00:05

OK I know it please 3 was by

00:13

far the hardest way as I think I'll tell you that so we was up much more difficult than

00:18

wanted to and I think that too was harder than 1 3 was harder than to what I think we reached the point where I we've tried trade to the maybe we wanted to go OK so this is what the histogram look like 3 others want there's a mistake on

00:36

the key that I posted this morning but some problem 5 on I work out the answer and it's actually been not deed which India's indicated on the by Jean-Marc about found that before I did OK so the quiz show been graded correctly the correct answer certified as B nowadays OK it's all about trying to

01:04

make a change to the before at the end of the day so here's here's where we are right so far we've had 3 quizzes and this is what the histogram looks like In other words all these folks here at any age these folks here in these and so on OK so

01:31

going into midterm 1 which is Friday because of doing really well right which is good that's way we want to see it so here's what's going to

01:44

happen mid-term 1 is Friday it will cover all of chapters 13 and 14 it turns out but

01:53

this is just perfect right accidentally write this lecture that I'm going give today will take us right to the end of Chapter 14 right what's going to happen is you're gonna review

02:07

chapters 13 and 14 and lectures 1 through 10 on Wednesday by way of a review for you right Stevens going to give a lecture that I've written

02:20

OK and will take the mid-term on Friday all right there's a copy of

02:25

last year's midterm examine what you'll see what Stephen will do on Wednesday so review it's going to be on the mid-term in some detail he will tell you How many questions there's going to be

02:39

will tell you something about what those questions are going to be OK so Wednesday's lectures a rather important 1 to attend OK but let me just tell you that

02:49

it's gonna look a lot like last year's midterm entirety posted that couple weeks ago right last year's midterm is already on the announcement page so you can see what that is it turns out

02:58

that last year's midterm would've been a perfect mid-term begin this year because there's nothing about Chapter 15 on the mid-term there's nothing about entropy calculations on that matter OK cancer but really about chapters 13 and 14 OK

03:18

so overdue today's finished Chapter 14 and the ones they were gonna review and on Friday will take the midterm exam another mid-term

03:29

this can be opened but open notes I'm not going to give you you know that shotgun Page of equations that I showed you on the screen earlier where there is a random equations over now bright open book open notes not open iPads or computers look at which you can use any calculated that he won any questions about that any questions about mid-term once OK so

04:14

Jean-Marc started to talk to you about idiomatic processing inundated attic process if the flow is turned off right this systems than a thermos bottles there's no

04:30

flaws of the dinner out but

04:37

friend in infinitesimal step of the process there can be work right so we don't normally the internal energy is given by the password right infinitesimal change in the internal energy is then an infinitesimal change indeed or an infinitesimal change in work at Freddie that process it's all about the work write the system is in a thermos bottle but another expression Videocon we obtained from the definition for the constant volume he capacity which we talked about some weeks ago but the constant volume heat capacities just before partial derivative of the internal energy with respect to temperature evaluated at constant volume but that's why it's called the constant volume the capacity OK so once I got capacity I can get I can express it as a derivative according to this equation here so for an ideal gas DW simply given by right we know the work is minus PTV and if I just substitute for P from the ideal gas equation I get this equation right here writers Peterson over the but since internal energy In work are equal the 1 another for an 80 batik process that means that these 2 things have to be equal 1 another all right that equals that pretty idiomatic process and so I can just set these 2 things equal 1 another like this and then I can divide through by the eliminated them from this side and it'll probably over here on the left-hand side and then apply integrate these 2 expressions now I had great 1 from 282 this 1 from V-1 here's what that integral looks like unjust immigrated from T 1 2 T 2 V 1 defeat to the girls the same in other words a here I'm integrating won over the integrating won over to the right side get locked into over T-1 log the 2 over the 1 but the and then I can just divine through by this he capacity not just doing a little algebra to clean this up and when I do that I take the exponential of both sides I get this expression right here all right which is an equation that we're going to use to describe media batik processes right it's your equation 14 . 3 7 a case of this and our oversee the that's gonna pop up as the next opponent when we take the exponential both sides know not that I flipped this over all right here at 62 over T-1 the 2 over the on my foot I put this always known to be 1 of the 2 so I could get rid of the minus sign that's all I'm doing there

07:42

madam not skipping any steps OK

07:45

so this is media battered reversible process involving an ideal gas so we've got this expression batik process that we just arrived earlier we drive this expression for an isothermal processes wikinews whichever 1 we but the Jean-Marc what you through this slide on Friday all right we've got 2 firms here right here nice affirmed that applies a T 1 hears in light of the that applies a T 2 what what were plotting years the pressure is a function of volume as we do an expansion these are thermal expansion here on these 2 isoforms we use the word

08:33

I firm because their constant temperature OK if

08:39

we wanna look at immediate back process that starts here for example but it's can cross over it's not a constant temperature process which

08:48

constant is heat OK we do an expansion that

08:56

means that the temperature has to fall so changing P with an expansion is larger for immediate that process than for nights promised 1 isothermal 1 because temperature decreases for the media batik process the temperature is going down during the CD batik process right obviously that's not happening with the ISO thermal process rights in other words if I look at T-1 line right I go from this initial volume to this final volume all right here's the change in pressure that happens AT T 1 everyone see that here's the 1 right here is the 1 that we're going from here to here right and the pressure difference would only be there as shown by this yellow bar here or if we want to look at the pressure difference that teachers who by for the Eiffel formal process years Cheechoo so here's it's pressure difference given by this yellow bar here even smaller right now we look at what the the Bannock process does it's going from the 1 to be too over this much larger range of pressure much

10:10

larger range of pressures here because temperatures changing too In this process

10:20

but the focus now it's not obvious from these 2 equations but there's a more profound the

10:33

implications of this AD batik business right that we've sort of we've set it but we

10:43

were very explicit about it right do you eat with the W because the 2 0 right but that has important implications obviously if I had a great deal from some initial internal energy to some final internal energy I'm just going to get the final minus the initial because he was

11:04

a state function right the

11:08

difference between any integral or is this could be the final minus the initial write mortgages call that don't you or eliminating about a process that has to be equal to the but if this process if this change in the internal energy is happening In a

11:30

thermos bottle the campy any flows of heat only work can occur all right then

11:38

this is change in the internal energy is going be given by just the amount of work that was done for it as long as it was Adia batik work it was work that was done on the

11:48

system when it wasn't a thermos bottle In other words the

11:54

Ayurvedic batik work is different from all other other cats other types of works because it is a state function just like you it would have to be it's a calling you right so that means for immediate Benedict process you know what we

12:12

saw earlier is if if we if we take it a normal process we do PV work if we break the work down into smaller chunks we can do less of that to get from an initial stake to a final state remember that we took the break we grounded out to make it into tiny particles we can add tiny particles and then we can do the minimal amount of work all right but if the work is 80 back there's only 1 way to do it but it's a state function you can there's only 1 way to do the adiabatic work only 1 EU batik

12:47

work it's a state that is like you does not depend on the path because all the batik pass between you why you have have to be identical rates of 80 batik work is special

13:03

right it's a state function just like the internal energy OK

13:12

now James Joe were to come back to the batik work business but

13:23

wouldn't take a detour but this is James

13:29

jewel he was born in 1918 in a little town outside of Manchester England Manchester England right here this is new 1 and OK and he was born in Salfit which is right over here OK Manchester big cities but

13:50

in those days not so big itself exactly pretty good good-sized town itself not that not when he died in 1918 its tiny little town every town in England had its own parade In fact that's true for most the Europe at this point in right every little town in Germany has its own brewery usually just 1 right and so every town has its own identity in terms of the beer that you can drink there by then and

14:18

still through this state logic stand by by and let me just tell you that making beer is

14:26

not like making soda bread to make call right Coca-Cola you there's some Khamis who go to land they come up with this mixture of of flavorings and you know they make a flavor packet right and what you if you go to jails on the green in you by a call right that not a thing of concentrated serpents get gets diluted with carbonated the far-right insult to make all the Disney the flavoring unique carbonated water any need sugar and it's dead easy to mix them together but every time you get hold of a machine it's just mixing these things together for you but the Serb actually has the water that has actually has the sugar in it In

15:15

beer you start with Bali are right there is no flavor packet that you dilute with water to get beer that has particular flavor right every bearded by everyone world has to go through all of these different processes and so if you think about it it's totally amazing that when you buy bite

15:35

Heineken but it always tastes exactly like Heineken we don't talk about it but distinctive Heineken taste they're making billions of of Heineken and every they have to do

15:50

all of this to every single model parts so what that means is that there is exquisite control

16:00

I made at a level that you might not even believe I'm sorry you 1 yes so there's a lot of process chemical

16:13

engineering that goes into making this absolutely reproducible for every bottle and is really a

16:20

chemical engineering feat that this can be done and this this was not something that we've learned a lot in the 20th century this is learned in the 18th century maybe even the 17th century Potter reproducible in making beer that tastes the same every time 1 of the key

16:44

is here right fermentation right the temperature here after the controlled right and this is true to a lesser extent these earlier processors to but in this fermentation process right the temperature

17:01

has to be controlled with better than 1 degree C precision OK and that's not enough to get abilities the same every time a lot of other things if you ever wanted I don't know if you're fascinated by such things but if you've ever you've never been to a big commercial brewery all of them will give you went to work pretty good will Budweiser brewery and you can get a tour of the Budweiser brewery you walk that place it is spotlessly clean you can't believe it right there is it's like a hospital in there right you look down at that this about 5 acres worth of Bob a stainless steel kettles and bottles and and like 2 guys running a factory of 5 acres making billions of bottles of Budweiser at all computerized made right process control is taking care of this whole everything that happens

17:56

years having an automated way right and you know Budweiser's Beach Beach would aid you know you look down there's a guy shoveling

18:04

Beechwood into a stainless steel of that that's about the size of his room practice actually Beechwood and that's stupid from for

18:13

fermentation beach Woods so

18:20

well what is any of this have to do with the money namics Jim

18:24

Jewell His dad was a brewer in himself or his dad made beer and selfish and like I said there was only 1 guy did that

18:34

and he understood chemistry from being a Brewers 2 regular hot run the brewery in fact he did run the brewery after his dad had some medical problems he went to school in Manchester for 2 years with his brother Benjamin study with a guy named James Dalton and anybody know that name but he needed comic

19:06

series but steadily James Dalton for 2 years and then there was some sort of health problems back home in his brother went back to run the brewery here never had any more college education than that but but

19:22

he was interested in you know he added amateurs interest in science and that really

19:30

was driven by understanding how to make a brewery run more efficiently pretty 1 understand what are the limits and efficiency that we can achieve in this brewery rights we can maximize our profits he was thinking of a very practical level it's 1 of the things you want to

19:44

understand is what is the relationship between working he heat when I was a pretty profound thing to 1 understand when you're brewing beer all right but he was

19:58

smart enough to understand that that was an important thing for him to appreciate in terms of the brewing process right and

20:07

so on the most famous experiment that he did involve taking away but using that to drive an agitator inside a vessel or what all right and imagine how hard this experiment would be put away here the drop this latest thing spins like crazy in a bucket of water and that's a thermometer you're going to measure the temperature change you are you kidding me right

20:34

the temperature is going to change right now by much right he

20:40

could measure the temperature of a one-two hundredth of a great Fahrenheit he was the only guy in the world who could make that measurement right in the measured

20:50

he saw a reproducible temperature change right and he

20:55

could correlate the temperature change with the distance that there's mass fell in with the size of his mass and the volume of the water he figured all that out the quantity of work that must be expanded at sea level in the latitude of Greenwich in order to raise the temperature 1 pound a lot awaiting that will by 1 degree Fahrenheit from 62 61 degrees Fahrenheit is equivalent to the man mechanical force associated with raising 772 . 5 5 pounds through 1 the measure that the 6 the the measure that to 1 part in 10 thousand you know it is

21:35

inconceivable how difficult was to do that and when he went around and gave talks in England and elsewhere in Europe nobody believed him Mike as he would show data he would say no here's my data are and measuring 1707 degree change there would Gulch there's no way you can do that reproducible but nobody else could make temperature

21:58

measurements with this level of precision but where did he learn how to do that in the blue line

22:03

I have been making precision temperature measurements for years but you gotta do that to run the stupid brewery 1st he took it

22:14

to a new level of mind you so that number is right there on his gravestone alright he shall the equivalence between work and he that's a pretty

22:29

important thing to appreciate an

22:32

earlier thinking yes you to

22:38

this number is still available to you if you should 1 nobody not

22:44

everybody's going on years you have to sign a license for you you got ever imagine what kind of murdered has to be recognized but now

22:56

not to like so that's not the

23:01

experiment we care about he tried to do a harder experiment

23:05

he's less famous right this is really famous for the experiment with await faulty get 1 degree change 700 OK

23:14

you try to do another experiment right you try to do this experiment right here the pressurized 1 ball this is user these great these are camping 0 glass involves the pressurized 1 but with some nitrogen the other 1 evacuated all right and then put a thermometer in this water bath and he open up this valve bright and

23:38

full write gas from falter this fall and is looking for a temperature change here and nothing happens so the question is

23:52

1st of all what was he thinking argue was convinced that if he did this he would see a temperature

24:00

change more alive like this guy I knew a lot of physical chemistry and the know

24:10

that there should be a temperature change if he did this carefully enough if the

24:14

volume of water year was small enough it wasn't right in his experiments he should see a temperature change so let's see if we can understand what he was thinking what could give what could he have been thinking part how many people have seen this before this is

24:33

a Lennard-Jones 612 potential good Wearing on

24:39

earth did you see it Stephen accomplishment of the who put their hand up where did you guys see this J. G.

24:49

Cannon what is right it's it's the

24:54

energy between 2 molecules like it or not going to form a covalent bond it's it's a non covalent bonding interaction were talking about here OK and so there's an equilibrium bond distance would say we've got to neon atoms I know if a far apart this is the distance between them here on this axis here this is the energy right now for an ideal gas there's no energy write an ideal gas this is the energy that you get is a function of distance are right in other words in fact in an

25:30

ideal gas we assume that the gas is a point particle we don't even as soon as any volume OK so there's no interaction energy as we

25:39

bring gas molecules called together nothing happens OK but you know real gas there's another attraction but that's what this is and then there's a short-range repulsion that focuses on this repulsion is approximately part of the 12 and attractions approximately the 6 so far right that this red line here is the sum of the repulsive potential plus the attractive potential in other words if I add his -dash lying to the Saskatchewan right here I get this red line and half of those given by this equation and that's

26:15

the winner John 6 potential OK

26:19

so there's what is the only 1 of the lender John 6 top potential callous what it tells us that there is and interaction energy epsilon and it tells us there's an equilibrium bond distance or EQ right that are accuse 19 here right but the minimum of this curve is active sorry to equilibrium by distance this is a vendor

26:41

walls bond that we're talking about here these

26:44

energies hundredweight members held a how big is 100 wave numbers not priests

26:54

how much how much thermal energy is there and wave numbers at room temperature to rights owes me I'm going to be a gas or liquid at room temperature but there because it's only

27:09

got neon atoms are only held together With 100 wave numbers of binding energy right affairs 200 wave numbers of thermal energy they're going to be out the door by the gonna be out here that be gas this is a Lakewood it with me no yes for an animal for an ideal gas intermolecular potentials liberate was dazzling right here at high pressures Of course you're here number 2 to take the gas pressurize it as hard as you can you eventually bang up against this repulsive wall here OK and this pressure that you measure for the system is higher than you would expect based on the and the words if you if you measure V the number of balls of gas and the temperature and you calculate what the pressure should be In a real gas if you press on the hardened the pressure is higher than you could ever achieve for an ideal gas at those same volumes number of balls and and temperature likewise if you had sort of normal pressures here are a few measure this pressure is actually lower than you would expect for this volume this number moles of

28:26

gas and temperature and a real gasses a lower pressure

28:30

here and a higher pressure here this is not ideal right this is it's not on ideology expressing itself OK now let me recall for you that there's something called the compressibility factor which is just the actual pressure times those molar volume divided by RTE but this is the really big not little OK so

28:57

in other words for an ideal

28:58

gasses would just be 1 witness I prefer real gasses not 1 to be higher than 1 at high pressure and lower than 1 at moderate pressure OK so if I look at what this compressibility factor is hears that compressibility factor again but don't fail me now or at high pressures this is pressure on the axis here right this is the compressibility factor here here's 1 is black line is wide OK at high pressures the compressibility factor is greater than 1 walleye because these gas atoms are banging in 1 another but

29:37

you can compress the Gasunie mortars got finite size and in a real in an ideal gas we assume the gas particles had no signs at all there just .period vertices in space OK

29:52

at full pressure but the compressibility factor is less than 1 because gas molecules are exerting an attraction on 1 another at long distances OK

30:06

and that lowers the right in the absence of those attractions would be more pressure on the vessel talking about right but if the if the molecules are attracting 1 another they are reducing the pressure that those gas molecules are applying to the outside of the vessel OK

30:28

now so these 2 regions this is a region repulsion dominate the the gas behavior in this is a region were attractions dominate the

30:39

gas behavior OK got all that now we're do a thought experiment right this is what I just told you is what Jim Jewell New intuitively right and probably you knew it so now

31:00

he does this thought experiment in his head let's say that we've got some gas molecules at a normal practice now I think you can appreciate that and again gas Adams are moving around OK and there's every possible intramolecular distance

31:19

causes collisions occurring OK but unimagined the average nearest neighbor distance but say that let's say you could calculate that How do I would do that take a bunch of snapshots of word all the molecules are frightening calculate what the nearest neighbor distances for each the new I take the average

31:50

of that the average nearest neighbor distance with me but say it's here fire at a particular pressure analysis may make the pressure lower fight the only way to do that would be to suck some of the gas out of the container or to increase the volume 1 of the 2 right OK take the molecules in Nobleboro experimental lower pressure that puts us here this would now be the new average nearest neighbor distance if you think you can see

32:26

by make the pressure lower that on average gas molecules the further part right OK

32:34

so if I start here at high pressure and I in here at low pressure this energy is the work required to separate these molecules I've gotta do that work for

32:45

every molecule in the container you with Maine the

32:55

question is where that energy come from because of other put its energy into the system because I got a goal from here to here by energy is going to come from somewhere where does it come from well 2 first-order it

33:13

comes from the gas itself right the gas can give up energy of the gasses at finite temperature White and that temperature is characterized by kinetic energy of the gas molecules

33:27

the kinetic energy gas molecules goes down the velocity of a gas molecules decreases the temperature will go down that was June jewels inside right this is what he understood all right if I increase the pressure I should pull molecules apart along this potential here initially called OK I know the only question is

33:57

my good enough at measuring temperature in designing the experiments alike and measure that Delta T and it

34:03

turned out he was the guy Delbert Eagle 0 which is the right answer for an ideal gas before an ideal gas these interactions don't exist so we don't expect there to be any

34:16

heat floats where you expend an ideal gas an ideal

34:22

gasses yeah all right there's no difference between this point and this point for an ideal gas in terms of its energy so there's no heat right with me on that OK so we had to he didn't have to but he met when he was given 1 of these talks

34:45

where everybody so laughter mother the room 2 sky William

34:50

Thompson without 1 of these talks he was a hotshot chemical physicist Over in

34:57

Scotland it's not too far from Manchester write a few days of or this guy's name he was

35:09

knighted variety became Lord Kelvin yes that help writes

35:17

that together we goes in the sky he goes and talk this guy after gives 1 of these James

35:22

jewels good gives 1 of these talks for measuring like 17 parts per 100 temperature change and people are just shaking their heads and Thompson's in the audience and the gums and says that sees him and says lot I think I can help you do this experiment in a way that we can measure this this temperature change I agree I think you're right it's happening right it's happening I think

35:43

what we're going to do is we're going to make the gas its own thermal back right what he was doing before is counting on the transmission of the thermal energy In these 2 fears to there's water right wires got an enormous heat capacity

36:01

OK and so you know you have to put a lot of heat in the water to get the temperature to to change very OK it but

36:11

if you're clever you can use the gas as its own thermal baths right so here's what they did Hi I'm sorry user-defined pressure undecided applying pressure on the side this is high pressure this is low pressure this is an orifice a tiny pinhole between these 2 chambers I've drawn and bigger but it's just a pinhole it's gotta be small you'll see why 2nd because what we do is we transfer the staff at high pressure to this low pressure region and we nature of the beast to pressures remained constant during the

36:51

process OK so this is non-trivial experiment even today you would need feedback control Of the pressure

36:59

to do this properly I don't know how they did in those days Friday must had some sort of pressure transducer I mean I don't know what that could have been right this is an insulated containers so there's no heat flows outside of the container all the heat is going to be transferred from year to year or vice-versa

37:20

right that's key to making this experiment work OK so you

37:25

go you blow this gas through this office hissing as this happens right can imagine that according to most of these 2 presidents of the pleased to pressures remain constant and you measure In both of those 2 compartments alright and

37:46

James jewel by golly knew how to measure temperature write to you the experiment is different now than what is a tiny formal

37:54

last year compared to what he was doing before Fourier water take no good luck right here this is gonna tiny capacity by comparison so this all right now there's a temperature change a much more likely to be able to measure it so so the math works work on the left-hand side P 1 times dealt we know that minus the 1 mind you on the right hand side saying thing for simplicity would prevail the little precipice always then there's views just equal to that differences that whole volume there and it's easy to settle volume right there by so that's the 1 that's here the final volume is bigger than the initial volume here the final volume is smaller than the initial volume the of the total work the some of the work on the left side and work on the right side but that's the 1 the 1 this is positive because that's smaller than men right here it's negative because that's bigger than that OK so we get minus Delta Pvt for that difference OK since the apparatus is insulated this is all insulation here few equals 0 and so you is equal to tell might dealt every region this equation we noticed that this is just a that if I move that over the left hand side and a bald eagle the queue I saw this as an item about the process by Delta a church to either 1 is equal to 0 OK and what they measured is the change in temperature at constant pressure for a process that involved no change in enveloping no the flow right that's the jewel constant coefficients but the change in temperature with pressure and what

40:05

jewel measured in his 1st experiment was 0 you see any change in temperature with pressure right and that's the right answer for an ideal gas OK so later

40:18

on we're not going drive this equation now but suffice it to say all right later on we will derive at it's not an issue for a 1 and so if you just believe me for the time being that this equation is correct look we can evaluate this derivative right here what was the partial derivative of volume with respect to temperature for an ideal gas was just an hour over P. right ready that I can do that derivative right plot that ended the a constant pain In that's 0 frankfurt . fi substitute for V I just get this whole thing again right before an ideal gas the dual Popsicle fishing should be 0 that's what measures In

41:08

his 1st experiment should the measured 0 but that's what he did mention all

41:13

right so they were very happy with Thompson's strategy for doing this experiment together the gradual Thompson coefficients that were not 0 White they could see exactly the of the physics that they hoped they would see write the gasket cooler when engendered through this office right and they could measure for different gasses this is what the data looks like today when we have all the modern conveniences to make these measurements with high precision right this jewel constant coefficients far clause OK we can look them up the tables of Jill answer coefficients for different gasses correlated different temperatures the jewel Thompson coefficient of air for example 3 degrees Kelvin 25 degrees 8 25 ATM is equal to 0 . 1 7 3 Calvin ATM right the and it's really known to very high precision if a jewel Thompson expansion carried out from pressure 58 yen departure 180 m estimate the final temperature finishing touches stranded degrees Kelvin the case were starting up the 300 degrees Kelvin and 25 ATM we're going expand In pressure 180 right that's a pretty big

42:39

pressure change factor 50 but we should be able measure something but now the easiest way to do

42:47

this calculation which is the way that will do right now is just like assuming that this dual constant coefficient is invariant over this range of temperatures but that's not true the jewel Thompson coefficient does depend Weekly on temperature but let's

43:04

just assume for the time being added does not in this because going feeling for how big this temperature changes are Price

43:12

58 PM but OK so the delta there were 2 measures just a joke article fishing times Delta paid because we're just in a linear rise this partial derivative OK so that's really easy because that's just the jolt article sometimes dubbed the and that's going to give us directly or delta T and so there is a jolt article fission changing prices 58 him at minus 8 degrees Kelvin some illegal from 300 K the 292 K but which is a cooling of 8 degrees that that's not a lot of cooling is it it's really not a lot of cooling you know when you think about the experiment the jewel in Thompson had to do no this

44:02

device that's got the 2 pistons the reason it works so well is because it doesn't have very much thermal mass the gas inside this these 2 pistons doesn't have a lot of thermal mass and so a small he change changes the temperature quite a bit but the downside is that if you stick a thermometer In those piston there is a lot of there isn't a great formal contact between the gas in the thermometer right the thermometers that lot the capacity right to change its temperature it's going so somehow they they figure all this out

44:39

right somehow they had thermometers ahead as they were so they must've been tiny thermometers otherwise would be no way they wouldn't see anything by because this is a pretty severe Breault experiment 58 PM as is the enormous pressure isn't right and so you know only measuring 8 degrees Kelvin yeah that would be easy for us to measure today but but you

45:08

know these guys are really very very good experimentalists OK so

45:14

what am I going here this is actually a plot from your chapter 14 what it shows is the temperature as a function of pressure OK what it shows is the temperature goes up and then it goes back down the right and it's the jewel Thompson coefficient is the Of these items out but the surprise and felt the traces OK so you'll constant coefficient is part is that rather negative here positive here and negative here "quotation mark any particular pressure there are 2 inversion temperatures the sign of the jolt article fishing changes here and positive this is the reason that we were just talking about this is the so-called normal region for the behavior of the gas and then as we go through this bottom part of this sideways for right inverts again not do I have Is there a nice intuitive way to think

46:20

about this now for me if you have 1 I would like to know what it is because this is never been an intuitive concept to me why

46:34

did into account to coefficient change signs like this from how can be positive the high-pressure and certain negative high pressure near the low pressure but positive in between but the fact that it's positive here that part I can understand that's what that's the explanation I gave earlier we got this potential organ move from here to here would have put energy into the system to make that change half the work this way that both physics apply here other physics here in here OK so now what we've just learned is how to design a refrigerator turns out in I'm not going to

47:23

what he sees as his running time you don't need to know this for the midterm exams but it's in your book actually write your books

47:32

watch you through how they follow in refrigerator works and maybe we'll talk

47:39

about it after the midterm exams OK