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Download English-US Transcript (PDF) MITOCW | ocw-5_60-s08-lec04_300k The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or view additional material from hundreds the MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR BAWENDI: Last time you talked about the first law of thermodynamics. And you talked about isothermal expansion, the Joule expansion. You saw a very important result. which is that for an ideal gas, the energy content is only dependent on the temperature, nothing else. Not the volume, not the pressure, it just cares about the temperature. So, if you have an isothermal process for an ideal gas, the energy doesn't change. q plus w is equal to zero for any isothermal process. And you also saw that du then could be written as Cv dT for an ideal gas always. This is not generally true. If you have a real gas and you write du is Cv dT, and your path is not a constant volume path, then you are making a mistake. But for an ideal gas, you can always write this. And this turns out to be very useful to remember. OK, now most processes that we deal with are not constant volume processes. So energy, which has this wonderful property here, du is Cv dt for constant volume process, which happens to be equal to d q, constant volume, because there's no change. there's no work if you've got a constant volume process. So du here is a very interesting quantity, because it's related to the heat that's going in or out of the system under constant volume process. But as I said, we're not operating usually in a constant volume environment. When I flail my arms around I generate work and heat. This is not a constant volume process. If I'm the system, what's constant when I do this? Anybody have an idea? What's the one function of state? I'm the system, the rest are the surrounding. What's the one function of state that's constant when I'm doing all my chemical reactions to move my arms around? Temperature? STUDENT: Pressure? PROFESSOR BAWENDI: Pressure, right. Pressure is constant. What is the pressure at? One atmosphere, one bar. So the most interesting processes are the processes where pressure is constant. When I had have a vial on bench top, and I do a chemical reaction in the vial, and it's open to the atmosphere, the pressure is constant at one atmosphere. When you've got your cells growing in your petri dish, the pressure is constant at one atmosphere, even if they're evolving gas, pressure is constant. So we'd really like to be able to find some sort of equation of state, or some sort of rather function of state that's going to relate the heat going in or out of the system with that function of state, because this isn't going to do it. du only relates to the heat under constant volume. And the heat is a really important thing to know. How much heat do you need to put into a system, or how much heat is going to come out of a system when something is happening in the system? All right, this is a really important quantity to know. Your boiling water or whatever, you want to know how much heat do you need to boil that amount of water under constant pressure? And this is where enthalpy comes in. You've all heard of enthalpy. H we're going to write it as the function of temperature and pressure. And the reason enthalpy was invented was exactly for that reason, because we need some way to figure out how to relate the heat coming in or out of a system under a constant pressure process. Because it's so important. And I should add and also under reversible work, where the external pressure is equal to the internal pressure. OK, so we're going to define enthalpy as u + pV, these are all functions of state here, So H is a function of state, and we're going to see now how this is, indeed, related to the heat flow in and out of the system. If you have a constant pressure, reversible work process. Let's take a system. Under constant pressure T1, V1, going to a second -- this is the system, so let me write the system here. And it's more dramatic if the system is a gas, p, T2, V2, And let's look at what happens to these functions of state, to H to u under this transformation. OK, so let's look at delta u. Delta u is q plus w. That's the first law. And this is a constant pressure path, so now I can write, this q is actually q under constant pressure. Little p means the path is a constant pressure path. And I'm doing reversible work. So that w is minus p, dV where p is the pressure inside the system, minus p delta V. Rearrange that, delta u is plus p delta V is equal to q p. All right, so this is the heat flowing in or out of the system, and these are all functions of state. This depends on the path. It tells you right here, the path is constant pressure. These don't depend on the path, right. V doesn't care how you get there. u doesn't care how you get there. In this case, p is a constant because the path is constant. So we can bring the p inside, delta u plus delta p V it's q p. Take this delta outside again, delta of u plus p V is equal to q p. And there you have it. There is the H right there. The u plus p V. Delta H is equal to q V. And this is the reason why enthalpy was invented, and why it's so important. Because we want to know this. So this for a finite change. If you want to have an infinitestimally small change, you end up writing dh is dq sub p. It's not always equal to the heat. It's only equal to the heat if your process is constant pressure reversible work. OK, so this is the kind of, this is the kind of concept that needs to be branded into your brain, so that if I come into your bedroom in the middle of the night and I whisper to you delta H, you know, you should wake up and say q p, right? Heat under constant pressure reversible work. This should become second nature. This is where the intuition comes from. This is why people right tables and tables of delta H's. Why you have delta H's from all these reactions, because this is basically the heat, and the heat is something we can measure, we can control. We can figure out how much heat is going in and out of something. This is what we're interested in. OK, so last time you looked at -- any questions on this first? Yes. STUDENT: [INAUDIBLE] from the T delta V to the delta p here? What was the reasoning behind that? PROFESSOR BAWENDI: p is constant here. It's constant pressure. OK, so now, last time you looked at the Joule expansion to teach you how to relate derivatives like du/dV. du/dV under constant temperature. du/dT under constant volume. You use the Joule expansion to find these quantities. Now these quantities were useful because you could relate them. The slope of changes, with respect to volume or temperature of the energy with respect to quantities that you understood, that you could measure. We're going to do the same thing here. So if we take as our natural variables for enthalpy to be temperature and pressure, and we have some sort of change in enthalpy, dH, and it's going to be related to changes in temperature and pressure through the derivatives dH through the slope of the enthalpy in the T direction, keeping pressure constant, dT plus the slope of enthalpy in the pressure direction, keeping the temperature constant, dp, and these are knobs that we can turn. We can change of temperature. We can change the pressure. These are physical knobs that are available to us as experimentalists. And so when we turn these knobs on our system, we want to know how the enthalpy is changing for that system. Because eventually they will tell us maybe things about how heat is changing further on. OK, but in order to relate turning these physical knob to this quantity here, which we don't have a very good feel for, we've got to have a feel for the slopes. If I keep the pressure constant. I change the temperature, what does that mean? What is dh/dT? If I keep the temperature constant, and just change the pressure, dH is going to change, but how is it going to change? What does this mean in terms of something I can physically understand? That's the program now for the next few minutes. What are these quantities? What is dH/dT as a function, keeping pressure constant, what is dH/dp, keeping temperature constant? All right, let's start with the first one, dH/dT, keeping the pressure constant.
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