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0:01
- Hi I'm Jeff Yarger I'm a Professor of Chemistry, Biochemistry and Physics and this video is going to overview Physical Chemistry for the Life Sciences edition number two,
0:14
chapter two in this textbook and as far as general information about Physical Chemistry for the Life Sciences or biophysical chemistry I have a website that I keep with general information on all topics in this area. You can also reach me at this email address if you need to reach me directly. So the first part of Atkin's book, the second edition goes through biochemical thermodynamics which is our macroscopic theory for understanding biochemistry and biochemical processes.
0:51
So we made a different video looking at chapter one which is the first law of thermodynamics and today we're really going to be looking at the second law of thermodynamics, and this is what I'd say is at the heart of thermodynamics and the first two laws really define what we mean by the conservation of energy being the first law. Incredibly fundamentally important. And it is something we kinda already have an intuition of from numerous other scientific fields et cetera. It comes to play a lot.
1:27
Now in the second law is where we're going to introduce entropy and this is really what I would say the crux of thermodynamics. Chemical or biochemical thermodynamics is really understanding entropy and its relationship a both a macroscopic level and a microscopic level to really get an understanding for the theory of thermodynamics that we use to understand biochemical processes. So like I've done before this is not meant to supplement reading the textbook chapter,
2:01
going through the example problems. Working things, looking at some of the checklists of the key concepts, discussion questions to make sure you understand some of the concepts being discussed. The excellent set of exercises and projects associated with this chapter is really how you're gonna you know understand this material the best. This video's really kinda meant to overview the topics covered in this chapter on this important topic of the second law of thermodynamics,
2:36
and what I'd like to do is basically provide one slide on each of the major subtopics that this book covers, and are listed here. And it's really breaking into what first mentioned which is the second law and its introduction and understanding of entropy, and then because of the huge importance of the Gibbs Free Energy in chemistry and biochemistry you know, the second part of this chapter after we're now able to introduce what entropy is and something about heat.
3:14
That allows us to look at kinda this heat work relationship that we use to define chemical work in the Gibbs Free Energy which we'll get to.
3:27
So the first is looking at kind of introducing before we actually introduce the second law, what Entropy is et cetera. It introduces some macroscopic concepts that we're very familiar with, and it's basically going, helping us to find what is kind of in a spontaneous or natural direction as a function of time that we're used to seeing, and it points out some things that we have a lot of intuition for. Like for example if I told you a thought experiment,
3:58
take you know, within a container all of the molecules in that container and put 'em up into small volumes. Say for example we compress some CO2 gas into a small little cylinder and it's a higher pressure and at room temperature and then I said, now relax that condition and let it expand into a larger volume container for example, so we would have all the molecules say in one area and then we allow it to expand
4:31
into a larger volume, or we just say we make an initial condition that even though it was in a larger volume we put all of the molecules in one area and we ask what would happen as a function of letting that constraint go whatever was holding those there or whatever created that initial condition what would happen? And we have an intuition what would happen. Gas molecules same with liquid they spread out to fill their container right? But you don't typically, you know and that would happen
5:04
if we made this initial condition it would spontaneously do that right? But the reverse doesn't happen, so there's a, in a sense an arrow or a direction that has an intuition to it. But what we don't see is the reverse happen ever, from intuition which is you have gas like in this room, we have gas molecules throughout this room. There's a chance why don't they ever all come together in one area, right, like shown here? So this kind of going back in this direction
5:40
is not spontaneous, and so this is showing matter of specific in kind of 2D of a specific number of particles,
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we can think of the same with something a little more vague like energy. Or something that isn't particles directly. But energy we could have a hotspot in an area indicated by red and then it gets colder in this direction so we have a temperature gradient in some sample, say we've heated this up real quickly, and what happens over time? What happens is spontaneously just over the course of time that temperature distributes across that via its thermal conductivity et cetera.
6:24
But what we don't see is the reverse. If we have heat distribute evenly, energy distributed evenly across say, a metal cylinder we don't all the sudden see part of it get really hot and the other part get colder even though that could conserve energy,
6:42
that's not what happens in real physical processes, and so the second law helps us understand this direction and they'll call it a lot of things. A direction in time, it gives it time's arrow.
6:59
But why things happen in a certain direction, and not in the other direction. So the book starts by setting up what some of these spontaneous natural changes are, so that we kind of have an intuition for 'em, and what the second law says is that for things to happen spontaneously in that is to increase its entropy, and so what we're gonna end up spending a lot of time doing is trying to really understand what entropy is from several different angles. From a microscopic perspective,
7:37
from a heat engine macroscopic what is it as related to heat that we have some intuition for, a macroscopic behavior. You can also look at it from fields that you wouldn't naturally think are directly related. Like from information theory and Shannon Entropy. How information directly relates to entropy and this is why you often hear it in computer science and especially in cryptography and everything what was the entropy of that et cetera. It has a direct relation to the macroscopic entropy
8:08
we're talking about here. The second law of thermodynamics has far reaching implications through all of fundamental physics and all scientific fields that use those fundamental theories. So Rudolf Clausius who was one of the really pioneers of thermodynamics and specifically entropy. Is famous for making one of the general statements about the second law of thermodynamics, which is "The entropy of the universe tends to a maximum." I tend to like to put that in a very specific
8:42
mathematical formula, math being the language we use to describe any science. So which is the change in entropy with respect to time, right is always gonna be greater than or equal to zero, and so this is often mathematically how we would state the second law of thermodynamics. And this is how it's often put into words, now one of the complications, the first law conservation of energy it's almost succinctly put in one statement that you can, and then it's just how we conserve that energy
9:19
and how we break it up to look at it in useful meaningful ways for specific problems, and then in macroscopic thermodynamic systems, especially biochemical systems et cetera. It typically makes sense to split it up into work and heat and to say those things are conserved, if the overall energy of an isolated system like the universe as far as we understand is conserved.
9:42
Now the second law while it can be stated as I stated it here with Clausius has lots of different
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basically fundamental statements that have been given to it.
9:57
So this being one of them a lot of times they'll put you know they'll first say of an isolated system that the entropy of an isolated system must always stay the same or increase as I've stated here. Some people will talk about it with respect to engines and cycles that in any cycle in any closed cycle system that you either have to entropy either has to stay the same or increase et cetera. So there's several different ways that the second law has been stated both in words and mathematically.
10:36
So I'd like to show another which is one of the other most common general ways to write the second law is to introduce entropy in almost kind of a definition way. Which is to say that the change in entropy is either equal to or greater than the change in the heat over temperature, and oftentimes as we've discussed before this. Delta sometimes this infinitesimal change which is also indicated by this derivative here. This is indicating that it's a path dependent.
11:11
While this will be a state function that will end up being path independent.
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But this is really a change, and oftentimes sometimes this gets left out the change, and we've talked about this before this can often be common like when we say the height of something. Oh you know the height of that mountain is 10,000 meters. What we really mean is it's a delta h it's delta it's with respect to sea level being zero. So a lot of things that we indicate in science are really changes in a variable. It's rarely absolute, but oftentimes we're so common
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to drop that we just call it the height. We don't call it the change in distance, or change in height of something. We just say it's the height of something or the altitude but it's really a change in something, and the same happens here. So often that gets dropped and what your book does is goes specifically into a special case of this. The special case where this isn't an inequality but an equality and it's an equality that the change in entropy is equal to the heat over the temperature.
12:27
The change in heat over the temperature in a reversible process, and it goes on to really try to describe, because you can really separate the second law in thermodynamics into reversible thermodynamics, and irreversible thermodynamics, by this. By whether the entropy is equal to this quantity or greater than, and if it's greater than, irreversible processes.
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Which can be spontaneous but you can also do these in such a way experimentally, et cetera. That you keep 'em reversible and it usually means kinda small incremental changes in something like you're very familiar with, with introductory physics. This is when we talk about frictionless things. Where we do things slow enough that we don't
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dissipate our work into heat et cetera.
13:17
So, this is is kind of how your book defines the second law and again it's a very common way to throw the restriction that we're gonna really look at entropy in a reversible sense, and one of the reasons your book does this instead of starting with these inequalities in a more general sense. Is really when we're doing introductory thermodynamics and almost everything we're going to cover in this course is all irreversible equilibrium thermodynamics.
13:47
There's a whole separate advanced topic on irreversible, non-equilibrium thermodynamics. Which I would say is often not covered much at the undergraduate chemistry, biochemistry level. It's typically reserved for more graduate level courses. But I think it's important to recognize, and especially in biology where irreversible, and non-equilibrium processes are very important for life itself. So it's important to realize that,
14:19
and then you know the book has several figures I show one here. Just kinda showing some of the change in entropy with respect to for example a ratio of temperature here. That you're increasing this entropy as a function of temperature et cetera.
14:40
So then there's really the first two laws of thermodynamics are the pillars that we build it upon, the zeroth law and the third law. Which often help define an absolute temperature scale and what we mean by an absolute entropy. Comes because of this statement, that the entropy of a system approaches a constant value
15:03
as the temperature approaches absolute zero which is helped defined. So that's why we use a Kelvin scale which is an absolute temperature scale from absolute zero being zero Kelvin up in temperature to say 298 which is around room temperature et cetera. It's an absolute temperature scale and it's typically what we use in the physical and chemical sciences. And because it's always approaching, in other words it's dispersionless as you get near absolute zero.
15:42
It stops changing, it comes in horizontally here, that we can always kinda define that at absolute zero as being zero entropy because your delta S is basically approaching zero in the limit as T goes to absolute zero. And so your book kinda shows how we typically re-normalize everything and call this the zero.
16:07
It's our defined zero of entropy and that now allows us to often write absolute entropies. Where we're always referring everything back to zero degrees absolute zero being what we define as the zero of entropy in the system, and then how we take entropies and how we look at those with respect to derivative properties or changes in entropy like heat capacity et cetera. Because we looked at heat capacity in chapter one as its relation to enthalpy now we'll see that it's directly
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related to entropy as well.
16:52
And then after kind of introducing what I would call that classical definitions of thermodynamics, it's through cycle, through engine cycles like Carnot cycles where you have isothermal and adiabatic processes which we covered in chapter one. Or defined isothermal constant temperature. Adiabatic now we'll say that as being constant entropy or constant heat in a system. Your book also because this is for more chemistry, biochemistry type audiences really takes some time
17:27
to also show how entropy is related from a molecular standpoint. Now this, can be put in much more rigorous terms after you've had some microscopic theoretical understanding. Quantum chemistry, quantum biochemical systems, spectroscopy et cetera. Where we can really define these number of micro states. Or a number of configurations in a system, and so we'll give a general sense for 'em now. But really when you come back to this in statistical mechanics et cetera is when you've had
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some of the microscopic understanding of what these micro states are, and so the log of those. Specifically the natural log so, written here is in a sense the log of the number of configurations time a constant which we often call Boltzmann's constant now we often give it a sub b is the entropy as well, and like I said this is just, and we can look at this as, so the book also kinda gives an explanation of entropy from a molecular standpoint and talks about for example,
18:41
the number of different configurations of how you can put hydrogen around oxygen in an ice crystal and shows the six different configurations and talks about configurational entropy. It talks about if you for example make in a two dimensional sense the volume bigger by making this length longer that you can see that if you were at a specific temperature here, that would now you would have more configurations because if you looked at for example,
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a particle in a box you would have more energy levels available to you all within a certain temperature range. So you would have more micro states, so this w would go up in this sense which means entropy would go up in this sense as well, and then I like to just remind that this is all because of the pioneering work of Ludwig Boltzmann. Who even, this is such an important way of looking at entropy especially from the molecular sciences standpoint that it was written on his tombstone,
19:46
as his real crowning insight into the fundamental nature of thermodynamics, and really it can't be over expressed. I mean this is really the gateway into our, our connection between our macroscopic theory of thermodynamics and our microscopic understanding in quantum mechanics, et cetera, and the bridge being the Boltzmann equation and the statistical mechanics or statistical probabilities that go into large numbers.
20:19
So then the book reminds us of things we've seen at kinda introductory chemistry level. That we can now start to look at the change in things and this is a state variable. Which means it's exact differential, so it's path independent, and so that we can look at it kinda the same way we did the enthalpy which we introduced when we were looking at the first law, and one thing you might ask is why aren't these delta S' because before we would often do this as the delta S
20:48
of say formation and this is meant to indicate that it's a standard state. So we're still at the standard state, the m is for molar which is fine. So we're gonna do it per mole, we're gonna turn those extensive variables of entropy into molar entropies to make them intensive. So we can understand that variable. But why doesn't it have a delta here, these are in absolute entropy terms. Because of the third law that we can always state that we're gonna reference this back to absolute zero
21:17
or our reference state for everything is the same. Zero entropy at zero degrees, absolute zero temperature in Kelvin. So that's what allows us to kinda drop these delta S' but these really are the change over that. It's just that we have a standard state that's the same for everything, that allows us to do these. So these are molar standard state entropies and it's be its stoichiometric coefficient and we sum up all the products and we can do this versus the reactions
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and so Hess's law kinda works the same here, and like I said we can say that this change in entropy that after we integrate it we would say, is a delta S like this is a state variable and it's independent so it works like the enthalpy did. It works like the internal energy did et cetera, where the change across it we can take whatever path is most convenient for a problem. The one where we can know the variables and that it would be the same if we took a different path okay.
22:23
And we covered your book covers chemical reactions because it's important in what we're dealing with here which is in physical chemistry. Where we wanna really, often are looking at chemical changes of a system.
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So that gives a brief introduction to entropy. Both from kind of a molecular standpoint, from a macroscopic standpoint and kind of more or less reminding us of things we saw in our introductory chemistry class. Maybe just looking at it a little more rigorously, putting it in kind of calculus or change mathematical terms et cetera. And so because of the importance of how often, once now that we understand this type of heat. That heat now is really in a reversible sense
23:12
related to temperature, that the heat in a system. Is related to the temperature or the change in entropy in a system, so now we really, and we can start to really quantify this term. We already had a sense for what temperature is, and now it's giving us a sense for this disorder. This entropy, this ability, these microscopic configurations this relation to probability and information theory et cetera.
23:44
We come back and we want to now look at just like with enthalpy, instead of looking at internal energy directly. We looked at a different type of energy that we called enthalpy and the reason we did it is we're often at constant pressure. Where the enthalpy is directly related to just the heat in a system, and that gave us by looking at it, energy in that dependent variables. Kind of allowed us to make some direct relation to heat. Now we'll be able to look at heat in this way,
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and what we wanna look at is energy, as it's related to chemistry. The change in chemical processes under what I would say are the typical variables in either biological systems, or normal chemical systems to do types of reactions which are often under constant temperature and constant pressure conditions, and so again we define a new type of energy and this, we call it the Gibbs Energy and it's 'cause it was formulated by Willard Gibbs, Yale, and he did so much seminal work in thermodynamics.
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That quite a few things Gibbs phase rule, other things are named after. It's defined this way, oftentimes your book and quite others will recognize that we already define this as the enthalpy so often times you'll see it just written as H minus TS, but just to write it out in its full form I would write it as fundamental variables that it's U plus PV minus TS. So we can look at that, we can think of it as a Double Legendre Transform on both PV and TS from our internal energy.
25:36
We can look at it, we can look at the change in the Gibbs Free Energy related to this, that it could be the change in the enthalpy minus the temperature, the change in the entropy if we're at constant temperature right? In other words if you can go through this.
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So you often see this, in fact one of the fundamental equations you see is that dH is or dG is dH minus TdS right
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or written oftentimes like this.
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Now that assumed when you were doing a derivative through this term here that temperature was constant, and often times it's almost always formally stated in textbooks, but often we're obviously just looking at lists of equations and it's one of the things I like to emphasize, really make sure you know when you're looking at different equations you know students will say god there's so many equations for the same thing. For enthalpy or for Gibbs Free Energy
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or entropy it's oftentimes just like before when we saw the entropy. For reversible systems it's this, for irreversible it's this it's often knowing when you write an equation that you write what the assumptions are. That this is at constant temperature, become very important in when you can use certain ones et cetera, and this I specifically write because of its incredible importance in biochemistry and life processes et cetera. So while the second law tells us that we maximize
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entropy we're gonna minimize our energy and specifically our Gibbs Free Energy and we're usually doing this at constant temperature and pressure,
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and your book kinda goes through the systematics of this and then it goes directly into some very important processes in biochemistry, in biological life processes like for example the ordering of water around hydrophobic molecules. Or this hydrophobic interaction, and how you can kinda understand this based on some things we already talked about, about how entropy looks at the amount of order, disorder and how you can order these water molecules
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around hydrophobic things and how that helps us understand at a microscopic level how you can decrease entropy, or how enthalpy or entropy type changes balance each other.
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Okay and then finally it talks about it in the way that we talk about constant temperature and pressure. About just chemical work that when you're at constant temperature and pressure and so the mechanical term
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drops away and so does the heat term and you can look at it as just the extra work or the available work in a chemical process for chemistry or for things to change, number of moles to change based on their chemical potentials and interactions and very importantly is just like we can define spontaneity. How we came back in the very first of this chapter to look at spontaneity and its relation to maximizing entropy. Spontaneity in these constant temperature pressure processes
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minimizes this Gibbs Free Energy, and so if the Gibbs Free Energy ends up getting less than zero it's a spontaneous process, greater than zero the change in Gibbs Free Energy is a not-spontaneous process et cetera. And so it's very important that we make that relationship back to entropy.
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So and then like I mentioned the book then, it's very critical after you've kind of looked at some of these concepts and grappled with them yourself that you really look through the key concepts, make sure you understand them. I list the key equations here, a lot of which we covered
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in looking at this overview that's really the mathematical definitions that really give us our biggest insight into this, and then it's critically, in fact hopefully we'll have time to make some videos on discussion questions and then go through the really doing this build and solidifies your understanding of these concepts and the key concepts is doing some of the exercises and projects associated with it. I hope this overview helped on the second law and it'll be followed up with future videos
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on each chapter within this text, thank you.
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