greatly. I'm going to try and make these things a lot more precise without using a lot of heavy mathematics here very shortly. So if we want to make these concepts more intuitive, it helps to have some concrete examples. And here's a picture that I want to ask, what are the forms of energy that you see here?

And there are a couple of obvious ones, the most obvious being the dam right here, and then the water on this side of the dam higher than the water on this side of the dam. The river's way down here, you can't even see it. So what kind of energy is that?

It's positional, and therefore it is potential. because this water on the left side of the dam, behind the dam, is much, much higher and can drop. So therefore, it's what we call potential or stored energy in the form of gravitational or positional.

You can also see right here, the water going through the sluices here, and there's, I'm sure, in here driving some sort of a generator, but these water molecules moving through here and blasting out through the sluice are showing you mechanical kinetic energy. So we have very obvious forms here. But you can also see on the side of the hillside a bunch of light. So there's your electromagnetic energy that's currently being transduced by all these plants into chemical potential energy. Here's another example that will make those ideas a little bit more clear.

We have two cats here. Now in this particular picture, I don't know why they did it this way, but this cat on the left is a leopard, the one on the right is a cheetah, but whatever, they're both spotted cats, so I guess that's fine. What kind of energy do we see in these pictures?

Well, there's energy in this one. The cat's just laying there on the ground. There's that obvious energy in this one where the cheetah is running.

So obviously the cheetah right here is exhibiting mechanical kinetic energy. It's moving and it's running and it's chasing something. What's it chasing? Well, it's chasing what this cat on the left side is demonstrating. What kind of energy does this cat have?

Well, he's not moving. He's breathing. But if you look at this, this cat right here is demonstrating potential energy. Not positional, though. It's not like the water on the side of the dam.

He's on the ground. This cat is not showing you any positional potential energy. What if it was up in a tree? And they do that. These leopards do that.

But that's not what he's doing. What he's showing you is chemical potential energy. His body is made of chemicals that store energy, that can be released.

And in fact, that's precisely what this cheetah is doing. It's chasing down a big blob of chemical potential energy that happens to have hooves and is running away from it at the moment. It wants to eat that blob of chemical potential energy, absorb all that energy, and then use it for kinetic purposes like chasing down more kinetic energy and so forth.

But that's what metabolism really is. It's this dance between the chemical potential energy and the kinetic energy of all different forms that your body is controlling. And that is what metabolism actually is.

Metabolism is controlling the energy states of the molecules inside your body. Okay, so now the goal is to take those intuitive ideas and make them more precise. And in particular, we're going to use this little picture here, this drawing, to give you a sense, a more precise sense of what exactly the first and second law are saying. Now, if you look here carefully, you'll see that there's a scale and there's a box on either side of the scale. What the box represents is some sort of system.

It could be this cheetah. It could be your body, it could be a car, it could be anything. But it's a physical system that exists in this universe.

And the issue with this system is that it's closed. In this particular case, we're assuming the system is closed. And what that means is a closed system cannot exchange matter or energy with any other system.

So we're assuming then that there's no energy coming into this system, no energy going out of the system, no matter coming in or matter going out, because again we know matter and energy are actually intertwined. from Einstein's famous equation E equals mc squared, and this then is all of the energy that's in the system before the system changes state in some way. Something happens within the system, something moves.

Afterwards, it's on this side. So this is the system energy state after the system has changed state. Okay, now if you look here, the total amount of energy before the system changed state and the total amount of energy after the system changed state is exactly the same, which is why the balance is set directly. directly on zero. So that's the first law.

The first law says energy cannot be created or destroyed. But notice that the energy has changed inside. All of the energy on the left was blue, and that blue is representing a particular form of energy that is available to do work within that system. And that idea, the energy of a system that's available to change its state, is what we call the Gibbs free energy, named after a physicist named Gibbs.

And so the free energy doesn't mean it's free in some way, you don't have to pay for it, it just means that it is available to do work within the system. Now after the system has changed state, some of that free energy... has dissipated. It's changed.

The total amount of energy is exactly the same, but now the free energy has been converted into another form. It's been converted into entropy, right? So this entropy by this definition now, entropy of this definition is the energy within a system that is not capable of doing work. Now, it's not quite precisely what you're taught in your physics classes. In your physics classes, what I'm calling entropy here is what they call entropy times the temperature of the system.

We'll get to that in a moment. But the point is that there is a change here. The total amount of free energy decreases and the entropy must increase. That is a statement of the second law. Okay, so what is entropy?

Entropy is the energy within a system that is unusable by that system. Okay, and that's the most intuitive definition I can give you in the simplest possible way without using mathematics. Now, I'm going to give you another sort of more precise way of... seeing it without mathematics by using this demonstration here, by these pens. And the pens represent a system.

So here are a set of three pens, and right now they're connected into a single object. And I want to measure the entropy of this system. Now one of the ways that I can do that is to measure the different ways that this system can change.

Now there's a lot that I'm going to skip here, and again, physics profs will probably get upset with me about this. it's going to get to the main point. Now imagine this system can only change in the following ways.

It can change in its attitude to the ground. Now if you're a pilot, you know what I'm talking about. The attitude of the aircraft, of an airplane, is how it is relative to the ground, whether the nose is going down or up or to the side or whatever.

Now in this case, I want to know how many different ways can I change this object's attitude towards the ground. And again, if you're a pilot, you know that there are three inputs that you have to control if you want to control something in space. You want to control its position in space. One attitude controller controls the elevators on the back of the aircraft, and it controls the nose. So the nose goes up and down.

That's called pitch. And then the other controller will control the ailerons, which are the things on the sides of the wings, which control roll, which will cause the thing to roll side to side like this. And then the last one is the rudder.

the back of the vertical stabilizer, that rudder is the third input which will control the nose of the aircraft going side to side. That's called yaw. So again, any pilot will tell you that to control your aircraft, you only need three inputs.

One input for pitch, one input for roll, and one input for yaw. If you have those controls, you can put your aircraft into any position you want relative to the ground. And that is telling us something. That tells us that this system, in this configuration...

has three degrees of motion, okay, three degrees of freedom. And those degrees of freedom simply are the three elements that I have to put in in order to change this position to anything I want. Now, I could design the system so that there's more.

The aircraft could have four or five inputs, and the pilot would have to have four or five inputs. But again, any pilot will tell you that that's a waste. There's no point in doing that.

It just makes your life much more difficult. So what we're doing is we're measuring the degrees of freedom of motion. in the simplest possible way.

So three we need. What about two? What if I was missing one of these three?

Well, in that case, if I didn't have any yaw, then I'd be stuck. I could go up and down like this and I could roll, but I couldn't put the aircraft's nose in either direction this way or this way. So three is a requirement. Three is the minimal amount of inputs required to change the aircraft into any attitude you want.

So that tells us then that the proper degrees of freedom of motion for the aircraft or for this pen configuration is three. There's three different ways I can do it. Okay, in the basic calculation of entropy, the entropy is proportional to the number of degrees of freedom of change or motion in the system.

Okay, now I'm going to take the system and I'm going to change its configuration. I change it from this to this, and now notice that all three pens are independent of each other. Okay, it's the same system.

It's made up of the same things, it's just in a different configuration. Now my question is this, does it have more or less entropy? Well, as I just said, entropy is proportional to the number of degrees of freedom that you have in the system.

How many different degrees of freedom do I have now? Well, each pen has its own independent motion now. So that means each pen has its own number of degrees of freedom.

And again, this pen, pitch, roll, yaw, this one, same thing, this one, same thing. Each one now has three degrees of freedom. Therefore, this configuration has nine degrees of freedom total. 1, 2, 3, 4, 5, 6, 7, 8, 9. Okay? So that means that the system in this configuration has more entropy than the system in this configuration where they're all connected.

That's how we measure it. That's the way in which we can measure the amount of entropy in the system. And what the second law says is this. Whenever a system changes state, the total number of degrees of freedom of motion cannot go down if the system is closed.

That's another way of saying it.

Transcript for:Understanding Thermodynamics in Metabolism

Transcript for:
Understanding Thermodynamics in Metabolism