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[SQUEAKING] [CLICKING] [RUSTLING] RAFAEL JARAMILLO: Hi. Today we're going to discuss the many D's of thermodynamics. So what do I mean? We're going to talk about lowercase d, lowercase Greek d, and uppercase Greek D. And I wanted to clarify why we have different D's that we use, when we use them, and give some physical intuition for what they mean. So, for example, when we write the combined statement of the first and second law, we have Du equals TdS minus PdV. In this case, the d's indicate exact differentials, which is equal to infinitesimal changes in state variables. I'll write that out. OK. The next D we want to talk about are the lowercase Greek d's. So, for example, conservation of energy gives us the following expression. dU equals dQ plus dW, which tells us that the total change of internal energy for a system equals the sum of heat and work. Heat and work our process variables. In this case, the lowercase Greek d's indicate inexa...

[SQUEAKING] [RUSTLING] [CLICKING] RAFAEL JARAMILLO: Hi. Today we're going to introduce phase diagrams of unary binary, and ternary systems with a real focus on ternaries. The challenge of drawing phase diagrams is how to capture a phase equilibria with flat pictures on a piece of paper. So before we begin, we're going to remind ourselves of the Gibbs phase rule. I'm going to keep this down here in the bottom of the board. Gibbs phrase rule says that the number of degrees of freedom in a system is the number of components minus the number of phases plus 2. So I'll keep this down here so we can refer to it. We'll start with unary systems. I'll draw the phase diagram of a very well known unary system for iron, temperature on the vertical axis, pressure on the x-axis. So this is the very well known phase diagram of iron-- alpha phase, high-pressure epsilon phase, beta, gamma, and liquid. So for a unary phase diagram, we have two independent intensive v...

[SQUEAKING] [RUSTLING] [CLICKING] RAFAEL JARAMILLO: And all right, so let's go, ideal gas processes. How to motivate this? It's not just that we like ideal gases because they have a simple equation of state. What we're going to see in a couple of lectures is that the process of mixing ideal gases is a model for the process of mixing real materials. So in case you're wondering why are we spending all this time on gases-- and ideal gases, for that matter-- there is a material science motivation for it. OK. Let's start with reversible adiabatic expansion. You looked at this a little bit at the last lecture. I want to look at it some more because it is really important. Reversible adiabatic expansion. So what to choose for independent variables? So this thought exercise again, you have a problem, you want to calculate something about that process. What are you going to choose for independent variables? Well, adiabatic means no heat. And we said it's re...

[SQUEAKING] [RUSTLING] [CLICKING] RAFAEL JARAMILLO: So we've gone through the first law, and we've gone through heat engines, which means it's time for the second law. So we're ready for the second law. All right, and this is what I call a plane for act. So I'm going to present this by way of Clausius's theorem. You'll see what that is in a minute. Then, we'll move on to reversible processes and entropy, and reversible and irreversible processes, and finally entropy maximization. So we talked about entropy in the first lecture with the baby book. And I think everybody does have this feeling of entropy as being mixed up and it's disorder, and that's true. That's true. And so one could state the second law of thermodynamics as something like the entropy-- the disorder in the universe is always increasing. Rather like the statement that the energy of the universe is always constant, that's not obviously useful for us as scienti...

[SQUEAKING] [RUSTLING] [CLICKING] RAFAEL JARAMILLO: So today, we are going to talk about heat engines. So what's a heat engine? A heat engine is any machine that takes heat and turns it into work. So an engine is something that does mechanical work. A heat engine is an engine that runs on heat. And as we'll see, no machine can turn heat into work with 100% efficiency. That would violate the second law of thermodynamics. But we try to engineer our systems to do it as well as we can. So here's the most obvious case of a heat engine in our day-to-day lives, and especially if you live in Texas right now, is that of power plants. So power plants take some fuel resource, coal, oil, gas, or nuclear. And you burn that to create heat and then use that heat to make mechanical work. So this picture in the upper left here is the Mystic Generating Plant, just a couple of miles from where I am. That is a combined cycle natural gas power plant that provides much of the elect...

[SQUEAKING] [RUSTLING] [CLICKING] RAFAEL JARAMILLO: All right. Good morning, 020. Today is the last lecture of technical content of the semester. So that's kind of exciting. And it's the last time we're going to use this little piece of graph paper, which is not particularly exciting. But, anyway, next week, we're going to change gears a little bit and do our second social and personal hour on Monday. And I'll send around reading for that shortly. And on Wednesday, we're going to do a Zoom game show. So I hope we have a good attendance for that because we're going to try to make it as fun as we can over Zoom. It won't be as much fun as in person. But, still. Anyway, that's next week. Today, we're going to work an example which pulls together some concepts which we've been using the last couple of lectures. So this is what we're going to work on today-- reacting systems that have gases and condensed phases. So we spent a coup...