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>> 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 do a decent grade in this class and we'll start talking
about statistical mechanics.
If you haven't found it yet here's the URL.
What we want to do is just sort of click through some
of these links because they contain all the information
for the course.
So -- oh, I stole this from some beautiful work that's been done
in the area of molecular dynamics.
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,
[inaudible] concept you can go to this paper right here.
All you have to do is you can click on this beautiful picture
on the front of our website and it will take you directly
to this paper and you can read more about it.
It might not make an [inaudible] 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.
Now, this is where I'm going to be posting announcements I want
to make for 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.
What I will do is I will post my announcements here.
They will be in inverse chronological order.
The most recent announcement will be at the top
and there will be a list of all these announcements
that we made during the course.
You'll have sort of a record.
If you missed some you can just scroll down and find them,
and I'll probably post an announcement
or two almost every day and so it would be a good idea
to just check this -- bookmark this link announcements
and check it once a day or so to 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's going to be posted here
on this announcement page.
This is the syllabus.
We'll go through this is a little more detail
because it's 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 with all
of the links on this website.
We don't want to print everything out,
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.
We're not there but we want to try and get there
because you [inaudible], it's a lot better.
Okay, so please don't print every slide from every lecture
and stick that in a notebook.
That'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 [laughter].
Honestly. It's true.
You go back to the very first lectures --
websites we created like 1995,
all of that stuff's still on the internet.
It never went away.
So we don't need to print all this stuff.
Let's not do that.
Now, we're fortunate that we got two lecture teaching assistants.
Steven [inaudible].
Steven are you in here?
Steven's right back there.
>> Right here.
>> Steven's an expert [inaudible], he knows everything
about the subjects that we're going
to be talking about in this course.
Don't let him tell you anything else.
[Inaudible], he was a TA for you last quarter for 131B.
Maybe you know [inaudible].
He's back there.
These two guys are going to be teaching all the discussions.
I'll have more to say about that in just a second.
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 [laughter] Steven's going to be the one
that moderates everything that goes on there.
So you'll be interacting with Steven through Facebook
and see him also in discussion.
All right, when know when lecture is.
We know where my office is.
It's in SI2 room 2137.
You want to know where SI2 is, yes, 2137 is on the second floor
and it's in this hallway that's behind a set of doors.
The purpose of which is to keep people
from randomly walking in [inaudible].
But you shouldn't be discouraged from coming and finding it.
This office is right in front of the building.
You open that set of doors,
walk down the hallway and find my office.
The door is virtually always open.
If I'm in there and the doors not open that's
because like I've got [inaudible].
Most of the time if you need to talk about something to have
to do with the class, the materials, you have a question
about something, you can come and ask me.
We're also going to have office hours right after lecture.
There's usually a shady chair
in the park [laughter] right outside this door
where we can sit and talk.
And so some of you I know will want to eat or some
of you will have other classes.
But if you don't and you have a question about lecture,
what I've found is the best time to ask that question is
when it's really fresh in your mind, you just heard it,
you didn't understand it, you want some clarification.
All right?
So I'm going to try to sit over in that chair
and answer my email and if no one shows up for five
or 10 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 you needed it for 131C.
There's the Facebook link.
The way we're hoping Facebook works is the way it's worked
effectively in the past is that students talk to one another
on this Facebook page and offer hints as how
to answer various types of questions and it turns
out to be very, very useful.
All right, in other words Steven doesn't have
to answer all the questions, although he will stir the pot
and answer questions when he can but you can talk to one another
about problems, quiz questions and so on,
and answer each other's questions as a class.
Things sort of automatically work that way.
It's a miracle, so exactly it will work that way this quarter.
That's what we're hoping for.
This is the normal boiler plant that we always have to post.
It has to do with adds and drops.
You can read it.
there will be quizzes almost every Friday.
There's a quiz this coming Friday.
We're going back to the quiz system.
If you had 151 we tried to get away from it.
That was [inaudible].
I had a lot of feedback about homework in 151 and almost all
of it was negative [laughter].
So, we're moving away from that model.
This class the problem we're
in there is no electronic homework option for us.
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 ever be graded, no one will know
if you do it except that if you don't do it the quizzes are
going to be focused on trying to figure
out if you did it or not [laughter].
So, it will be helpful for you to do it.
all right, we will usually have the quiz the first 20 minutes
of each Friday, [inaudible].
It's worth 200 points up to 600.
There will be seven quizzes.
You can choose the top five.
In other words you can drop two quizzes for any reason.
Right? If you're going
to be gone you don't need to talk to me.
[Inaudible].
If you completely blow a quiz right, or sleep late.
I don't know [laughter] [inaudible].
You don't need to worry.
You've got two dropped quizzes not just one.
Okay? We're going to average --
we're actually 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 guess, that might seem
like a different way to you but none of the
above will be an option on every question.
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.
If the answers not there then the answer is none 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's non-trivial
to do well on these quizzes.
There will be five quiz questions and that means
as I will explain in just a second is
that you miss one you've still got an A,
if you miss two you've got a B,
you miss three you still got a B, you miss four --
[laughter] four you've got a C. Okay?
So you can afford to miss one, 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 [laughter] --
here's our Facebook,
here's Steven's notes, welcome statement.
All right, check out the Facebook page [laughter].
Okay, in addition to the quizzes we're going
to have two mid-term exams this quarter.
That's different from previous quarters.
One on April 27th, one of May 25th.
These are both on Friday, they will both be in class,
they are 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 this later on.
The final is on Tuesday June 12th.
That will be comprehensive.
It's worth 200 points.
There are six discussion sessions 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. The way these discussion sections will be
structured is that Steven and [inaudible] are going
to prepare a discussion study guide.
Many of you are familiar with this concept from the classes
that you've had with me before.
Probably other profs.
The discussion study guide has three or four problems on it
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 on any aspect
of the course that you have.
All right?
Ask them any question that you want.
If we run out of questions we're going to work
through this discussion study guide together.
Maybe in small groups or I can make sure that we understand how
to do these key questions.
But 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 the problems out,
we'll be able to do that.
right? We're going to post the one
for this week later on this morning.
I think we've been working on it this weekend.
It should be done right about now and so hopefully early
in the afternoon I'll post it, you can look at it,
you have discussion tomorrow you can be prepared for that.
Okay, homework problems will be assigned on Monday of each week.
Blah, blah, blah.
I'll show you the homework page in just a second.
The class [inaudible] will be continuously upgraded
on the tripped [inaudible] website.
Okay, and the way the grades are going to be assigned
in the course, and if you had 151 you're very familiar
with this scheme.
You need to get 80% of the course points,
which in this case is 480 points.
So there's 600 total course points.
All right, you have to get 480 to get some flavor
of A. The high side where the dividing line is between A
and A minus, and I do that depending
on where there's a break in the distribution.
All right?
But I guarantee you if you get 80%
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 [inaudible] draw the lines where it makes sense
to draw them, but that's a hard cut off between 60 and 61.
That's where the B cut off is, [inaudible] analogues 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 [laughter] do quite
well [inaudible].
All right, [inaudible] these are unrelated topics
that we don't really [inaudible] too much on.
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 is going to be
about you can click on this lecture from last year,
you'll have a pretty good idea.
Now believe it or not I tape 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.
That will be the new lecture for this quarter.
All 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
that I gave last year, which I worked really hard
on by the way.
Okay?
Here's the discussion study guide for this week.
It's not actually posted yet but we'll post it later on today.
And in principle there will be a YouTube video for this lecture
which is a new experiment that I'm doing.
I find the concept very frightening [laughter].
I'll post that over here if I continue
to do this experiment after one day.
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 on week four because there's a mid-term.
Okay? So there's a lot of information on this page
to remind you of when 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 is worked out.
Click on this and you got a little PDF
of the key on your computer.
Okay? Likewise for the other chapters.
Here's all of them we're 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 be a long table that looks a lot like this.
Here's last year's table.
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 mid-term exam keys and so on and so forth.
Every once in a while I post how am I doing in which I work
out what you're effective course grade is.
If there's some unusual weighting.
In this case I don't think there is,
but I don't think there will be.
In other words you can just look at your course points
and if you're 80% or higher you've got an A. if you're 60%
to 80% you know you got a B and so on.
Here's what the histogram of the class is going to end
up looking, in all likelihood.
This is what it looked like last year.
These are all A's.
All right?
So 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 that if you get 79%
of the course points you're going
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 these blue lines I draw --
see how there's a break in the distribution here?
Boom [laughter]!
See how there's a little gray in this distribution here?
Boom! All right, I draw the lines
between the pluses and the minuses.
All right, seem 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 necessarily if it's a plus or minus.
Okay, you ready?
So I use PowerPoint [laughter].
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 can do this.
It would be way better."
I'm pretty easy to talk to.
You can tell me that.
I'm not going to be upset.
Right? I would be happy to receive your criticism.
These presentation will be posted to website one
of 10 days before or after.
It's usually after.
Takes notes to augment each slide.
So not everything you need
to know is written down on this slide.
I try to keep the slides free of a lot of text and a lot
of clutter so that they're easier to understand.
Right? So I'll be saying a lot of what you need to be knowing
with 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 and then the next slide number.
Each slide will have a unique serial number.
This is slide [laughter] 19 as it turns out.
Lecture one.
See how this description works?
That's supposed to be 19.
This is supposed to be [inaudible] [laughter].
You get the basic idea.
There's a serial number -- every slide --
like if you want to come to me in the part,
"I didn't understand something on slide 4-76.
We'll go right to that, we can talk about it
where we can both find it.
That tends to be a useful thing to do.
Okay, so you -- many of you know how my system works.
I will talk at your in lectures, write these lectures,
post all this stuff together.
Steven and [inaudible] and I are going
to write the discussion study guides.
So you're going to be getting a lot of information from me.
You're going to be seeing me for almost three hours a week.
Then you're going to see one of these two guys or 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 that I'm going
to be telling you in a different way.
Right? They're going to tell you it in a way
that makes more sense to them.
This is [inaudible] really makes sense to me.
All right, but here's another way to explain the same thing.
It makes a whole 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.
By now you guys all know that's the key
to doing well in a class like this.
And so hopefully we've 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 *** it
and if you can't get it then go look at the solutions.
You understand all that already.
Okay? So, quiz Friday.
We're going to get started with this craziness.
Right? We'll only need 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 you be here right at the beginning of class.
There'll be a stack of Scantrons in the back there somewhere.
Pick up a Scantron when you come in.
Please take just one even though we have quizzes all quarter.
I would really appreciate it
if you didn't take 10 Scantrons [laughter].
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.
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.
All right?
So, please take just one.
All right, now I said I didn't know what the name
of the class is and that happens to be true.
[Laughter] But, let me tell you what's going to be
in it because that I know.
Here we are today at the beginning of week one.
We've 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 learned about quantum mechanics [inaudible].
In 131B you learned about spectroscopy
from Professor [inaudible].
Maybe? Right?
In 131C, in principle we have to cover all the rest
of physical chemistry [laughter].
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
in this 131a curriculum.
Right? And what that means is it won't be an in depth study
of all of these remaining subjects.
It won't be.
It can't be because we don't have time to do it.
but I'm going to try to convey to you what I consider
to be some of the most important concepts.
I hope you agree.
[Inaudible] in the class because I think it 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 confusion subject
or 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 haven't, please read it now.
Right, this is confusion stuff and as I indicated the quiz
on Friday will be on the stuff [inaudible]
in the first half of chapter 13.
Here's where the midterms going to be.
Note that the mid-term does not align with the end
of this block right here.
I may try to push this block back to the left
but in the past I have been successful in doing that
or shorten the subject.
This happens to be a very important subject.
A lot of courses have this whole 10 weeks dealing
with this subject.
That would be the appropriate way to teach this subject.
We can't do that in this course.
Then we're going to talk about chemical kinetics.
Again this is a whole class.
We are going to condense it down to a few weeks.
We're going to hit the high points [inaudible]
chemical kinetics.
Finally underlying chemical kinetics is the subject called
reaction dynamics.
I'm not sure if we even got to this last year.
Right? This subject [inaudible] can take up a whole 10 weeks.
I will try to find room for this because it's important.
It's important [inaudible] this and understand what it's about
or at least a few concepts.
[Inaudible] here's where the midterms are going to be.
The dates of these midterms are selected based
on how my travel schedule turns out because I want to be here
for as many lectures as possible.
So on days where there's a mid-term I'm not going
to be here.
Those two guys are going to give the mid-term exam.
I don't think that will present problems for anybody.
All right?
But in terms of me being in here
and giving a lecture that's absolutely the best way
to do this.
Any questions on anything having to do
with logistics of the course?
>> The quiz questions, would they be similar
to the homework problems [inaudible]?
>> Yes they will.
Will the quiz questions be similar
to the homework problems?
Yes they will.
What I will do is I post the sample quizzes tomorrow or later
on today so you can look at what quizzes look like.
What quiz questions look like.
[Inaudible] calibrated on that.
Right?
So those will be on the announcements page
of our site hopefully later 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 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 you understand extremely well
after studying it for 20 weeks.
These are the pioneers of quantum mechanics.
Isenberg, Drodinger, the [inaudible] not shown here.
All right?
What's quantum mechanics tell us?
Well, among other things it tells us
that if we assume a different [inaudible] potential
for the electron we're going to generate energy levels.
Right? Soon as you can find the electron you force discreet
energies allows energy to be produced.
Right? In quantum mechanics that allows us
to calculate those [inaudible] are.
Right?
Also to figure out what the electron is.
We can calculate the complex conjugate
of the electrons special distribution.
Right? Depending on what
that [inaudible] potential looks like.
All right?
So quantum mechanics taught us
that there is discrete [inaudible] energy levels
in atoms and molecules.
We didn't know that for sure before quantum mechanics
came along.
And in fact all
of the [inaudible] before 1924 this would have been considered
to be extremely controversial issue.
In fact, why were atoms discovered?
anybody know?
[ Inaudible ]
Propose.
[ Inaudible ]
Well there's an English dude named Dalton [laughter].
There might have been a Greek dude.
[ Inaudible ]
Yeah.
But Dalton was the guy who [inaudible].
Atoms.
Atoms got to exist based on all of this experimental data
that we've got and one thing
that explains the experimental data [inaudible] 1806.
Okay?
Did Dalton discover molecules?
No. A guy names [inaudible] proposed molecules.
[Inaudible], all right [inaudible]
in the 1800s right about here.
Right? Did everyone just hear about atoms and molecules
and buy into this concept lock stock and barrel?
Not at all.
Right? The existence of atoms
and molecules were controversial during this whole period
of time here right up until Einstein observed Brownian
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?
Right?
You know how this thing wiggles
around when you're looking at it.
It's jiggling, right.
That's Brownian motion.
What is it, is it's collisions of atoms,
molecules with the bacterium and that optic is small enough
so that those collisions are not isotropic in terms
of the [inaudible] bacteria.
[Inaudible] hitting it in one direction,
then [inaudible] 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 isotropic way.
It's microscopic object and that's the source
of these fluctuations.
That was the only source of these fluctuations
and that was the only explanation that made any sense.
So right up into 1906 this subject was discussed
in scientific meetings.
All right?
There was a so-called positivist who believed in the existence
of atoms and molecules.
All right?
This was considered a controversial issue
for almost a hundred 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 thermal dynamics.
Right? [Inaudible] you'll see knowing
that discrete states exist is absolutely essential
when putting this construct of statistical mechanics together.
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?
[Inaudible] really.
I mean atoms are discovered here,
molecules are proposed somewhere around here
and here is just this [inaudible] discourse that's
going on.
In the middle of this these guys put together thermal dynamics
and statistical mechanics.
Really quite extraordinary.
These are the guys mainly responsible
for the statistical mechanics part.
Maxwell, Ultzman, Gibbs.
Those are names that you probably know already.
Here's Maxwell.
The guy was a genius.
Scotsman. Maybe one of the less important things
that he did contribute to the Maxwell-Boltzmann distribution.
He actually derived Maxwell's Equation,
which are unbelievably important.
He invented three-color photograph it turns out.
Right? In his spare time [laughter].
Right? Theory of compound colors.
He id the first three-color separation, right,
to generate photographic image and here it is.
Right?
This is a ribbon, Scottish Tartan it turns out,
appropriate because he's Scottish.
He told the photographer do this, [inaudible] photographs,
all three of them black and white, RGB;
red, green, blue filters.
Put them together to generate a color rendering.
This is the very first color photograph.
Right? Maxwell did that.
The guy was full on genius.
Boltzmann, cantankerous character.
Volatile, 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.
Maxwell-Boltzmann distribution.
Right? Pretty central to thermal dynamics
and statistical mechanics.
[Inaudible].
How many people have seen that equation?
[Inaudible] the license plate
of Professor Tobias' Prius [laughter].
That's his Prius with Klog W. [Inaudible] his car [laughter].
And this is his grave in Indiana.
S equals K log W [laughter].
In case you're wondering that was his idea.
Willard Gibbs, one of the first great American chemists.
Right? This guys an Austrian.
This guys a Scotsman.
All right?
It's nice to have an American make an appearance.
That's right, we don't hear
about any American's [inaudible] [inaudible] [laughter].
Gibbs. Right?
Entered Yale at 15 years old, stayed there and got his PhD.
True story.
One of the first PhD's
in chemical engineering in the United States.
In -- do I have it on here?
Something like 1863.
Stayed there, right, as an unsalaried professor
of mathematical physics.
Just worked there, which was not uncommon at that period of time.
You didn't -- you had to publish papers.
You could still get appointed as a professor
but they couldn't pay you anything.
You had to work your butt off, teach classes, do research
but you got paid nothing.
This was not uncommon in the US and Germany at this time.
But, eventually -- this is --
he worked out [inaudible]
of thermodynamics during this period of time
when he was unpaid and Johns Hopkins offered him $3,000 a
year salary so then Yale countered
with a $2,000 a year salary [laughter] and he took the job.
He stayed at Yale.
All right?
This man was [inaudible].
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.
He died in 1903, so this guy was one
of the first great American chemists.
And he's buried in the famous Grove Street Cemetery.
If you're ever in New Haven,
Connecticut in Yale for some reason.
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 [inaudible] too.
In fact if you -- Grove Street Cemetery is one
of the few cemeteries that's got a great we site.
If you put anybody's name in here,
right, that's buried there.
They'll show you their gravestone.
Pretty cool [laughter].
Okay, why do we need statistical mechanics?
We've got thermodynamics and we can calculate,
think about [inaudible] molecules using all the
thermodynamic information [inaudible] in CRC handbook.
Right? Why do we need statistical mechanics?
Right? What does that bring to the table?
Ah, here's a Wikipedia -- piece of a Wikipedia page on ammonia.
All right?
Standard [inaudible] change of fusion.
It'll be a formation.
[Inaudible] capacity.
Standard [inaudible] change of formation.
Standard [inaudible].
And we can look up all these numbers and use them.
Right? And that's what thermodynamics is all about.
Right? Is how to parameterize physical behavior of substances.
The problem is, it makes no connection
to the attributes of molecules.
In other words 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.
I've measured its microscopic properties.
But I can't calculate anything having to do with 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,
[inaudible], bond distances.
Number of atoms, number of [inaudible].
It allows us to calculate these numbers
from these molecular attributes.
That's the key.
And I [inaudible] and basically [inaudible] thing
to be able to do.
All right?
You take the molecule and learn how it's structured and then
when we're done learning
about the structure we can calculate [inaudible] on that.
Right? We want to learn how to do that.
That's really, really important.
This is one of the first papers where that was done.
[Inaudible] back in 1939 by these two guys.
All right?
Here's the equation we're going to be familiarizing ourselves
with later, and the important thing
in this equation is a parameter called Q. this is something
called the partition function.
It is the central construct in statistical mechanics.
Right? Q is the key.
If we can understand Q we can understand this link
between molecules and their structure
and thermodynamic variables.
We're going to get into that.
We want to really get to the point
where we understand Q in some detail.
Now, I used to teach this stuff, I use a really great book
by a guy names Leonard Nash.
Do you see how thin this book is?
[ Inaudible ]
It is a thing of beauty.
Right? It's perfectly concise, easy to understand
and it explains this really esoteric subject
in a clear understandable way.
And so how many of you hope to have a career
in science or engineering?
I hope by now there's a lot of you.
You appreciate the fact that you can't find all the information
you need on [inaudible] [laughter].
[Inaudible] some of it's wrong.
There's a few key books that you ought to have in your library
and this is one of them [inaudible]
because it costs like $4.
All right?
This down here are a list
of all-time greatest hits [laughter].
Okay? Buy all of these.
Used of course.
We don't need to buy new books.
Right? But these are all irreplaceable,
unbelievably valuable books
that you would use throughout your life,
every time [inaudible].
Some subject -- you're reading something in science magazine
and you don't understand in the area of biochemistry.
You open up this book right here.
It's in there.
all right?
You know what I'm talking about?
So this is one of these gems.
Right? There's no replacing it as far
as I'm concerned, this book.
Right? It is special in terms
of how clear it makes this explanation
of statistical mechanics.
Okay, now we're probably not going to finish this lecture,
but let me just tell ya -- let's get started.
I think you guys recognize this as the Morse Potential.
Right? These are the bond vibrational states
and this molecule, here is the harmonic approximation
to that potential -- I'm not telling you anything
that you don't know.
everybody knows [inaudible] spectroscopy in this room.
Am I right?
[ Inaudible ]
Now, we can approximate this green guy here
with this ladder right here.
Right? This is the V equals zero state.
That's the ground vibrational energy level.
One, two, three, four.
Okay? And so we can talk now
about the three dimensional ray of molecules.
Here -- this is my short form notation for a molecule.
Let's just forget about zero point energy for now.
All right?
There's an energy level, there's another one.
[Inaudible] energy, and there's three molecules here; A,
B and C. and that's what that [inaudible] helps.
Okay, so now if this is [inaudible] free molecule has
zero energy [inaudible] looks like this.
Yes. If it has zero energy then all three of these guys have
to be zero and what we're neglecting now the zero
point energy.
Right? Let's just call equal zero to zero
for energy in this system.
Right, everyone agree?
That's the only molecular configuration that is going
to add to zero energies for molecules A,
B and C. There's no way for any of these other energy levels
to [inaudible] otherwise the system will not have
zero energy.
Now let's consider the case
where we've got three quantum energy distributed
over three molecules.
Right? How do we do that?
Well we take all three quantities in one molecule,
put it in A, put it in C, put it in B. all right?
That's one way to distribute these three [inaudible] 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 [inaudible] energies
into one molecule, one to another, zero to the other,
and it turns out that there's one, two, three, four, five,
six different ways to do that if you work it out.
And here they are.
Right? That's two qualities to one, one [inaudible]
to the other and zero in the other.
That is three and there's six different ways to do that.
And finally you could put one quantity to each
of the three molecules
and there's really only one way to do that.
I think that you can see intuitively.
Okay? So there's one, two, three, four, five, six, seven,
eight, nine, 10 ways
to put three [inaudible] energy into three molecules.
Everyone agree?
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 [laughter].
Like this [inaudible].
Ten microstates.
Man, there's 10 microstates
but there's only three configurations of microstates.
Three configurations.
It's easy to say that these 10 microstates [inaudible] three
configurations, [inaudible].
See this? Does this look confusing and [inaudible]?
No. It's easy to understand.
That's the number of [inaudible] 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.
[Inaudible] has to be two and that also has to be two.
That's the number of molecules
in quantum state one; zero, zero, zero.
Quantum state two is zero, zero, zero.
Quantum state three, one, one, one.
All right?
So this guy is two, zero, zero, one.
Boom! That's his configuration.
You with me?
>> Yes.
>> Look at this guy.
One, one, one, one and one.
So that's a lot.
One, one, one, one.
That's a one right there.
And one, one, one, one, that's a one right there and zero.
That guy describes the configuration of all of these.
Okay? So we've got the shorthand notation that we can use
for the configuration.
This guy is zero, three, zero, zero.
Boom! Okay?
I haven't said anything profound.
Okay. 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 diagrams [inaudible] of molecules?
That could be tedious.
Right? We need a formula.
Can we derive a formula that allows us to figure
out something about these microstates?
Starting with the first [inaudible].
Okay, so [laughter] let's look at this guy.
Right? Let's say I want to [inaudible] --
I want to occupy these two.
Right? I can put it in there or I can put it next to --
into V or I can put it into C.
In other words there's three ways that I can put
that first quantum, that first V equals two
into these three molecules.
It can go into molecules A, B or C. Then,
if I choose A there's only two places left
over where I can put the next one quantum energy.
Then the second one [inaudible] either between two molecules
and finally the zero has to go right there
into molecule B. right?
That's the last parcel of energy.
So this system has three quantum energy.
All right?
And the number of ways to generate this is three, right,
three different places [inaudible] first one times two.
Two different places to put that second quantum.
Times one, only one remaining place for that last quantum.
But [inaudible] equals six.
Boom! That correctly predicts the number of microstates
in this configuration.
[Inaudible].
Now, let's try the same thought process
with configuration one [inaudible] equals three.
Starting with the three [inaudible].
So we could put in A, B or C. that controls [inaudible] here.
[Inaudible].
So the next two are going to be zeros
with the first zero here or here.
Right? It's got to go -- remain two.
Okay, so we start here.
We put our two zeros here.
We start with B we put our 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 to B or I could do the other way around.
Right? Put B in first and then C
after putting A [inaudible] A. all right?
So I mean you have to adjust the number of quantum states here
by a factor or two factorial it turns
out because there are two verbally distinguishable ways
to insert these two guys,
or these two guys, or these two guys.
That one goes in first and that one goes
in second or vice versa.
All right?
Will we make that adjustment if we're going
to have three factorial divided by two factorial
or three possible microstates.
Configuration three, that's this guy.
We have all three of these guys in quantum state one.
Right? Starting with [inaudible] two, [inaudible] three.
But there are three verbally distinguishable ways.
Right? So it's three factorial,
divided by three factorial or one and boom.
They result in one state.
Okay? So this is our equation.
The number of microstates doubles.
That's [inaudible] factorial, [Inaudible] molecule.
That's the number of states occupying in zero.
[Inaudible] molecules that have zero quantum,
[inaudible] have one, others have two.
And so take this random example apply those numbers
in to our equation and you get 168 microstates for this guy.
I think which you would have
to agree would be messy to work that out.
After that -- we're going to do this again on Wednesday.
So if you didn't [inaudible] don't worry,
we're doing it again on Wednesday. ------------------------------dd0eb9c1ef6f--