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0:01
- Hello, I'm Professor Jeff Yarger. I'm gonna be introducing fundamental concepts in thermodynamics today. And thermodynamics is really asking what is going on with energy? And so we can start with what is energy, which is actually more complicated to define than you would think. So as put even in the Encyclopedia Britannica, this is something that's very difficult to define precisely. And we can think of it as anything that produces an effect typically has an energy associated with it.
0:39
So, and really thermodynamics is the macroscopic study of energy in its various forms, and we'll see this as we go through it.
0:49
But one of the first things to keep in mind about thermodynamics is it is a macroscopic theory. So microscopic theories like classical mechanics, where for every single particle, or element, or compound, or atom or whatever we're talking about, we design position and momentums for all of these. And what took over classical mechanics to quantum mechanics, we define a probabilistic wave function that has the probability of every one of these components, or atoms, or molecules, et cetera,
1:20
and their position, and how they evolve in time. How the wave function and probabilistic waves evolve in time, et cetera. Well, when we're talking about a macroscopic system, with 10 to the 23 a mole of particles, or a mole of atoms, or a mole of,
1:38
you know, compounds, et cetera, this is a ton of variables to keep track of. So if you take a lot of these microscopic theories, and then play them through probabilistic statistics, you find out what comes out is a macroscopic theory, thermodynamics, which defines things with macroscopic variables with many fewer variables to define the complete state of a system, especially when you're working in kind of reversible, or equilibrium, slow dynamic type of systems,
2:14
and so this is really the study of thermodynamics. And to give a little motivation for this, I think this quote states it best by Einstein.
2:25
A lot of times what we're looking for in theory is simplicity,
2:30
and of all the theories he was familiar with at the time, and he was there for the evolution of quantum mechanics and everything else, the one thing he was most convinced of is that, classical thermodynamics would probably not be overthrown. It's such a well-established, elegant theory, and it has been tested and tried in the macroscopic world, the world in which we live, so often. So hopefully that gives a little motivation for why of any fundamental topic in physics
3:02
that we're gonna learn as chemists, thermodynamics is probably the most important, and definitely the most used, 'cause we're typically working in the macroscopic world.
3:14
So let's go through and introduce this, by introducing some of the concepts. And it starts with getting a little vernacular and vocabulary and some of the terminology associated with it. So usually when we're talking about thermodynamics, we define a part of the universe that we're interested in looking at, we'll call that the system. Everything else in the universe we'll call the surroundings. And then usually there's something that constrains or divides the system from the universe.
3:45
Sometimes it's imaginary, sometimes it's real constraints, sometimes they're conditional over time, et cetera, but those constraints or walls often define a lot of the vernacular vocabulary we use in thermodynamics. So for example, things you remember from already from introductory chemistry, physics class, almost every science class you've had some type of thermodynamics in the past is that, you consider a system open when you can flow particles or a number of moles of different atoms
4:22
or molecules or compounds back and forth between the system and the surrounding, we call that open, where matter's allowed to flow back and forth, and it's open to energy if we allow energy to go back and forth between the two. Well, if you use constraints or walls that keep that from happening, we'll call that a closed system. And if you close it to the point of not just closing off where matter can go through it, but not even energy or heat or anything can transfer
4:49
in and out from the system to the surroundings, we would call that an isolated system.
4:54
So that gives you some of the vernacular.
4:59
A list here, which we won't go through exhaustively, but these are in lecture notes, and is typically covered very well in the textbook, we use in thermodynamics as well as most textbooks, but this just gives you a sense of some the terminology we use in thermodynamics. So we're usually looking at different heat effects, and work effects, and so when you restrict, using walls or your constraints to restrict the heat in a system, and you don't allow the heat to change,
5:31
so we can say dq, or the change in heat is zero, then that's considered an adiabatic system. And if you allow heat to go back and forth, or you don't restrict that, we typically call it diathermal, or that you allow thermal fluctuation across it, right? If instead of restricting the heat, the total amount of heat, but you just restrict temperature from staying the same in the system, we call that isothermal,
6:03
and that means there's no change in temperature during some thermodynamic process. If we, as we already mentioned, if we stop the number of moles, which usually use the capital N for, or matter, we use a small m for that, we don't allow it to go back and forth between the system and the surroundings we call it closed, otherwise it's open.
6:29
Oftentimes as chemists we're not talking about the total amount of matter, but we're talking about individual components. So for example, in air maybe we allow just the oxygen to permeate in and out between the system and the surroundings. So that's semi-permeable to certain components, and then instead of talking the total number of moles, capital N, we usually use a sub-i to indicate the ith component or some number of components within a more complicated system.
6:57
And again, if we don't restrict that, it's open. If we restrict hard, rigid walls, so that it's a fixed volume, then that's isochoric.
7:09
However, if we allow more flexible walls, kind of like what we think of ideally as a balloon, but we restrict in a sense the force per unit area, or the pressure, and allow the volume to expand or contract based on that external force, then that's by restricting the pressure so there's no change in pressure, dP is equal to zero, we call that isobaric. And then again, if we restrict the total amount of energy, the internal energy in the system. And again, energy usually is a capital E
7:42
is what is used most commonly, but in thermodynamics we're almost always putting things from the systems perspective. Not the entire universe, just the part of the universe we're interested in. And so that's typically in most textbooks, and most notes use a capital U for internal energy,
8:04
or just the energy of the system. And again if we restrict that, and it's isolated and you can't change that, it's an isolated system, and otherwise it's an open system.
8:14
So this lends to thermodynamics as a macroscopic theory,
8:20
that the variables are macroscopic in nature, and let's go through some of the common ones we run across when we're looking at thermodynamic, or how macroscopic systems change, and the theory you use. So I put at the top composition for a very specific reason. This is designed for a biochemistry or a chemistry audience, and the number one thing that we're doing macroscopically, as chemists, or biochemists, is you define chemistry by changing chemical compositions.
8:57
By doing reactions, which means changing compounds, or molecules, or adding things together, breaking them apart. So we're by our very nature as chemists, the most important macroscopic function we're looking at is the number of moles in the system, or how matter is changing, but specifically, how different components within a system are changing. And so we usually use a capital N for the total number of moles, and that can be the sum over
9:26
however many ith components there are, right? And so thermodynamics is always each energy term for the energy of the system, the internal energy, can be broken up into conjugate field energy variable sets.
9:45
And they're always extensive intensive in nature. So the total number of particles is an extensive quantity, to remind you from freshman chemistry or physics, how I think of intensive and extensive,
10:02
an intensive variable is something that if you take a system and you doubled it, and you say, did the variable of interest double or change as well? So for example, if we just take theoretically
10:18
a couple centimeters cubed right here and I said, how many particles are in there right now? And I say now I double that box, and I say how many particles, well, you know, that number doubled as well. So the total number of moles probably doubled, or the amount of matter doubled. But if I ask what's the pressure in this little box, and then I double it, what's the pressure of double that box the pressure stayed the same, so that's an intensive parameter.
10:46
While one that stays the same as you double it, the extensive one is one that typically scales with the size of the system. And it's also very important to keep in mind that every single one of these extensive parameters here
11:04
are typically used in an intensive way. And so you can make everything as a chemist, we almost make every extensive variable intensive just by dividing by the number of moles. So if you take the ith component and divide by the total number of moles, then it becomes intensive, it doesn't change.
11:27
So if you take the total volume, but instead you take the molar volume, so the total volume, the volume divided by the total number of moles, et cetera, you can see how this plays out. And even entropy we typically do it over molar entropy, et cetera, so this is one way to, a common way that we make these extensive parameters intensive in nature. But the natural extensive have intensive pair matches, so the conjugate variable to the total number of moles is its chemical potential.
12:04
Its potential to react, to do chemistry, for each one of those components. For volume, it's intensive, pair is the pressure, the force per unit area. You can take it from a volume, which is looking at three-dimensional space, and you can take it down to two-dimensional space like an area, and its intensive is its surface tension, or one-dimensional, just the length, and that goes in a sense, it's the tension or the force on that.
12:41
We can go do things with electrical charge instead, and this is electrons, electrical charge, a lot of electrochemistry, et cetera, we can do magnetic fields, and look at again like the magnetic moment,
12:56
and its associated magnetic field, for example.
13:04
And then finally, the one I include at the bottom, which is heat, so all of these represent, different types of what we generally just call work. So this would be the most familiar, which is what we generally think of as just mechanical work, how PdV work, or pressure volume work. But this is chemical work, in a sense. This is how chemistry changes things, et cetera, and then this is electrical work, and magnetic work, et cetera. But besides having these in a sense mechanical or work type,
13:41
chemical and mechanical work type terms we also have in a sense something that gives us a relation to the microscopic. Which is how the temperature and what we're gonna be defining in this course and trying to understand more and more, which is the entropy of a system, how it changes. And this gives us a direct relationship, entropy, to information, Shannon theory, to fundamental formulation for what information is, for what a bit of information is. It has far-reaching implications in that,
14:18
as well as to the microscopic, to quantum mechanics, to classical mechanics, to individual particles, and how these configurations change, and how they change and can cause propagation of heat.
14:38
So each one of these conjugate variables, like temperature into entropy, like pressure into volume, like chemical potential into the number of moles, right? They come as conjugate pairs, and they get added or subtracted to the overall energy. Each one of 'em are energy terms themselves. Pressure volume is an energy. Temperature, the change in entropy is an energy. The chemical potential into its, the number of moles of each one of those is an energy, and then we just add or subtract those
15:15
to get the overall energy of the system. So energy is so fundamental, and typically what we're looking at thermodynamics, that we look at it in several different ways. And so this shows the ones that are typically most used,
15:33
you know, in biochemistry or chemistry, which is we look at them by looking at the energy and then basically manipulating these conjugates around.
15:44
Which one is the dependent variable versus the independent variable? So we do that by reformulating the overall energy of the system into different, you know, more or less forms of energy, which are all in a sense different. So we look at the Helmholtz energy, often called the Helmholtz free energy, or the Gibbs energy. The enthalpy of the system, et cetera. I would say in chemistry it's typically the enthalpy in Gibbs free energy we end up looking at most.
16:17
And this changes the natural variables. The natural variables for the internal energy are how the entropy changes, how the volume changes in the number of moles. But by switching to, for example, the Gibbs free energy, which is defined here, now we switch that from not the entropy as the dependent variable, but the temperature, and not the volume but the pressure, as being the variables that we look as far as changing. And it even points to why often as chemists,
16:51
we focus so much on the Gibbs free energy. Which is, oftentimes you want to look at how chemistry happens. That's how the number of moles of something changes. But you don't want to change multiple variables at the same time, so practically as chemists, it's typically much easier to hold the temperature and pressure of a reaction constant so that you can really look at what's going on in the number of moles in a system, than it is for example to look at the internal energy directly
17:20
where you would have to hold the entropy and the volume of a system constant to be able to really focus in just on the chemistry of the change in the number of moles in a system. I also like to point out, a lot of this information, this fundamental information, while it's in lots and lots, thermodynamics is a very established theory, and books have been written about it since the Industrial Revolution.
17:48
But Wikipedia has excellent fundamental examples,
17:56
and goes through this in really good detail.
18:01
So with those potentials that we do,
18:07
we usually look at what we define as,
18:16
the first law of thermodynamics, which is looking at that energy is conserved in a system,
18:25
and we can define energy in terms of either heat, or different types of work. And generally in chemistry we're not dealing with magnetic work or electric work et cetera,
18:39
but we often do separate out chemical work, because it's what we're looking at most often as chemists.
18:46
And so heat always has a unique term to it, and we're gonna look at this in a lot more detail. In fact, we'll have a completely separate video on thermodynamic laws and/or postulates that kind of define the field. This is meant to be more of a general overview. But heat always comes as this term that we're gonna look at in a lot more detail, which is entropy.
19:10
Work, usually we define mechanical work by just how it changes its pressure-volume relation, and it's often called extra work when it's a surface tension or when it's an electric charge, or when it's a magnetic field, et cetera. But again as chemists, we almost always separate out chemical work, because this often why we're doing thermodynamics is to predict whether a reaction will happen or not, or what the changes are in different reactions, and how the number of moles are changing,
19:40
can we predict it, et cetera? But this is usually where as chemists and biochemists we stop. And this is often called the combined first second law, or really what I think of as the fundamental equation I write down most often in thermodynamics. 90% of thermodynamic problems, I start right here.
20:03
And just to give you a brief sense of where we're heading, we're gonna look at some of the mathematics as well, in the near future, and kind of how you get from here to here. In other words, how you change the internal energy to these other oftentimes more useful forms of energy that we want to look at in a system. Like for example, again, the Gibbs free energy, when if we hold temperature and pressure constant, the change in the Gibbs free energy
20:31
just goes as how the number of moles in the system changes, which is often seminal in chemistry to be able to look at. And this is looking at Legendre transforms, how we go from these changes, and again, it's covered on this Wikipedia. And we'll cover this in a mathematical examples in thermodynamics in a future lecture.
20:56
So I like to also summarize something again,
21:01
is given to you in Wikipedia, but it kind of also states why these different
21:09
thermodynamic potentials are important, and it's also important to say that there's a convention to what we consider positive heat and positive work, et cetera, and it's kind of shown here. And this often causes a lot of practical confusion when working problems is bookkeeping, whether we're talking about,
21:31
the convention is is that heat is positive going into the system, and work is positive when it's done by the system on its surroundings, so as summarized here. And by in a sense mixing up these conventions, it can cause a lot of practical headache when working problems, so I like to mention that. But what we do is often practically try to make it as easy for us as possible, and because this macroscopic theory, as we'll see, when we look at some of the mathematics
22:02
allows us to define very few macroscopic variables that define the complete thermodynamic state of the system. We often look for natural variables that are held constant so that we can look at some specific component, like I've already stated. So, while the change in internal energy is how the overall energy changes, the change in the Gibbs free energy is the non-mechanical work done on a system, or in other words the chemical work on a system.
22:34
And often it's why we use this so often in chemistry to predict whether a reaction will happen or not, for example.
22:45
The other thing I want to, you know, enthalpy is very common to look at, because again it's the non-mechanical work that we're looking at, as well as the heat, which we all know as chemists we often have some control over temperature, we're interested in entropy effects, et cetera. Finally, I mentioned this for completeness, but we rarely talk about the Helmholtz free energy. In physics it's commonly represented as a capital F. In chemistry, biochemistry it's typically a capital A
23:17
for Helmholtz free energy. And it's because this does have, is basically the overall total work in the system, and just generally it's not nearly as applicable for experimental chemists and biochemists.
23:34
But that said, one of the things is in computational, where it's much easier to hold volume fixed in a computational system, while experimentally it's often much easier to hold pressure fixed in a system. But you'll see I introduced this, even though we won't be using it much practically in biochemical thermodynamics.
23:59
And so this just again resummarizes some of the things we're gonna look at in the future. We're gonna go through some of the mathematical relationships, we're gonna look at all the laws that really allow us to derive this equation, and these, et cetera. I'll mention one other thing, which is sometimes you see this is as a negative work when they define it as positive PdV, and so again this often comes as a convention.
24:28
Finally, I want to say where we're heading. After this introduction, we're gonna look at, in a sense, the laws or postulates that allow us to formulate this basic equation in thermodynamics, and use it solve practical problems. We're gonna spend an entire lecture just looking at some of the mathematics in thermodynamics so that we feel comfortable with this,
24:54
because it's really using partial derivatives, and being able to use basic multi-variable calculus that really allows us to use thermodynamics to its full potential as chemists or biochemists.
25:11
This semester we're gonna focus almost exclusively on equilibrium thermodynamics, which is often tied a lot we'll see versus reversible, versus irreversible processes, and how this plays out in entropy and other functions. But defining really what equilibrium is, from a microscopic level, what reversibility versus irreversibility, we'll look at some of that. And then also I think it's very critical, our gateway to looking at thermodynamics from an experimental practical standpoint,
25:42
to make measurements is often calorimetry, so we'll have a lecture just introducing some basic calorimetry concepts and instrumentation, et cetera. A lot of what I'm gonna be covering will be covered in a lot of detail not only in textbooks, but I provide a set of lecture notes that have been produced over the years that are at biopchem.edu under the Lecture Note heading.
26:13
So thank for you listening to this introduction to thermodynamics, I look forward to talking to you guys in the future.
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