Lecture 01. Syllabus, Homework, & Lectures.
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Man pageDigital elevation modelMashingVancomycinKnotBohriumNana (manga)Methylmalonyl-CoA mutaseDrop (liquid)Set (abstract data type)Ice frontStorage tankWalkingSetzen <Verfahrenstechnik>Reaction mechanismPaste (rheology)ElectronElectronic cigaretteWhitewaterAnomalie <Medizin>ExplosionWaterfallLecture/Conference
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Man pageSodium hydrideVancomycinManganeseDominican RepublicGrading (tumors)BeerEnolMethylmalonyl-CoA mutaseGrading (tumors)TopicityCollectingSet (abstract data type)WursthülleSense DistrictWaterTiermodellElectronic cigaretteThermoformingAreaWhitewaterLecture/Conference
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Transcript: English(auto-generated)
00:06
So what we're going to do today is we're going to go through and talk about the logistics of the course, how you're going to get graded, what you have to do to get a decent grade in the class, and then we'll start talking about statistical mechanics. If you haven't found it yet, here's the URL.
00:21
What we want to do is just sort of click through some of these links because they contain all the information for the course. That's what I'll do. So, oh, I stole this from some beautiful work that's been done in the area of molecular dynamics.
00:41
And we're going to be hopefully talking about molecular dynamics at the end of the course. And if you want to know more about this picture here, which depicts something called a conical intersection, or the esoteric concept, you can go to this paper right here. All you have to do is if you click on this beautiful picture
01:01
on the front of our website, it'll take you directly to this paper and you can read more about it. It might not make an enormous amount of sense until we get to the point where we talk about this subject later in the course. Okay, so the very first link on the website is something called announcements.
01:20
Now, this is where I'm going to be posting announcements that I want to make in the class. I'm really not very good with Facebook, and I'll talk more about that in a second, which is the reason why I post my announcements to this page, instead of doing something more intelligent, because I know you are all Facebook experts.
01:40
But what I will do is I will post my announcements here. They will be in inverse chronological order. So the most recent announcement will be at the top, and then there will be a list of all the announcements that we made during the course. So you'll have sort of a record. If you miss some, you can just scroll down and find them. And I'll probably post an announcement or two almost every day. So it would be a good idea to just check this, bookmark this,
02:03
link announcements, and check it once a day or so, and see if there's anything. Maybe I changed the homework assignment. Maybe there's some information about the quiz that's coming up on Friday. Maybe there's sample midterms. All of that stuff is going to be posted here on this announcement page.
02:21
This is the syllabus. We'll go through this in a little bit more detail, because this is kind of important. But the first thing I would like to impress upon you is that we don't want to print everything from this website. We don't want to carry around a folder. That's got all of the links to this course.
02:42
We don't want to print everything out of all the homework assignments. Right? Everything is going to be electronic in this class, except for the quizzes and the exams. Virtually everything else will be electronic, and that's the way we want to keep it. We want to converge towards having a perfectly paperless course.
03:01
We're not there yet, but we want to try and get there, because ecologically, it's a lot better. Okay, so please don't print every slide from every lecture. Stick that in a notebook. And it's a perfectly useless thing for you to do, because these slides are going to be posted on this website until you are old people.
03:23
Honestly, it's true. If you go back, the very first websites we created, like in 1995, all of that stuff is still on the internet. It never went away. So we don't need to print all this stuff. Let's not do that.
03:43
Now, we're fortunate that we've got two lecture and teaching assistants. Steven, you have Halsey? Steven, are you here? Steven's right back there. Steven. Steven's an expert psychosophist. He knows everything about the subjects that we'll be talking about this quarter.
04:02
Don't let him tell you anything else. And Jim Mark-Johns, he was a TA for you last quarter, so you were in 131B. Maybe you know Jim Mark. He's back there. These two guys are going to be teaching all the discussions. I'll have more to say about them in just a second.
04:20
Steven's going to be moderating our Facebook site. The Facebook site's going to be important to you, but since I don't know anything about Facebook, Steven's going to be the one who moderates everything that goes on there. So you'll be interacting with Steven through Facebook and seeing him also in discussion. All right, we know what lecture is.
04:41
We know what my office is. It's in SI2, room 2137. You want to know where SI2 is? Yes. 2137 on the second floor, and it's in this hallway that's behind a set of doors,
05:00
the purpose of which is to keep people from randomly walking in to these offices, which you shouldn't be discouraged from coming to find me, right? This office is right in front of the building. You can open that set of doors, walk down the hallway, find my office, the door is virtually always open. If I'm in there and the door is not open, it's because I've got
05:21
like a cramped deck on here or something, but most of the time, if you need to talk about something, you have anything to do with your class or the materials, if you have a question about something, you can just come and ask me. We're also going to have office hours that happen sort of right after lecture. There's usually a shady chair in the park right outside the
05:42
store where we can sit and talk, and so some of you I know will want to eat, and some of you will have other classes, but if you don't, and you have a question about lecture, what I have found is the best time to ask that question is when it's going to be fresh in your mind. You just heard it. You didn't understand it. You wanted some clarification. All right, so I'm going to try and sit over in that chair
06:04
and answer my email, and if no one shows up for five or ten minutes, I'm going to go walk back to my office and have lunch myself, all right? So if you need to find me, that's where I'll be right after lecture. This is the text. I know you all have it because we needed it for 131C.
06:20
There's our Facebook link. The way we're hoping Facebook works, and the way it's worked effectively in the past is that students talk to one another on this Facebook page and offer hints as to how to answer various types of questions, and it turns out to be very, very useful. In other words, Stephen doesn't have
06:41
to answer all the questions, although he will stir the pot and answer the questions when he can, but you can talk to one another about problems, quiz questions, and so on, and answer each other's questions, and in the past, things have sort of automatically worked that way. It's a miracle, and so hopefully it will work exactly that same way this quarter.
07:01
That's what we're hoping for. This is the normal boilerplate that we always have to post. It has to do with ads and drops. You can read it. There will be quizzes almost every Friday. There's a quiz this coming Friday, and going back to the quiz system, if you had 151, we tried to get away from it.
07:22
That was met with enormous persistence. I got a lot of feedback about homework in 151, and almost all of it was negative, so we're moving away from that model. In this class, the problem is there really is no electronic homework option for us.
07:41
In other words, even if we wanted to do electronic homework, there isn't any mechanism for doing it. The paper homework, logistically, is a nightmare in a class of this size to do well, so there will be assigned homework. None of it will be graded, and no one will ever know if you do it, except that if you don't do it, the quizzes are going to be focused on trying to find
08:00
out whether you did it or not, so it will be helpful for you to do it. All right? We will usually have a quiz the first 20 minutes of each Friday, except it will be a week where the quizzes are worth a lot, 200 points on the 600. There will be seven quizzes, only you can choose the top five.
08:21
In other words, you can drop two quizzes for any reason. If you're going to be gone, you don't need to talk to me. You can completely blow a quiz, right, or sleep late. I don't know how I'm going to sleep late.
08:41
You don't need to worry. You've got two dropped quizzes, not just one. Okay? We're going to average those, or actually we're going to total those five quizzes to get those 200 points. Each quiz is going to be worth 40 points times five is 200. Boom. All right? Each quiz will be multiple guests. That might seem like a giveaway to you, but none
09:03
of the above will be an option on every question. And the questions, many of them, in fact, most of them are going to be numerical questions where you have to work out a problem, choose the right answer, and if the right answer is not there, the answer is none
09:22
of the above, and none of the above will be an option that we use. Okay? So these quizzes are actually quite difficult. Previous classes have told me it is nontrivial to do well on these quizzes. There will be five quiz questions, and what that means,
09:42
as I'll explain in just a second, is if you missed one, you've still got an A. If you missed two, you've got a B. If you missed three, you've still got a B. If you missed three, you've still got a B. If you missed four, you've got C, like a C. Okay? So you can afford to miss one.
10:01
You can't afford to miss more than one. Most of you want an A in this class. Okay? Oh, here's the, I don't know why. Here's our Facebook. Here's Stephen's notes. Welcome statement. Right? Check out the Facebook page when you have a chance.
10:22
Okay. In addition to the quizzes, we're going to have two midterm exams this quarter. That's different from previous quarters. One on April 27th, one on May 25th. These are both on Fridays. They're going to both be in class. They're both going to be worth 100 points. They're both going to be completely problem-oriented, and I'll have a lot more to say about these later on.
10:42
Final's on Tuesday, June 12th. That'll be comprehensive. It's worth 200 points. There are six discussion sections listed here. Here's where they're located. Here's who's going to be teaching them. You can go to one, two, or all six every week. No limit.
11:03
The way these discussion sections will be structured is that Stephen and Gia and Mark are going to prepare a discussion study guide. Many of you are familiar with this concept from the classes that we had with me before, probably other problems. The discussion study guide has three or four problems on it
11:21
that we consider to be central problems to the material that we covered or are covering during that week. Okay, so what will happen in discussion is they will take your questions on any aspect of the course that you have, right, ask them any question that you want. If you run out of questions, we're going to work through this discussion study guide together,
11:41
maybe in small groups, all right, and make sure that we understand how to do these key questions. All right, we're going to post these discussion study guides on the lecture page. You'll see where there's a link for those. So if you want to look at it before discussion, try these problems out. We'll be able to do that, all right. We're going to post the one for this week, later on this morning.
12:02
We've been working on it this weekend, which should be done right about now. And so hopefully early in the afternoon I'll post it. You can look at it. If you have a session tomorrow, you can be prepared for that. Okay, homework problems will be assigned on Monday each week, blah, blah, blah, blah. I'll show you the homework page in just a second. Your class name will be continuously upgraded
12:22
on the Triple E website, okay, and the way the grades are going to be assigned in the course, again, if you have 151, you're already familiar with this scheme. You need to get 80% of the course points,
12:41
which in this case is 480 points, because there's 600 total course points. All right, you have to get 480 to get some flavor of A. I decide where the dividing line is between A and A minus, and I do that depending on where there's a break in this distribution. All right, but I guarantee you, if you get 80%
13:01
of the course points, you're going to get some flavor of A. If you get between 60 and 80, you're going to get some flavor of B. Again, I draw the lines where it makes sense to draw them, but that's a hard cutoff between 60 and A, 60 and 61, that's where the B cutoff is,
13:22
NCEs, analogous, and so on. Okay? So in principle, everyone in this class can do well, and historically, everyone in this class, the vast majority of the people in the class, do quite well.
13:40
I'll show you in a second. All right, exam regrading, academic dishonesty, these are unpleasant topics that we don't really need to talk about too much. All right, lectures. Here's the lectures that I gave last year. You see how there's an asterisk next to each one of these lectures? So if you want to see what the next lecture's going
14:02
to be about, you can click on this lecture from last year, you know, a pretty good idea. Now, believe it or not, I take each one of these lectures and I try to improve them, so there will be a new and improved version of this lecture posted later on today. It won't have a star by it, it won't have an asterisk,
14:20
that will be the new lecture for this quarter, right? I did make some changes, and so, but I am lazy enough to tell you that the lecture that I'm going to give you today is closely related to the one I gave last year, which I worked really hard on, by the way.
14:40
Okay, here's the discussion study guide for this week. It's not actually posted yet, but it will be posted later on today, and in principle, there will be a YouTube video of this lecture, which is a new experiment that I'm doing. That's my, the concept very frightening, I'm full set. Over here, I continue to do this experiment
15:02
after one or two lectures. Okay, here's where the exams are. Notice that each quiz is listed. Here's quiz one, week two, here's quiz two, here's quiz three, there's no quiz in week four because there's a midterm. Okay, so there's a lot of information on this page.
15:20
I'll remind you of what the quizzes are going to be. Here's the homework page. Homework one is to do all the odd problems in chapter 13. Here's the key, right, every problem's worked out. Click on this and you can download a PDF of the key here.
15:43
Okay, likewise for the other chapters. Here's all the homework I'm going to do this quarter. It's a thing of beauty. Results, as we get them, they will be posted to this website. This will end up being a long table that looks a lot like this. Here's last year's table.
16:01
Quiz one, quiz two, quiz three. Here's the key to the quiz. Here's the grade book in which the quiz grade is tabulated. Here's the midterm exam key and so on and so forth. Every once in a while, I post, how am I doing in which I work out what your effective course grade is, if there's some unusual weighting. In this case, I don't think there will be.
16:21
In other words, you can just look at your course points and if they're 80% or higher, you know you've got an A. You're doing 60 and 80, you know you've got a B and so on. Here's what the histogram for the class is going to end up looking in all likelihood because this is how it looked last year. These are all A's.
16:41
All right, see all this red line? That's the 80% line. I'm going to draw that right through the middle of a big group of students like this because I'm going to promise you that if you get more than 80% of the course points, you will get some flavor of A. The other side of the coin is if you get 79% of the course points, you're going
17:01
to get some flavor of B, a B plus. Okay, but I'm going to draw that line right at 80, I'm going to draw that line right at 60 and then these blue lines, I draw. You see how there's a break in the distribution here? Boom. See how there's a little break in the distribution here? Boom. All right, I draw the lines
17:21
between the pluses and the minuses. All right, see fair enough? It's completely transparent. You might not like it, but you'll know how you're doing. All right, except you won't know necessarily if it's a plus or a minus.
17:41
Okay, you ready? So I use PowerPoint. You all know that by now. I'm trying to get better at PowerPoint, so if you have suggestions for me, maybe you're really good at PowerPoint, you can say, you know, you could do this, you could do way better. I'm pretty easy to talk to, you can tell me
18:02
that I'm not going to be upset, all right? I would be happy to receive your criticism. These presentations are posted on our website one to ten minutes before or after each lecture, usually after. Take notes, I'll give those each slide. So not everything that you need to know is written
18:21
down on these slides. I try to keep the slides free of a lot of text and flutter so that they're easier to understand, so I'll be saying a lot of what we need to be knowing for each slide. And if I was sitting in your seat and I was taking notes, in my notebook I would write the slide number, and then anything that you think is important,
18:42
and then the next slide number, each slide will have a unique serial number. This is slide 19, as it turns out. See, lecture one, see how the system works? That's supposed to be 19.
19:00
This is supposed to be 20. You get the basic number, so there's a serial number. Every slide is quarter, like if you want to come and talk to me in the park, I didn't understand something on slide 476, I can go right to that. We can talk about it, or we can both find it.
19:20
That tends to be a useful thing to be able to do. Okay, so many of you know how my system works. I will talk at you in lecture, write these lectures, post all this stuff together. Steven and Jan-Mark and I are going to write these discussion study guides. So you're going to be getting a lot of information from me, you're going to be seeing me
19:41
for almost three hours a week. Then you're going to see one of these two guides, four more, if you go to more than one discussion, they're going to be teaching the discussions, hopefully they will tell you the same stuff I'm telling you a different way. All right, they're going to tell you it in a way that makes more sense to them. I said, what kind of sense really makes sense to me?
20:01
Right, but here's another way to explain the same thing that I think makes a lot more sense, that's the whole reason why we have these guys teaching the discussions, they're going to put a different spin on the same material, that tends to be very helpful for you. Then you're going to do the homework, and that's the most important part of this process in terms of actually learning the material, doing problems yourself,
20:21
find out what you guys all know, that's the key to doing well in a class like this. So hopefully we made it easy for you to do the homework, we posted solutions, the way to do the homework is not to look at the solutions and then go and do the homework, it's to attempt the homework, work really hard on it, and if you can't get it, then go with the solutions.
20:40
You understand all that, right? Okay, so quiz Friday, we're going to get started with this craziness, right, it will only be 20 minutes or so, hopefully not too much longer than that, and we'll take it right at the beginning of class, so it's important that you be here right at the beginning of class. There will be a stack of scantrons
21:01
in the back there somewhere, pick up a scantron when you come in, please take just one, even though we're going to quiz this whole quarter, I would really appreciate it if you didn't take 10 scantrons because these scantrons are expensive for us, and if that starts to happen, we're going to have to do something dumb like forcing you to buy the scantrons yourself at the bookstore,
21:22
I mean we don't want to do that, okay, we want to bring just the right number of scantrons for the class each week, right, so please take just one. All right, now I said I didn't know what the name of the class is, and that has to be true,
21:43
but let me tell you what's going to be in it, because that I do know. Here we are today, at the beginning of week one, we got 10 weeks, right, we're going to start off by talking about statistical mechanics and thermodynamics, so first of all, let me just back up and say, in 131A you learn about quantum mechanics from Professor XS,
22:06
in 131B you learn about spectroscopy from Professor Martin, right, in 131C, in principle, but we have to cover all the rest of physical chemistry.
22:25
Now, I'm sure that you agree with me that this is a foolish way to organize a three class sequence, and we understand that now, and we're going to reorganize this class in future years, but this quarter we're going to cover everything else
22:43
in this 131C curriculum, right, and what that means is that it won't be an in-depth study of all of these review subjects, it won't be, it can't be, because we don't have time to do it, but I'm going to try and convey to you what I consider to be some
23:01
of the most important concepts, I hope you agree, there's cool stuff in this class, because I think there really is. Okay, so I know you started to do chapter 13 with Professor Martin, but we're going to go back from the beginning and work on this subject, okay, because this is a super confusing subject,
23:20
this statistical mechanics, okay, we're going to stop and talk about that, if you read chapter 13 at the end of last quarter, great, right, if you have it, please read it now, right, this is confusing stuff, and as I indicated, the quiz on Friday will be on the stuff sort of in the first half of chapter 13.
23:40
Here's where the midterm is going to be, notice that the midterm does not align at the end of this block right here, I may try to push this block back to the left, but in the past, I haven't been successful in doing that, or to shorten the subject, this happens to be a very important subject, a lot of courses have this whole 10 weeks dealing
24:03
with this subject, that would be the appropriate way to teach this subject, you can't do that this morning. Then we're going to talk about chemical kinetics, again this is a whole class, we are going to condense it down to just a few weeks, we're going to hit the high points, try to convince some of the main themes of chemical kinetics.
24:22
And finally, underlying chemical kinetics is this subject called reaction dynamics, I'm not sure if we even got to this last year, right, this subject tries to take up a whole 10 weeks, I've been trying to find room for this because it's important, it's important
24:41
that you see some of this and understand what it's about, at least a few concepts. Okay, so here's where the midterms are going to be, the dates of these midterms are selected based on my travel schedule it turns out, because I want to be here for as many lectures as possible, so on dates when there's a midterm, I'm not going to be here,
25:00
those two guys are going to give the midterm exam, I don't think that will present problems for anybody, but in terms of me being here and giving the lectures, that's absolutely the best way to do this. Any questions on anything having to do with the logistics of the course?
25:21
Yes, they will, will the quiz questions be similar to the homework problems, yes they will, what I will do is I will post sample quizzes tomorrow or later on today, so you can look at what quizzes look like, what quiz questions look like, I want you to be calibrated on that, so those will be on the announcements page of our site, hopefully later
25:42
on this afternoon, if not tomorrow. Any other questions? Okay, so what is statistical mechanics, who invented it, what is it, why do we need it, and how do we start thinking about this subject? Quantum mechanics was discovered in 1924, this is a timeline
26:03
from 1800, there's 1900, there's 2000, here's when quantum mechanics was discovered in a period of time, starting in 1924, and I know this is one thing that you understand extremely well after studying it for 20 weeks.
26:20
These are the pioneers of quantum mechanics, Heisenberg, Schrodinger, de Broglie, Dirac, not shown here, all right, what does quantum mechanics tell us? Well, among other things, it tells us that if we assume a different confining potential for the electron, we're going to generate energy levels, right,
26:45
as soon as you confine the electron, you force discrete energies, allow energies to be produced, right, and quantum mechanics allows us to calculate what those eigenvalues are, right, also to figure out where the electron is, we can calculate the complex conjugate
27:01
of the electron spatial distribution, right, depending on what that confining potential looks like, all right, so quantum mechanics taught us that there are discrete quantized energy levels in atoms and molecules, we didn't know that for sure before quantum mechanics came along, and in fact, all of the time before 1924,
27:23
this would have been considered to be an extremely controversial issue, in fact, one of our atoms discovered, anybody know, proposed,
27:49
well, there's an English dude named Dalton, there might have been a Greek dude, yeah,
28:11
but Dalton was the guy who actually said, X got to exist based on all this experimental data
28:21
that we've got, the one thing that explains all this experimental data is X, 1806, okay, did Dalton discover molecules, no, guy named Avogadro proposed molecules, Italian guy, all right, later on in the 1800s, right about here, all right, and did everyone just hear
28:43
about atoms and molecules and buy into this concept, lock, stock, and error, not at all, right, the existence of atoms and molecules was controversial during this whole period of time here, right up until Einstein observed Brownian
29:01
motion in 1906, right about here, all right, everybody know what Brownian motion is, you know, how many people have looked through an optical microscope at a bacteria, all right, you know how that thing wiggles around when you're looking at it, it's jiggling, right,
29:24
that's Brownian motion, what it is, is it's collisions of atoms and molecules with the bacterium and that object is small enough so that those collisions are not isotropic in terms of the perimeter of the bacteria, there's more waters hitting it in one direction
29:41
and then more waters hitting it in another direction and so it jiggles based on this influence of these collisions and when that was observed by a physicist named Brown, of course, Einstein correctly interpreted his observation, he said what's happening is atoms, molecules are colliding in an anisotropic way with this tiny microscopic object
30:03
and that's the source of these fluctuations and that was the only explanation that made any sense and so right up until 1906, this subject was discussed in scientific meetings, all right, there were the so-called positivists who believed in the existence of atoms and molecules, all right,
30:22
this was considered a controversial issue for almost 100 years, that's pretty amazing, right, what's really amazing is that in the middle of this controversy all of these guys together figured out statistical mechanics and thermodynamics, all right, and then you'll see knowing
30:41
that discrete states exist is absolutely essential to really putting this construct of statistical mechanics together, if you don't have states, it's hard to think about statistical mechanics, which has something to do with the occupation of these states, the statistics of that, all right, so it's astonishing really, I mean, atoms are discovered here,
31:03
molecules are proposed somewhere around here and here there's just this vitriolic discourse that's going on and in the middle of this, these guys put together, thermodynamics and statistical mechanics, really quite extraordinary, these are the guys mainly responsible for the statistical mechanics part, Maxwell, Boltzmann,
31:24
Gibbs, those are names that you probably know already, here's Maxwell, this guy was a genius, Scottsman, maybe one of the less important things that he did was contribute to the Maxwell Boltzmann distribution, he actually derived Maxwell's equations,
31:40
which are unbelievably important, he invented three colour photography it turns out, right, in his spare time, all right, theory of compound colours, like he did the first three colour separation, right, to generate a chromatographic image and here it is, right, this is a ribbon, a Scottish tartan it turns
32:03
out, appropriate because he's Scottish, he told the photographer how to do this, three filters, three photographs, all three of them black and white, RGB, red, green, blue filters, put them together to generate a colour rendering, this is the very first colour photograph, right,
32:22
Maxwell did that, guy was full on genius, Boltzmann can taper his character, follow, prone to depression, eventually hung himself when he was 62 years old because he got so depressed at one point in time, depression is a terrible disease,
32:41
Maxwell Boltzmann distribution, right, pretty essential for thermodynamics and statistical mechanics, S equals K log W, how many people have seen that equation outside of the license plate of Professor Tobias's Prius? That's his Prius with it, K log W, don't go in anyone's car,
33:11
and this is his grave in Vienna, S equals K log W, in case you're wondering, that was his idea,
33:23
right, Willard Gibbs, one of the first great American chemists, right, this guy's an Austrian, this guy's a Scotsman, alright, it's nice to have an American make an appearance, alright, we don't hear about any Americans in quantum mechanics, it's all Germans, probably a French guy, Gibbs, right,
33:48
entered Yale when he was 15 years old, stayed there and got his Ph.D, sorry, got the first Ph.D in chemical engineering in the United States in,
34:03
do I have it on here, something like 1863, stayed there, right, as an unsalaried professor of mathematical physics, just worked there, this was not in common at that period of time, if you didn't, if you hadn't published papers, you could still get appointed as a professor, they just wouldn't pay you anything,
34:21
right, you had to work your butt off, teach classes, do research, but you got paid nothing, this was not in common in the U.S. and Germany at this time, but eventually this is, he worked out, often saw thermodynamics during this period of time when he was unpaid, and Johns Hopkins offered him a $3,000 a year salary, and so then Yale countered
34:42
with a $2,000 a year salary, and he took the job, stayed at Yale, right, his family was there, he loved New Haven, at that period of time, if you've ever been to New Haven, well, let's just say, it was a nice town in those years, and he died in 1903, so this guy was one of the first great American chemists,
35:06
and he's buried in the famous Grove Street Cemetery, if you're ever in New Haven, Connecticut, and Yale for some reason, maybe you go to grad school there, this is a beautiful cemetery that dates to the late 1700s, you can go in there, you can find these two, in fact,
35:23
if you, Grove Street Cemetery is one of the few cemeteries that has a great website, and you can put anybody's name in here, right, just bury it there, and it'll show you their gravestone, it's pretty cool. Okay, why do we need statistical mechanics?
35:41
We've got thermodynamics, and we can calculate things about all the amounts of molecules using all of the thermodynamic information that we can look up in any CRC handbook, all right, why do we need statistical mechanics, right, what does that bring to the table, here's a Wikipedia,
36:04
a piece of a Wikipedia page on ammonia, all right, standard enthalpy change of fusion, standard enthalpy of formation, heat capacity, standard enthalpy change of formation, standard molar enthalpy, and we can look up all these numbers
36:22
and use them, right, and that's what thermodynamics is all about, right, is how to granitize the physical behavior of substances, the problem is, is it makes no connection to the attributes of molecules, in other words,
36:44
I can look at this number here, heat capacity, but there's no way for me to calculate this number starting with the molecular properties, for example, methane, CH4, right, I know what the structure of methane is, I know what the bond distances are, I know everything about that molecule, you measure spectroscopic properties,
37:02
but I can't calculate anything having to do with the thermodynamics of that molecule from thermodynamics, thermodynamics doesn't give us the tools to do that, statistical mechanics builds that bridge, right, it allows us to go from the properties of ammonia, bond angles, bond distances, number of atoms,
37:22
number of normal modes, it allows us to calculate these numbers from these molecular attributes, that's the key, and I think you'll agree, that's an amazingly important thing to be able to do, alright, we can take the molecule, we can learn about its structure, and then when we're done learning
37:41
about the structure, we can calculate the thermodynamic parameters from that, alright, we want to learn how to do that, that's really, really important, this is one of the first papers where that was done for ammonia back in 1939 by these two guys, alright, and here's the equation that we're going to be familiarizing ourselves with later, and the important
38:03
thing in this equation is a parameter called Q, this is something called the partition function, it is the central construct in statistical mechanics, alright, Q is the key, if we can understand Q, we can understand this link between molecules and their structure and thermodynamic variables,
38:24
we're going to be getting to that, we want to really get to the point where we understand Q in some detail, yeah, I use, to teach this stuff, I use a really great book by a guy named Leonard Nash,
38:41
can you see how thin this book is, it is a thing of beauty, right, it is perfectly concise, easy to understand, and it explains this really esoteric subject in a clear understandable way, and so how many
39:00
of you hope to have a career in science or engineering? I hope by now, that's a lot of you, you appreciate the fact that you can't find all the information that you need on the computer, it's not there, alright, some of it's wrong, there's a few key books
39:24
that you ought to have in your library, and this is one of them, partly because it costs like $4, alright, it's down here on my list of all time greatest hits, okay, buy all of these, use the course,
39:41
we don't buy any new books, alright, but these are all irreplaceable, unbelievably valuable books that you will use throughout your life, every time you open up a subject, you're reading something in science magazine that you don't understand in the area of biochemistry, you open up this book right here, it's in there, alright, you know what I'm talking about,
40:04
so this is one of these gems, right, there's no replacement as far as I'm concerned for this book, right, it is special in terms of how clear it makes this explanation of statistical mechanics, okay, now we're not going to finish this lecture, but let me just tell you,
40:22
let's get started, I think you guys recognize this as a Morse potential, right, these are the bound vibrational states of this molecule, here's the harmonic approximation of that potential, I'm not telling you anything that you don't know, everybody knows about vibrational spectroscopy in this room, am I right,
40:42
now we can approximate this green guy here with this ladder right here, right, this is the B equals zero state, that's the ground vibrational energy level, one, two, three, four, okay, and so we can talk now
41:01
about the three dimensional array of molecules, here this is my short form notation for a molecule, let's just forget about the zero point energy for now, there's an energy level, there's another one, they're evenly spaced in energy, and there's three molecules here, A, B, and C,
41:24
that's what that denotes, okay, so, now if this is such that three molecules has zero energy, our energy level diagram looks like this, yes, if it has zero energy, then all three of these guys have to be zero,
41:41
and right, we're neglecting now the zero point energy, right, let's just call B equals zero to zero for energy in this system, right, everyone agree, that's the only molecular configuration that's going to add up to zero energy for molecules A, B, and C, there's no way for any of these other energy levels to be occupied, otherwise the system will not have
42:02
zero energy, now let's consider the case where we've got three quanta of energy distributed over three molecules, right, how can we do that, well we can put all three quanta into one molecule, put it in A, put it in C, put it in B, all right,
42:21
that's one way to distribute these three quanta of energy across these three molecules, put all the energy into one molecule, there's three ways to do that, another way to do it would be to put two quanta of energy into one molecule, one into another, zero into the other, and it turns out that there's one, two, three, four, five,
42:43
six different ways to do that, if you work it out, and here they are, right, that's two quanta into one, one quanta into the other, and zero into the other, that adds up to three, and there's six different ways to do that, and finally, you could put one quanta in each
43:01
of the three molecules, and there's really only one way to do that, I think you can see intuitively, okay, so there's one, two, three, four, five, six, seven, eight, nine, ten ways to put three quanta of energy into three molecules, everyone agree?
43:24
So we're going to refer to each one of these guys, that guy, that guy, these are microstates, that's what we're going to call them, there's one there, there's one over there, here's one down here, right, there's ten of these guys, ten microstates,
43:44
now there's ten microstates, but there's only three configurations of microstates, three configurations, it's easy to see that these ten microstates exist in just three configurations, there's no additional, you should express them in three configurations too, okay, see this, does this look confusing and cryptic, now it's easy
44:03
to understand, that's the number of quanta in V equals zero, right, that's the number of molecules in V equals zero, two, two here, two here, these are all the same configurations, so if that's two, that has to be two, and that also has to be two,
44:21
that's the number of molecules in quantum state one, zero, zero, zero, quantum state two, zero, zero, zero, quantum state three, one, one, one, alright so this guy is two, zero, zero, one, boom, that's his configuration, you with me, look at this guy,
44:48
one, one, one, one, one, and one, so that's a one, one, one, one, one, one, that's a one right there, and one, one, one, one, one, that's a one right there, and then zero, that guy describes the configuration
45:02
of all of these, okay, so we've got this shorthand notation that we can use for the configuration, this guy is zero, three, zero, zero, boom, okay, now I haven't said anything in profile, okay,
45:25
now we need to count the number of microstates associated with each configuration, is there a formula that we can use, in other words, are we going to have to go through the exercise of making these diagrams, well we've got all the values and number of molecules, that could be tedious, we need a formula, can we derive a formula
45:45
that allows us to figure out something about these microstates, starting with the first, two quantum mechanics, okay, so let's look at this guy, all right, let's say I want to put a two quantum,
46:00
I want to occupy the equals two, I can put it in there, or I can put it into B, or I can put it into C, in other words there's three ways that I can put that first quantum, that first B equals two, into these three molecules, it can go to molecules A, B, or C, then if I choose A,
46:22
there's only two places left over where I can put the next one quantum of energy, then the second one quantum of energy will go to either of the remaining two molecules, and finally the zero is going to have to go right there into molecule B, right, that's the last parcel of energy, so this system has three quantum energy, all right,
46:40
and the number of ways to generate this is three, right, three different places to put that first quantum, times two, two different places to put that second quantum, times one, only one remaining place to put that last quantum, right, three times two times one is three factorial,
47:02
that equals six, boom, that correctly predicts the number of microstates in this configuration, three factorial. Now, let's try the same thought process with configuration one, where there is B equals three, starting with the three quantum, so we can put it
47:22
in A, B, or C, we chose A here, then the next one will go up, so the next two are going to be zeros, we can put the first zero here, or here, right, it's got to go in the remaining two, okay, so we start here, we can put the two zeros here,
47:41
we can start with B, we can put the two zeros here, the difference is that there are two verbally distinguishable ways to put these two guys into the molecule, I can put three quantum into A, and then I can put this guy into C, and that guy into B,
48:00
or I can do it the other way around, right, I can put B in first, and then C, after putting A, three quantum energies into A, all right, so we have to adjust the number of quantum states here by a factor of two factorial, it turns out, because there are two verbally distinguishable ways
48:25
to insert these two guys, or these two guys, or these two guys, that one will go in first, and that one will go in second, or vice versa, when we make that adjustment, we're going to have three factorial divided by two factorial, or three possible microstates, configuration three,
48:47
that's this guy, where we have all three of these guys in quantum state one, all right, starting with the first thing, we're going to go into the three molecules, the second we're going to go into reading two, third we're going to go into reading three, but there are three of these two firmly distinguishable ways, right,
49:04
so it's three factorial, divided by three factorial, or one in BOO, there is only one state, okay, and so this is our equation, the number of microstates W,
49:21
that's N factorial, N is the number of molecules, that's the number of states occupied in zero, the number of molecules that have zero quantum, number that have one, number that have two, and so I'll take this random example, plug those numbers in to our equation, and you get 168 microstates for this guy, I think you would have to agree,
49:43
it would be messy to work that out, and I'll come back, we're going to do this again on Wednesday, so if you didn't get any of that, because I went fast, don't worry, we're going to do it again on Wednesday.