foreign okay so thank you for waiting so this lecture is an introduction uh to some basic principles in thermodynamics it's meant to be fun normally I lecture on the board um this is much more interactive you're all holding um the text for today which is statistical physics for babies by Chris Ferry and then two demos an instant hot pack and an instant cold pack that we'll use so wait wait until I tell you and we'll pop those hot and cold packs into context so so I want to start by reading from the text so I'll just read this to you and you can read along with me okay this is a great book all right so this is a ball this ball is on the left now it's on the move so we gave it some thermal energy so it's moving okay now it's on the right so I moved over here okay so now we have six balls all right so we have six balls here in a space that's divided by a dashed line and two so it's clear that the balls can go left and they can go right and we gave them some thermal energies and now they're on the move so they're bouncing around so sometimes you might find more on the left and sometimes you might find more on the right but you'll almost never find them all on one side right that would be pretty surprising it doesn't seem impossible but it'd be surprising if things are random we all agree with that okay so we normally find them like this right it looks pretty evenly distributed around the space okay so now that was the first 10 pages now I'm gonna I'm gonna lecture a little bit on that so let me let me give you a slightly more scientific uh explanation of what we just read no Chuck was right there Okay so so just for today when I have slides I get squished over to the right hand sideboard normally I lecture on the board right in the middle so I apologize today these lecture notes are going to be posted they are already posted to Stellar if you have trouble seeing so we're going to do is we're going to draw a cartoon of non-interacting gas molecules in a box so we're going to start like this we're going to have a box and the box has a divider on the right hand side is vacuum and the left hand side are six gas molecules and I'm going to give them some thermal energy so they have a finite temperature they're kind of zooming around and they don't interact with each other they just bounce off the walls so the first thing we're going to do is we're going to remove the partition so I'm going to draw a dashed line where the partition was and at the instant we remove the partition they're still over here on this side bouncing around so remove partition right so we remove the partition Okay now what's going to happen yeah okay so so this is what's going to happen so what I'm going to say is the next step is we just wait we don't do anything we just wait and we probably don't have to wait very long right we don't have to wait very long before the gas molecules are randomly distributed around the space zooming this way in that so right okay so you all buy this so let me tell you what happened in thermodynamics speak okay so this is a key word in thermodynamics this happens spontaneously the volume of the system here at this moment when I remove the partition was small and spontaneously without us having to do anything it got bigger so all we had to do was wait it was a spontaneous process so you can see the volume spontaneously adjusted within the limits that we impose that is the box is still there to increase the amount of disorder in the system okay so now I'll ask you a question why the probabilities it's there's a greater number than that but that's exactly where we're heading let me rephrase that that was the correct answer because the more the more disordered state is more likely so we're using a frequentist definition of statistical likelihood all right back to the book okay so now he does a better job explaining this than I did so let's go back to the book all right so now we're on page 11 where the balls now have different colors okay so so now we have six balls now each ball is a different color so there's only one way you can have all the balls on one side that way is have all the balls on one side what if we want to put five balls on the left and one ball on the right how many different ways can we do that six different ways right the ball on the right can be the red yellow blue orange green or purple ball so there are six ways to do that now if you started counting up the different ways to have two balls on the right and three and four balls on the left you would find there are 15 different ways to do that but what was the most likely situation three and three right it was sort of even so if you count up all the different ways you can have three balls on the left and three balls on the right you'll find that there are 20 ways so it was 1 6 15 20. so that seems too simple right but that's the answer the reason why this is the expectation this is our expectation from everyday life is because it's more likely there are more different combinations that look like this than any other type of State and you know in this case you know this has a is one combination like this and 20 combinations like this so you would say there's like something like a one in twenty roughly five percent chance of finding all the balls on the left that doesn't sound that small right you take odds on that but when you start doing this calculation for a mole of atoms or a mole of molecules you'll find that the likelihood is geometrically small meaning is never going to happen so we later on in the course much later we're going to come back to these Concepts and do calculation with something like what is it likelihood of finding all the air in this room suddenly over here all right um none of us would be very happy about that fortunately the likelihood is so small you'd have to wait you know many many many many ages of many universes long and you still probably would never see it happen okay so so we're okay with that um so physicists but I should say scientists because this book was written by physicists so there's an implicit bias in here physicists call the number of different combinations entropy so that's what entropy is so a state with a low number of combinations is a low entropy State like a state with all the balls on the left is a low entropy state a state with a high number of combinations is a higher entropy state okay so even if the balls all start on one side as in my example they're going to end up here because this is more likely right it's an increase in entropy so the second law of Thermodynamics says that things move from low entropy to high entropy we'll rephrase that later on in a couple weeks right be a little more technical about it but that is you know one form of the second law that entropy always increases in the universe never decreases so that explains why we see these more likely scenarios in order you can if you like push all the molecules back into the left but the key word there was push right to do that would take some work so you can do work on a system and decrease its entropy right you can clean your room right so you can decrease the entropy of a finite system but in so doing you're still increasing the entropy of the universe you're just shifting it around okay so things naturally go from organized to messy just like my kids rooms and now you know statistical physics okay so do you feel like you know statistical physics I love this book now we're going to fill in some of these Concepts on the board any questions on the reading if it's yours now so if anyone didn't get I think IO how many people did not get a copy one two three Thomas for anyone else okay all right so we'll get more copies for you so now we're going to um talk about um Solutions okay so yes um so uh we'll we'll cover this in a couple weeks but the quick answer is that the entropy of a system left alone never decreases it either stays the same or increases but if a system is not left alone if it actually can interact with its surroundings entropy is something that can be exchanged so I can actually if I were a system I could lower my entropy by giving some to you or you could decrease my entry by taking some that's fine when you what the work you're doing um generates Heat you cool off that generates entropy the most famous example of this is Maxwell's demon it's a thought experiment you can fall down quite an infinite Rabbit Hole or a textbook Rabbit Hole reading philosophical style treaties on Maxwell's demon Maxwell's demon is a little demon that sits in between this box and only without gas molecules go to the left and so in Maxwell's demon is like a little Turn Style for gas molecules and it's called Maxwell's demon because it was thought of as a thought experiment to disprove the second law and there have been a hundred plus years of physics papers showing that the for example there's an information Theory approach to Maxwell's demon that Maxwell's demon has to know that the molecule is approaching therefore it has to receive at least one Photon and you can calculate the physics of the interview generation of that Photon generation and absorption by the demon so he can make the decision to open the gate you can't get around the second law so we'll get there I don't know if that exactly answered your question but it was a little you know we'll get there again and more with more time to spare in a couple lectures so yeah um just Google Maxwell's demon it's kind of fun okay so now we're going to talk about Solutions so here comes the first demo maybe the last demo there aren't a lot of Demos in this class but this one is so easy I did the same demo in 3001 so many of you were in 3001 so I'm sorry I'm ripping myself off here but it's topical so all right so there is water there's water in the dish you can't see it um so what I'm going to do is I'm going to make a solution I'm going to mix two substances one substance is food coloring which is of course also water but pretend this is like some other substance it's food cut it's water like it's some dye molecule solvated so insulation and the other substance is water right so I'm going to mix them and you can see what happens okay so let's see okay so while this is going you guys know what's going to happen right it's just it's sort of it's sort of I find kind of fun and calming to watch it happen all right so over here we're going to talk about um Solutions so okay so we're going to talk about solutions for the case of non-interacting molecules so I'm going to draw some pictures all right so let me see uh three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen okay so here's the starting condition we have some uniform material it's made of some molecules I don't know right so here it is here's the uniform material in a box and these are the molecules that make up the material and its properties are uniform okay so now what we're going to do is when a label we're going to label certain molecules can you guys see that barely we're labeling certain molecules so what's one way you could label molecules physically yeah no what I mean is we're going to make a physical change to the molecule so it's carrying a label huh some kind of fluorescent tag you could make it a different isotope there's different ways to label right or just as a font experiment you just go in and you take let's say five of these molecules and color them blue to pick a color right which is kind of what we're doing one two three four five okay so I went in and I labeled those molecules and now I'm going to wait what do I expect to happen yes yeah you kind of expect it to even out right for the case of non-interacting well because initially everything looked even and then we did something we made it uneven and now you kind of expect it to even out so I'm going to draw again 15 and you kind of expect the labeled molecules to spread out maybe like that right okay they're not all on one side anymore you get it I didn't want to spend all day up here drawing circles it's more convincing if I do like 20 or 30 circles but I decided to stop at 15 circles so what's actually happening right um I mean you understand that and you believe that I'm just going to describe that in thermodynamics language so what happens is that diffusion okay so the process by which this concentrated area of labeled molecules becomes diffuse is diffusion and it happens spontaneously right I don't have to go over there with my Atomic tweezers and move the blue food coloring molecules until they all look even I think by the end of this course period it will be uniformly blue it takes about half an hour at the temperature of an overhead projector okay so that's the diffusion process and again that word spontaneously it's happening spontaneously and it's mixing the label molecule so um what can you say about the entropy of this situation do is it is the entropy from the second frame to the third frame is it going up or down it's going up something's becoming more disordered right that's true the entropy is going up there's more different configurations that look like this all mixed up and configurations that look like this everything on one side right so it's more likely it's more entropy all right so now I'm going to erase this board and redo it for the case of molecules and now we're going to interact with each other yes please but before when we're talking about uh yeah no it doesn't mean instantaneously exactly that's right it does not mean instantaneously um there are many good examples of this um of systems that are out of equilibrium that are slowly relaxing if you go to very ancient Cathedrals you'll see that the windows appear to be pooling at the bottom of the window frames they're slowly like flowing right things seem static in the case of gas molecules it'd be about hundreds of nanoseconds in a reasonable space so the time scales might vary yeah that's a good question it doesn't mean instantaneously it just means without without outside influence right thank you okay so now let's do the case my favorite example here is a there's a there's a something called the tar drop experiment and this is a university in Australia where they took some tar and they put it in a vessel and they poked a hole in the bottom of the vessel and they put a video camera on it and it's been running for decades and I don't remember but once every eight or nine years um a drop you get a drop and it's there's a webcam for this thing you can go and watch it you know so spontaneously it's dripping but it's pretty slow okay so now we're going to do the case of interacting molecules so the previous example and the example you're watching over there is effectively no interaction between the labeled molecules and between the labeled molecules and the unlabeled molecules there's not a lot of intermolecular forces in between the blue dye and let's say a distant water molecule or between two distant blue dye molecules not a lot of interaction so what about when there is interaction let's let's do the cartoon case and then and then we'll start um this is this is how we get towards the hot and cold packs so we have a uniform material all right one two three four five thirteen fourteen fifteen all right so we're starting again with the uniform material and now I'm going to uh let's see I sort of label sum right so just as before I'm going to label some this time the ones I'm going to label are all right I'm going to label them in a way that is sort of more like what you expect from the equilibrium situation for the non-interacting particles label Sun okay so now I've labeled them I've labeled them as quasi randomly and now I'm going to make a caveat label some so that they so that they attract so I'm going to label these with some sort of a molecular tag that likes to be close to other like molecular tags so there's an attraction here so now we're talking about forces and interactions between molecules so what happens if I label these so that they interact and then I wait what do you expect to happen yeah they're only attracting so like it would be as if the blue dye molecule were attracted to other blue dye molecules in that case right okay so if they're attracted to each other and there's no other forces in this let's see you might expect after waiting for some time that now the molecules have clustered Okay so in this case inter-atomic or molecular if these are atoms I would talk about inter Atomic forces if they're molecules also like intermolecular forces same thermodynamics inter-atomic or molecular interactions cause spontaneous unmixing right so we talked about mixing and now it's unmixing so this can happen too and there'll be plenty of examples maybe you're already familiar with some okay and you can also I won't draw this so you could also consider the case of repulsive interactions so let's say that those molecules instead of attracting each other were repelled from each other think about how you sit in a lecture room when it's an exam and we told you not to sit next to anybody do you become completely disordered or more ordered more ordered you become more ordered because if I have a person I know that I only have to go two chairs or to find another person and I go two chores over to find another person that's order right so is that increase in entropy or decrease in entropy that's a duties in entropy right so from this Central frame to the right hand frame is that an increase in entropy or decrease in entropy decrease it's a decrease in entropy and the case of the students taking an exam in a lecture all that's also a decrease in entry relative to say right now where you look more disorder than that there's some clusters there's some loan people that it's sort of more distorted okay yes not quite but balance is the key thing we're heading exactly towards this idea of balance so thank you for saying balance okay so um now everyone let's see so you got this idea of disorder and a basic notion of entropy and now we're starting to introduce the fact that molecules can interact with each other and an interaction is typically characterized by an energy of any interaction so there's energy involved and I think these are Concepts which are already familiar with so we're going to now review endothermic and exothermic reactions right in this context so who's here a heard of endothermic and exothermic all right everybody raise their hand except for actually um all right so so now we get the now we get to play with the hot packs but wait wait till I say you play with the hot packs all right so we're going to start with endothermic process endothermic process endothermic example okay so an example of an endothermic process is ammonium nitrate dissolving in water so I'm going to draw it like this n moles of ammonium nitrate plus M moles of water are going to react and the reaction product is going to be a solution okay so even though this kind of just looks like you dissolved or you just mixed you can still talk about it as a reaction so this over here is pure solid so this is what we call in thermodynamics a pure material and it's in its standard State ammonium nitrate will sit in a jar it's a solid around temperature and atmospheric pressure all right and this over here is a pure liquid okay so this is a pure solid and this is pure liquid and what's what's this on the right hand side it's a mixture it's a liquid solution in thermodynamics and this is something is this terminology you have to get used to it the word solution and the word mixture are basically interchangeable solution to us does not mean it's a liquid solutions could be liquid gas or solid in fact in this class usually if they're solid so just get used to it there's no way around it so this is a but this is a liquid solution in this case it's a liquid solution or mixture if you like liquid solution okay so I need to uh get more board space here okay so this process um this process absorbs a finite amount of heat from the surroundings it's an endothermic process so it absorbs an energy Q This is the units of joules it's an energy from the surroundings sometimes this is called the heat of solution later on in this class we'll show that this is related to the enthalpy of solution we'll start using the word enthalpy but for today's lecture it's enough to think about heat and energy Okay so in going from left to right does the energy of the system increase or decrease it increases because it's endothermic it got energy from the surroundings right does the entropy increase or decrease it increases and it's okay if you don't have an intuition for that now the reason it increased is because on the left hand you had a solid phase and then every n moles of that solid went into a liquid phase and liquids tend to have much higher entropy than solids they're more distorted right a solid is like everyone at every other chair a liquid is somehow more disordered so that was right so in this case the energy and entropy both increase okay so um before we learned that nature likes to increase the entropy of the system so that would seem to drive the reaction to the right but if you've taken a physics class you were probably told that nature likes to decrease the energy which would drive the reaction to the left all right and both of those things are true in the right context so what gives all right so we're going to find out what gives okay so um open your uh take your instant cold packs which is the uh not the one that says warm relief the one that's blue all right so okay so this is a dynorex instant callback this is a snapshot from the safety data sheet dynorex instant cold pack if you're ever looking for your first choice for gloves I guess it's the Tillotson Healthcare Corporation all right so this is the SDS and this is telling you that it's um made of ammonium nitrate pellets surrounded by a small rupturable plastic bag filled with water so we're gonna figure this out does this reactions stay on the left hand side or does it go spontaneously at the right hand side so what do you think everyone who thinks it's going to go to the right south or raise your hand yay okay so squeeze together so here we go I'm going to squeeze together okay ah [Applause] cold all right so is it cold yeah so is it spontaneously went to the right or the left where does it go it goes to the right so it's absorbing heat from your hands right you feel cold all right so in this case um in this case entropy right yeah it spontaneously went to the right which means entropy increased but the energy also increased so it's like we weren't sure what was going to happen but in this case entropy drives I'm being really sloppy here it's like entropy drives the reaction it's the entropy consideration nature thinks about it figures out the right balance and say entropy is going to win we're going to make a solution okay so um so then then okay so now we're going to do the opposite case which is exothermic exothermic process that was satisfying right I like that so exothermic process for example crystallization of sodium acetate from from a solution so we started with a solution and we're going to crystallize sodium acetate so CH 3 c o o n a let's see the way I wrote this was like this X h two o Z reacts the reaction is like this it goes with some heat q and it becomes ch3 c o o n a y I'm going to put a little solid there because it came out of solution formed a solid Crystal and then um and then C H three c o o n a x minus y H2O okay so someone tell me um uh well okay so I told you this is a solution right this is a this is a solution it's a liquid solution of x moles of sodium acetate into Z moles of water all right what is someone repeat for me what is this material what is this phase so all I told him about State all right and what is this material over here this phase it's liquid is a pure material it's still a solution right so we have Solutions on both sides but they have different concentrations we've conserved moles right we haven't created a destroyed matter all right so this is a liquid it's a liquid solution um but in the Hot Pot in the hot pack we're about to use it's super saturated so ask me questions in a minute about what that means we'll come back to that concept later in the class it's a supersaturated liquid solution so it's non-equilibrium then over here we have a pure solid and over here we have a liquid solution and what do you think would be the right term to characterize this liquid solution a liquid solution in equilibrium with the solid solute is a saturated solution yeah saturated so if you uh if that didn't come to your you know tongue right away that's fine that's a concept which we're going to cover in detail right in a number of weeks from now all right so we start with a supersaturated solution and we get a saturated solution okay so um okay so I told you this was exothermic so I'm not going to ask you you know what's the sine of Q this process releases this process releases heat energy cue to the surroundings so um all right so would you say the energy of this system increases or decreases from as it goes from left to right decreases exothermic it lost energy okay so energy all right what about the entropy of the system does it increase or decrease from left to right decreases right it decreases you started with all the sodium acetate in a liquid state and then you took some about and made it a solid and I told you before that the solids tend to have lower entropy so the entropy decrease so energy and entropy they decrease both keys that they both decrease okay all right so nature likes to maximize entropy but it also likes to minimize energy so what's going to happen okay so demo number two right so grab your instant hot pack let's see uh uh there we go until this is um instant hot pack from danieling Rapid and Aid hot and cold therapy Product Company Limited and it is uh made up of sodium acetate and water right that's what that's what's in here um so I'll tell you what's actually uh just use I'll show you a video of what my what this might look like in a minute but let's test it let's do the experiment let's figure out if it goes left or right so I did this the other day it's like um fold top to bottom to pop inner fluid bag and Shake okay so I'm folding the top to the bottom certain amount of strength required to be in this class ah there we go okay oh it's like it's hot this is like a PE credit I should get a PE credit for this all right who's got popping I hear some popping sounds it gets hot right okay so what's going on ah yeah okay so what happened some people are still struggling it's actually really tricky um those of you whose bags popped can you tell me what happened somebody tell me what happened it warmed up it got hot so did the reaction where's equilibrium here to the right or to the left to the right so it's it's weird right entropy decreased so in this case unlike the previous case so in the previous case entropy seemed to win nature got to increase its entropy but in this case energy seems to win nature got to decrease its energy so the balance was different let me show you a video of what what these look like all right so we've seen two examples um and we've done two experiments and we've seen that in one example uh entropy seemed to Rule the Day uh win the day but in the other example and entropy or energy seems to rule it I forget which one I said first all right so so on the one hand we have entropy or disorder and the other hand we have energy or what we will more commonly used in this class which is enthalpy they're not identically the same thing so we'll cover enthalpy in plenty of detail um in later lectures but for today we can use them interchangeably so on the other hand we have energy and or enthalpy and this question of balance is everything so here's a plank and there's the fulcrum and this is basically thermodynamics thermodynamics is Nature's Way of balancing entropy with enthalpy and so what we're going to do is is spend a semester learning how to calculate the balance for all sorts of difficult physical situations mostly with solids but also reacting chemicals liquids solid gas systems and systems of Interest right to Modern Material Science so uh what happens when we get the final answer so okay I'm going to move on I have a couple slides to share now with um to introduce you to the concept of phase diagrams which is the way that we communicate with each other in Material Science what the answer is what's the balance before I move on we have any questions about um uh these these uh hot and cold packs endothermic exothermic processes Okay so you might not know in advance the balance right one chemical system we we just showed you room temperature and atmospheric pressure preferred to maximize entropy the other system at the same set of conditions prefer to minimize energy um so fortunately there's a there's a rigorous theoretical framework to calculate the balance and that's what we're here to learn once you've calculated the balance for a given material you want to communicate that answer to other people and this is where phase diagrams come in Phase diagrams are the tool the visual tool by which within Material Science we communicate what that answer is what nature will prefer the given set of conditions so I want to show you some examples of phase diagrams if I have one deliverable in this class to you when you walk out of here in December is that you know how to use phase diagrams and you know where they come from that's the core of thermodynamics and Material Science unlike let's say mechanical engineering right um so so this is the water phase diagram let's see I assume that most people have seen the water phase diagram before what's kind of cool about this water phase diagram is that it covers a very large range of pressure so this is pressure on the y-axis and the x-axis is temperature and the colors here show you what the right balance is between enthalpy and entropy so for example at a given pressure let's say atmospheric pressure where is that here right when you heat up you go from Ice which is a low entropy state to water which is a medium entropy state to I'm like down here to uh Vapor which is a high entropy state on the other hand it turns out pressure goes the other direction pressure we haven't talked about volume but pressure increasing pressure favors smaller material that makes sense right so as you go from The Vapor to this solid and then these other phases of ice which you might find in the core of distant planets the volume per mole becomes smaller crystal structure becomes different they're different materials so this kind of you have like 11 phases of device I think there are 12 known now um they're labeled with these different Roman numerals and so this is one thing that we get used to in thermodynamics is that there are many different solid phases of a material they're in a sense different different phases they're different materials they behave differently they have different structure and therefore they have different properties um I was just speaking with one of my Europe uh advisees who she spent her summer at JPL testing the mechanical properties of drill bits on different phases of ice why because they're going to land a Rover on Europa and they want to drill through um they want to go ice fishing they want to drill through the ice core of Europa to get to the liquid underneath and they might expect different phases of ice than the normal terrestrial eyes that we're familiar with and they'll have different properties and therefore it will wear the drill bit differently and they have to know how it will wear the drill bit right you'd hate to fly all the way to Europa and have something like the drill bit failure ruin the mission so it's kind of interesting I just you just told me about this just before this class so here's another example here's a binary phase diagram here the y-axis is temperature and what's the x-axis I heard something like concentration which is about right it's composition so um this is a sort of complicated diagram which you're going to know by the like the back of your hand when you walk out of this class so this is the copper zinc system this is called the liquidus line above this line the system is a uniform liquid mixture below this line there's a slew of solid phases um Alpha Beta Gamma Delta Epsilon ETA which phase or combination of phases see this region I know is a mixture of Alpha and beta you'll learn that which how the system behaves depends on where you are in temperature pressure and composition and that's something you know this is an equilibrium phase diagram well established because that's brass it's an important metal alloy and we'll learn how to calculate these phase diagrams there's a lot more so the types of phase diagrams that's a binary phase diagram a classic eutectic phase diagrams don't have to be composition temperature and pressure they can be electrical potential in PH so a poor Bay diagram like you would use to predict corrosion or to optimize a battery gives you the phase that you might expect as a function of aqueous solution pH and electrochemical potential or electrical potential relative to a standard electrode here's a ternary phase diagram so here instead of two elements or pure materials we now have three titanium tungsten and carbon so this is going to be all sorts of high performance titanium tungsten Alloys in there here there is no more room left on the page to do temperature and pressure so those are in some sense in the third and fourth Dimensions but they're there and this is something that's near and dear to my heart because I work on a lot of oxide and sulfide electronic materials this is a Richardson LM diagram which isn't quite a phase diagram but it does tell you whether nature predicts the metal or the metal oxide as a function of temperature and oxygen partial pressure so this is very useful if you are for example making a transistor you have to know how to control the oxidation process of silicon or if you're smelting or any number of other sort of interesting processes that are important so we're going to learn how to how nature finds this balance and we're going to learn how to interpret these phase diagrams but in practice calculating one of these phase diagrams would take you a really long time and you'd get a paper out of it and you'd feel very accomplished but what if you're out there in the world and you have to make engineering decisions and you have seven minutes before your boss tells you what percentage carbon do we want in this Steel right you don't go to the Blackboard you go to computer computerized tools so the idea that you could calculate phase diagrams with a computer that idea is called Cal fed it's kind of funny that that idea would have an acronym but it does it's called Cal Fab and there are many cal fed software packages out there what they do is they take materials data from databases which often are proprietary and they calculate the balance for a given temperature or pressure or composition or a pH or electric field or what have you and they tell you the answer so we these are really indispensable once you leave here and you go off to your next position whether it's in research or industry or what have you and so we're going to spend a little bit of time in this class getting familiar with one of these thermal calc the reason why we're going to get familiar with thermocalic is because they have a free educational version and it's relatively user friendly so you have a thick a couple weeks until we're actually asking you to use thermocalc in your presets but if you want to just download this on your computer install it get ahead of any problems attempts to work well in both PCS and Macs and play around a little bit so this course the thermodynamic section of this course basically has three parts the first seven lectures are introducing the concept of equilibrium that is this balance right how does nature determine the equilibrium situation the most balanced situation for any given set of conditions and then we're going to apply that concept we apply the concept of equilibrium to increasingly complex physical systems to calculate these phase diagrams to figure out how to where they come from how to make them how to read them how to use them and then at the very end of the course we're going to come back to some foundational material we're going to come all the way back to statistical physics for babies and do some slightly more sophisticated analyzes of of entropy and how it relates to let's say configurations and molecules do some foundational work we might even mention Carnot Cycles at the very end of class okay um I already told you about the resources online so I'll leave you with this um so Arnold summerfeld was one of the fathers of quantum mechanics the point is that he was a smart person no dummy when it comes to science and this is a very famous quote there's a website devoted to quotes about thermal by the way but this is the one that gets most often related so I'll read it he said thermodynamics are the funny subject the first time you go through it you don't understand it at all uh the second time you go through it you think you understand it except for one or two small points the third time you go through it you know you don't understand it but by that time you're used to it so it doesn't bother you anymore right and this is consistent with most people's experience of learning thermal um this is a bit of a disclaimer because this is the first time you go through it so this is a tricky subject and you shouldn't feel badly about yourself if you leave this course thinking that I know how to use a phase diagram okay Thermo calc that's neat but what just happened all right that's that's perfectly natural