WEBVTT 00:00:00.000 --> 00:00:11.713 align:middle line:90% 00:00:11.713 --> 00:00:14.130 align:middle line:84% RAFAEL JARAMILLO: All right, so let's talk about processes 00:00:14.130 --> 00:00:15.360 align:middle line:90% and thermodynamics. 00:00:15.360 --> 00:00:26.800 align:middle line:90% 00:00:26.800 --> 00:00:35.520 align:middle line:84% So we talked about thermo being this weird thing 00:00:35.520 --> 00:00:42.310 align:middle line:84% that can tell you about starting state and the final state. 00:00:42.310 --> 00:00:49.940 align:middle line:90% 00:00:49.940 --> 00:00:53.240 align:middle line:84% But it doesn't really have a clue 00:00:53.240 --> 00:00:58.550 align:middle line:84% as to the process that takes you from one to the other. 00:00:58.550 --> 00:01:09.270 align:middle line:84% That is thermo doesn't describe real world processes. 00:01:09.270 --> 00:01:17.980 align:middle line:90% 00:01:17.980 --> 00:01:19.540 align:middle line:84% But that doesn't mean it's useless. 00:01:19.540 --> 00:01:39.710 align:middle line:84% The concept of state functions, which are history independent, 00:01:39.710 --> 00:01:41.330 align:middle line:90% allows us to make predictions. 00:01:41.330 --> 00:01:52.510 align:middle line:90% 00:01:52.510 --> 00:01:55.460 align:middle line:84% So for example, if someone told you the pressure, temperature, 00:01:55.460 --> 00:01:58.453 align:middle line:84% and volume of the system at the beginning 00:01:58.453 --> 00:02:00.370 align:middle line:84% and then told you the pressure and temperature 00:02:00.370 --> 00:02:02.950 align:middle line:84% of the system at the end, with that information 00:02:02.950 --> 00:02:06.250 align:middle line:84% you could calculate the volume without knowing 00:02:06.250 --> 00:02:11.670 align:middle line:84% the process that took it from A to B. So that's useful. 00:02:11.670 --> 00:02:14.260 align:middle line:90% 00:02:14.260 --> 00:02:16.680 align:middle line:84% So here's the property of state functions. 00:02:16.680 --> 00:02:38.970 align:middle line:84% Any process connecting A to B will give same results 00:02:38.970 --> 00:02:40.485 align:middle line:90% for the final state. 00:02:40.485 --> 00:02:47.260 align:middle line:90% 00:02:47.260 --> 00:02:59.290 align:middle line:84% These are the final state variables, 00:02:59.290 --> 00:03:01.030 align:middle line:84% because they are state variables. 00:03:01.030 --> 00:03:09.340 align:middle line:90% 00:03:09.340 --> 00:03:13.230 align:middle line:84% So you want to calculate something. 00:03:13.230 --> 00:03:15.510 align:middle line:84% You want to do the easiest calculation you can, 00:03:15.510 --> 00:03:22.940 align:middle line:84% conceptualize the simplest process to calculate it. 00:03:22.940 --> 00:03:34.810 align:middle line:90% 00:03:34.810 --> 00:03:36.250 align:middle line:84% So in the same way that we choose 00:03:36.250 --> 00:03:39.910 align:middle line:84% a system, its components, and its boundaries out 00:03:39.910 --> 00:03:43.840 align:middle line:84% of convenience depending on the problem we're trying to solve, 00:03:43.840 --> 00:03:49.980 align:middle line:84% you calculate the simplest process to calculate out 00:03:49.980 --> 00:03:52.410 align:middle line:84% of convenience, not necessarily the process 00:03:52.410 --> 00:03:53.580 align:middle line:90% that nature actually takes. 00:03:53.580 --> 00:03:57.820 align:middle line:90% 00:03:57.820 --> 00:04:09.640 align:middle line:84% So the simplest processes to calculate are reversible. 00:04:09.640 --> 00:04:15.760 align:middle line:90% 00:04:15.760 --> 00:04:19.873 align:middle line:84% So reversible process, that's a new concept. 00:04:19.873 --> 00:04:21.040 align:middle line:90% That's a new concept for us. 00:04:21.040 --> 00:04:22.630 align:middle line:84% And it has a very deep and important 00:04:22.630 --> 00:04:23.960 align:middle line:90% thermodynamic meaning. 00:04:23.960 --> 00:04:26.140 align:middle line:84% It means a process that does not change 00:04:26.140 --> 00:04:28.360 align:middle line:90% the entropy of the universe. 00:04:28.360 --> 00:04:31.030 align:middle line:84% That is a system plus its surroundings. 00:04:31.030 --> 00:04:35.110 align:middle line:84% And we'll see that in the next couple of lectures. 00:04:35.110 --> 00:04:37.810 align:middle line:84% Reversible processes have these properties-- 00:04:37.810 --> 00:04:43.510 align:middle line:90% 00:04:43.510 --> 00:04:58.330 align:middle line:84% the system plus surroundings are in equilibrium at all times. 00:04:58.330 --> 00:05:02.360 align:middle line:90% 00:05:02.360 --> 00:05:05.250 align:middle line:90% That's an assumption. 00:05:05.250 --> 00:05:15.330 align:middle line:84% This violates our day-to-day notion of an arrow of time. 00:05:15.330 --> 00:05:21.790 align:middle line:90% 00:05:21.790 --> 00:05:24.460 align:middle line:84% It's really inconsistent with most of our experience. 00:05:24.460 --> 00:05:29.200 align:middle line:90% 00:05:29.200 --> 00:05:45.770 align:middle line:84% In practice, a reversible process would take forever. 00:05:45.770 --> 00:05:49.640 align:middle line:84% So we're imagining a process, which doesn't actually exist. 00:05:49.640 --> 00:05:52.590 align:middle line:84% But it makes a calculation easier. 00:05:52.590 --> 00:05:55.340 align:middle line:84% So in order for a process to be in equilibrium at all times, 00:05:55.340 --> 00:05:57.215 align:middle line:90% it has to go arbitrarily slowly. 00:05:57.215 --> 00:06:02.577 align:middle line:90% 00:06:02.577 --> 00:06:04.660 align:middle line:84% In order for our process to be able to go forwards 00:06:04.660 --> 00:06:08.610 align:middle line:84% or backwards, we need to be able to play the movie forwards 00:06:08.610 --> 00:06:13.060 align:middle line:84% or backwards without being able to tell which one is forwards 00:06:13.060 --> 00:06:14.260 align:middle line:90% and which one is backwards. 00:06:14.260 --> 00:06:19.330 align:middle line:84% That violates our day-to-day notion of the arrow of time. 00:06:19.330 --> 00:06:21.400 align:middle line:84% And the requirement to go arbitrarily slowly 00:06:21.400 --> 00:06:23.860 align:middle line:84% means that in practice, a reversible process 00:06:23.860 --> 00:06:26.620 align:middle line:90% would take forever. 00:06:26.620 --> 00:06:28.450 align:middle line:84% But it makes calculations really easy. 00:06:28.450 --> 00:06:34.590 align:middle line:90% 00:06:34.590 --> 00:06:37.480 align:middle line:90% Is that surprising to anybody? 00:06:37.480 --> 00:06:39.400 align:middle line:84% Or we're comfortable with the concept 00:06:39.400 --> 00:06:41.930 align:middle line:90% of a reversible process? 00:06:41.930 --> 00:06:47.080 align:middle line:84% None of your day-to-day processes are reversible. 00:06:47.080 --> 00:06:50.980 align:middle line:84% If you think you can think of one, just toss it out. 00:06:50.980 --> 00:06:52.740 align:middle line:84% And we can try to figure out why it's not. 00:06:52.740 --> 00:06:54.490 align:middle line:84% Those are kind of fun thought experiments. 00:06:54.490 --> 00:07:04.440 align:middle line:90% 00:07:04.440 --> 00:07:05.850 align:middle line:90% Let's describe processes. 00:07:05.850 --> 00:07:13.010 align:middle line:90% 00:07:13.010 --> 00:07:15.140 align:middle line:84% In the last lecture, we described systems. 00:07:15.140 --> 00:07:18.230 align:middle line:84% Now we're going to describe processes. 00:07:18.230 --> 00:07:20.000 align:middle line:84% So things you can do to a system-- 00:07:20.000 --> 00:07:28.000 align:middle line:84% you can work on it, you can heat it, 00:07:28.000 --> 00:07:35.365 align:middle line:84% or you can add or subtract stuff. 00:07:35.365 --> 00:07:38.820 align:middle line:90% 00:07:38.820 --> 00:07:40.570 align:middle line:90% These are things you can do. 00:07:40.570 --> 00:07:43.785 align:middle line:90% These are verbs in thermo. 00:07:43.785 --> 00:07:49.350 align:middle line:90% 00:07:49.350 --> 00:07:52.210 align:middle line:84% All of these are verbs in thermo. 00:07:52.210 --> 00:07:55.870 align:middle line:84% They're actions that you do on a system. 00:07:55.870 --> 00:07:59.360 align:middle line:90% Work, what is work? 00:07:59.360 --> 00:08:03.410 align:middle line:84% It's a mechanical way of exchanging energy, 00:08:03.410 --> 00:08:10.940 align:middle line:90% mechanical exchange of energy. 00:08:10.940 --> 00:08:17.830 align:middle line:90% 00:08:17.830 --> 00:08:21.610 align:middle line:90% So we use w, and what's that? 00:08:21.610 --> 00:08:26.210 align:middle line:84% Kilogram meter squared per second squared, 00:08:26.210 --> 00:08:30.550 align:middle line:90% that's the units of energy. 00:08:30.550 --> 00:08:32.710 align:middle line:84% Just a little bit of dimensional analysis-- 00:08:32.710 --> 00:08:36.260 align:middle line:84% you guys separate that out, it's kilogram meter 00:08:36.260 --> 00:08:44.180 align:middle line:84% per second squared per meter equals force times distance. 00:08:44.180 --> 00:08:47.660 align:middle line:90% 00:08:47.660 --> 00:08:50.950 align:middle line:84% That's force, and that's distance. 00:08:50.950 --> 00:08:51.450 align:middle line:90% That's fine. 00:08:51.450 --> 00:08:54.600 align:middle line:90% 00:08:54.600 --> 00:08:57.060 align:middle line:84% In thermo, we normally separate that out a little bit 00:08:57.060 --> 00:08:58.300 align:middle line:90% differently. 00:08:58.300 --> 00:09:03.030 align:middle line:84% We grab kilogram per meter per second squared. 00:09:03.030 --> 00:09:06.400 align:middle line:90% 00:09:06.400 --> 00:09:07.040 align:middle line:90% What do I need? 00:09:07.040 --> 00:09:09.730 align:middle line:84% What do I need to multiply this by in order 00:09:09.730 --> 00:09:10.735 align:middle line:90% to get the same units? 00:09:10.735 --> 00:09:13.370 align:middle line:90% 00:09:13.370 --> 00:09:16.120 align:middle line:90% What do I need? 00:09:16.120 --> 00:09:17.630 align:middle line:90% STUDENT: Volume, meters. 00:09:17.630 --> 00:09:21.910 align:middle line:84% RAFAEL JARAMILLO: Volume, yeah, meters cubed. 00:09:21.910 --> 00:09:22.590 align:middle line:90% So what's this? 00:09:22.590 --> 00:09:28.840 align:middle line:84% This is a pressure times a volume. 00:09:28.840 --> 00:09:30.350 align:middle line:84% So when you take Intro Mechanics, 00:09:30.350 --> 00:09:32.100 align:middle line:84% let's say in a physics class, you normally 00:09:32.100 --> 00:09:34.950 align:middle line:90% do force times distance work. 00:09:34.950 --> 00:09:37.260 align:middle line:84% But when you take Intro Thermodynamics, 00:09:37.260 --> 00:09:40.420 align:middle line:84% you normally do pressure volume work. 00:09:40.420 --> 00:09:42.430 align:middle line:90% Course C is where I got this at. 00:09:42.430 --> 00:09:46.000 align:middle line:84% But this is P, PVV work, we call it. 00:09:46.000 --> 00:09:47.238 align:middle line:90% That's work. 00:09:47.238 --> 00:09:47.905 align:middle line:90% What about heat? 00:09:47.905 --> 00:09:51.130 align:middle line:90% 00:09:51.130 --> 00:09:56.360 align:middle line:84% Well, it's kind difficult to define, actually. 00:09:56.360 --> 00:10:18.710 align:middle line:84% Heat is a process that exchanges energy without mechanical work 00:10:18.710 --> 00:10:20.570 align:middle line:90% or mass exchanges. 00:10:20.570 --> 00:10:25.130 align:middle line:90% 00:10:25.130 --> 00:10:27.395 align:middle line:84% So heat is defined by what it's not. 00:10:27.395 --> 00:10:28.520 align:middle line:90% It's kind of a weird thing. 00:10:28.520 --> 00:10:32.670 align:middle line:90% 00:10:32.670 --> 00:10:34.560 align:middle line:84% And for heat, we're going to use q. 00:10:34.560 --> 00:10:36.510 align:middle line:90% So work is w, heat is q. 00:10:36.510 --> 00:10:38.850 align:middle line:84% They both have units of energy, joules. 00:10:38.850 --> 00:10:48.530 align:middle line:90% 00:10:48.530 --> 00:10:50.390 align:middle line:84% So we have described state variables, 00:10:50.390 --> 00:10:52.130 align:middle line:90% which are history-independent. 00:10:52.130 --> 00:11:00.500 align:middle line:84% But we also have process variables 00:11:00.500 --> 00:11:04.030 align:middle line:90% that are process-dependent. 00:11:04.030 --> 00:11:13.470 align:middle line:90% 00:11:13.470 --> 00:11:27.940 align:middle line:84% So infinitesimal increments, infinitesimal of process 00:11:27.940 --> 00:11:41.620 align:middle line:90% variables are denoted as-- 00:11:41.620 --> 00:11:46.090 align:middle line:84% I'm going to put this in quotes, "inexact differentials." 00:11:46.090 --> 00:11:52.480 align:middle line:90% 00:11:52.480 --> 00:11:54.325 align:middle line:90% That is dq/d work. 00:11:54.325 --> 00:12:00.130 align:middle line:90% 00:12:00.130 --> 00:12:09.600 align:middle line:90% Using d, not D. 00:12:09.600 --> 00:12:11.070 align:middle line:90% This is annoying. 00:12:11.070 --> 00:12:13.390 align:middle line:84% Don't blame, don't shoot the messenger. 00:12:13.390 --> 00:12:17.400 align:middle line:84% This is one really key area where thermo deviates 00:12:17.400 --> 00:12:20.340 align:middle line:90% from multivariable calculus. 00:12:20.340 --> 00:12:27.160 align:middle line:84% So try not to get confused because it is confusing. 00:12:27.160 --> 00:12:29.220 align:middle line:84% There's a mini lecture I recorded. 00:12:29.220 --> 00:12:30.930 align:middle line:84% It's up on the website called, the Three 00:12:30.930 --> 00:12:34.050 align:middle line:84% d's of Thermodynamics, because it gets kind of hairy. 00:12:34.050 --> 00:12:37.230 align:middle line:84% We use a lot of d's to denote differences. 00:12:37.230 --> 00:12:38.980 align:middle line:84% So hopefully, that's useful at some point, 00:12:38.980 --> 00:12:42.820 align:middle line:84% if not now, then maybe in a week or two in the class. 00:12:42.820 --> 00:12:50.810 align:middle line:84% In thermodynamics this Greek dx means path dependent. 00:12:50.810 --> 00:12:57.230 align:middle line:90% 00:12:57.230 --> 00:12:58.105 align:middle line:90% That's what it means. 00:12:58.105 --> 00:13:01.010 align:middle line:90% 00:13:01.010 --> 00:13:03.400 align:middle line:90% So what is a process variable? 00:13:03.400 --> 00:13:07.690 align:middle line:84% If you have a state A and a state B, 00:13:07.690 --> 00:13:10.610 align:middle line:84% a process variable is a variable, 00:13:10.610 --> 00:13:18.450 align:middle line:84% which depends on the process it takes to get from A to B. 00:13:18.450 --> 00:13:26.550 align:middle line:84% So you might have path 1 with work 1 and heat 1, 00:13:26.550 --> 00:13:33.080 align:middle line:84% and path 2 with work 2 and heat 2. 00:13:33.080 --> 00:13:36.260 align:middle line:84% And those are different because they're not state variables. 00:13:36.260 --> 00:13:37.876 align:middle line:90% They're process variables. 00:13:37.876 --> 00:13:42.160 align:middle line:90% 00:13:42.160 --> 00:13:45.280 align:middle line:84% If we were on campus, the nice analogy to use 00:13:45.280 --> 00:13:47.380 align:middle line:84% is the amount of work you need to get 00:13:47.380 --> 00:13:49.480 align:middle line:84% from the second floor of building 1 00:13:49.480 --> 00:13:52.240 align:middle line:84% to the fifth floor of building 32, 00:13:52.240 --> 00:13:54.810 align:middle line:90% or just pick a pair like that. 00:13:54.810 --> 00:13:56.757 align:middle line:84% There is myriad ways of connecting those two. 00:13:56.757 --> 00:13:58.090 align:middle line:90% Because the campus is connected. 00:13:58.090 --> 00:13:59.548 align:middle line:84% You can go upstairs and downstairs, 00:13:59.548 --> 00:14:01.420 align:middle line:84% you can take elevators, you could 00:14:01.420 --> 00:14:04.960 align:middle line:84% get between those two points in a very large number 00:14:04.960 --> 00:14:06.880 align:middle line:90% of different combinations. 00:14:06.880 --> 00:14:10.430 align:middle line:84% And the amount of mechanical work you need to do 00:14:10.430 --> 00:14:12.770 align:middle line:90% will vary with combination. 00:14:12.770 --> 00:14:17.240 align:middle line:84% But the change in your gravitational potential energy 00:14:17.240 --> 00:14:20.990 align:middle line:84% between the starting and final point, that's a fixed change. 00:14:20.990 --> 00:14:23.480 align:middle line:84% That's an example of process variables 00:14:23.480 --> 00:14:25.360 align:middle line:90% versus state variables. 00:14:25.360 --> 00:14:26.360 align:middle line:90% But we're not on campus. 00:14:26.360 --> 00:14:26.930 align:middle line:90% That's so sad. 00:14:26.930 --> 00:14:28.430 align:middle line:84% You're just going to have to imagine 00:14:28.430 --> 00:14:30.050 align:middle line:84% all the work you'd have to do to get 00:14:30.050 --> 00:14:33.630 align:middle line:90% from building 1 to building 32. 00:14:33.630 --> 00:14:36.990 align:middle line:84% So this is infinitesimal increments and process 00:14:36.990 --> 00:14:38.220 align:middle line:90% variables. 00:14:38.220 --> 00:14:51.920 align:middle line:84% Infinitesimal-- I think I need new markers. 00:14:51.920 --> 00:15:03.030 align:middle line:84% And state variables are denoted as exact differentials. 00:15:03.030 --> 00:15:14.490 align:middle line:90% 00:15:14.490 --> 00:15:24.460 align:middle line:84% So for example, dT, dP, dV, and so on, 00:15:24.460 --> 00:15:32.580 align:middle line:84% using regular lowercase d as in a total differentiable 00:15:32.580 --> 00:15:33.105 align:middle line:90% in calculus. 00:15:33.105 --> 00:15:35.980 align:middle line:90% 00:15:35.980 --> 00:15:40.470 align:middle line:84% So all I can do is tell you that understanding that can only 00:15:40.470 --> 00:15:44.230 align:middle line:84% come through practice, for sure at the beginning of the class. 00:15:44.230 --> 00:15:45.648 align:middle line:90% So all I can do is tell you-- 00:15:45.648 --> 00:15:47.940 align:middle line:84% I'm going to try to switch the purple so things show up 00:15:47.940 --> 00:15:50.530 align:middle line:90% a little better. 00:15:50.530 --> 00:15:52.750 align:middle line:84% So let's talk about how we classify processes. 00:15:52.750 --> 00:16:03.300 align:middle line:90% 00:16:03.300 --> 00:16:13.380 align:middle line:84% So an isothermal process is a process at fixed temperature. 00:16:13.380 --> 00:16:19.937 align:middle line:90% 00:16:19.937 --> 00:16:21.270 align:middle line:90% What about an adiabatic process? 00:16:21.270 --> 00:16:22.020 align:middle line:90% Anybody know? 00:16:22.020 --> 00:16:33.312 align:middle line:90% 00:16:33.312 --> 00:16:34.520 align:middle line:90% STUDENT: It's like very fast. 00:16:34.520 --> 00:16:37.050 align:middle line:84% STUDENT: Does it permeate through a boundary? 00:16:37.050 --> 00:16:38.027 align:middle line:90% STUDENT: Heat is 0. 00:16:38.027 --> 00:16:39.860 align:middle line:84% RAFAEL JARAMILLO: I heard a couple of things 00:16:39.860 --> 00:16:41.152 align:middle line:90% which are equivalent, actually. 00:16:41.152 --> 00:16:42.890 align:middle line:90% Somebody said very fast. 00:16:42.890 --> 00:16:47.210 align:middle line:84% Somebody else said, no heat flow across the boundary. 00:16:47.210 --> 00:16:50.470 align:middle line:84% So the strict definition is no heating across the boundary. 00:16:50.470 --> 00:17:03.910 align:middle line:90% 00:17:03.910 --> 00:17:07.540 align:middle line:84% In reality, heat will always flow from a hot object 00:17:07.540 --> 00:17:10.420 align:middle line:90% through a cold object. 00:17:10.420 --> 00:17:13.160 align:middle line:84% But if you've insulated your system, 00:17:13.160 --> 00:17:20.490 align:middle line:84% whether it's your house or a beaker in the lab, 00:17:20.490 --> 00:17:24.910 align:middle line:84% then that heat flow could be slowed down. 00:17:24.910 --> 00:17:28.290 align:middle line:84% So one way of approximating an adiabatic process 00:17:28.290 --> 00:17:30.310 align:middle line:90% is to run it quickly. 00:17:30.310 --> 00:17:33.270 align:middle line:84% If you run a process very quickly, 00:17:33.270 --> 00:17:36.570 align:middle line:84% the entire process can run before an appreciable amount 00:17:36.570 --> 00:17:40.170 align:middle line:84% of heat flows across the boundary. 00:17:40.170 --> 00:17:43.660 align:middle line:84% So that's why a fast process can be equivalent, 00:17:43.660 --> 00:17:46.200 align:middle line:90% so I like both of those answers. 00:17:46.200 --> 00:17:59.850 align:middle line:84% Isobaric-- isobaric process is that fixed P. And isochoric, we 00:17:59.850 --> 00:18:15.230 align:middle line:84% don't use as much, it's fixed V. And we'll 00:18:15.230 --> 00:18:18.020 align:middle line:84% see that means that there can be no work done on the system 00:18:18.020 --> 00:18:21.050 align:middle line:90% if the volume is fixed. 00:18:21.050 --> 00:18:26.410 align:middle line:84% And then there is classifying boundaries. 00:18:26.410 --> 00:18:30.080 align:middle line:90% 00:18:30.080 --> 00:18:32.320 align:middle line:84% We've seen this a little bit so far. 00:18:32.320 --> 00:18:39.230 align:middle line:84% But as a practical matter, the way that we set up processes 00:18:39.230 --> 00:18:42.000 align:middle line:90% are by defining boundaries. 00:18:42.000 --> 00:18:48.930 align:middle line:84% So for example, an insulating boundary, 00:18:48.930 --> 00:18:51.900 align:middle line:90% and no or say, slow heat flow. 00:18:51.900 --> 00:18:57.630 align:middle line:90% 00:18:57.630 --> 00:19:08.085 align:middle line:84% Diathermal-- heat but no mass transfer. 00:19:08.085 --> 00:19:16.980 align:middle line:90% 00:19:16.980 --> 00:19:31.970 align:middle line:84% Open or closed, is mass the transfer allowed or disallowed? 00:19:31.970 --> 00:19:35.910 align:middle line:90% 00:19:35.910 --> 00:19:40.890 align:middle line:90% And rigid, fixed volume. 00:19:40.890 --> 00:19:46.060 align:middle line:90% 00:19:46.060 --> 00:19:50.370 align:middle line:84% So when we run processes, we can somewhat 00:19:50.370 --> 00:19:52.170 align:middle line:84% determine what kind of process we're 00:19:52.170 --> 00:19:56.140 align:middle line:84% going to run by setting up the boundary conditions. 00:19:56.140 --> 00:19:57.390 align:middle line:90% And this is a practical thing. 00:19:57.390 --> 00:19:58.515 align:middle line:90% This is a practical matter. 00:19:58.515 --> 00:20:01.650 align:middle line:84% And all of us who run labs, we do this every day 00:20:01.650 --> 00:20:02.550 align:middle line:90% in various ways. 00:20:02.550 --> 00:20:07.140 align:middle line:90% 00:20:07.140 --> 00:20:10.620 align:middle line:84% So classifying processes, classifying boundaries, 00:20:10.620 --> 00:20:11.970 align:middle line:90% and so forth-- 00:20:11.970 --> 00:20:15.660 align:middle line:84% let's talk about other things associated with processes. 00:20:15.660 --> 00:20:18.810 align:middle line:90% What about heat capacity? 00:20:18.810 --> 00:20:21.860 align:middle line:84% Most folks have encountered heat capacity before. 00:20:21.860 --> 00:20:24.380 align:middle line:84% Heat capacity, we're going to use C. 00:20:24.380 --> 00:20:34.700 align:middle line:84% And it is the change in heat, an incremental amount of heat 00:20:34.700 --> 00:20:46.510 align:middle line:84% for an incremental change of temperature, heat increment, 00:20:46.510 --> 00:20:47.530 align:middle line:90% temp increment. 00:20:47.530 --> 00:20:56.560 align:middle line:90% 00:20:56.560 --> 00:21:02.470 align:middle line:84% Is heat capacity a state variable or a process variable? 00:21:02.470 --> 00:21:03.442 align:middle line:90% STUDENT: Process. 00:21:03.442 --> 00:21:04.900 align:middle line:84% RAFAEL JARAMILLO: Process is right. 00:21:04.900 --> 00:21:07.480 align:middle line:90% Why is it a process very well? 00:21:07.480 --> 00:21:11.800 align:middle line:84% STUDENT: Because the dq is path-dependent. 00:21:11.800 --> 00:21:13.150 align:middle line:90% RAFAEL JARAMILLO: Yeah, exactly. 00:21:13.150 --> 00:21:14.740 align:middle line:84% It's a process variable because it 00:21:14.740 --> 00:21:17.840 align:middle line:90% depends on a process variable. 00:21:17.840 --> 00:21:20.690 align:middle line:84% One corollary of the postulate that there 00:21:20.690 --> 00:21:24.020 align:middle line:84% exists state functions, is that state functions can only depend 00:21:24.020 --> 00:21:26.280 align:middle line:90% on other state functions. 00:21:26.280 --> 00:21:28.610 align:middle line:84% So if something depends on a process variable, 00:21:28.610 --> 00:21:32.330 align:middle line:84% it itself, is a process variable. 00:21:32.330 --> 00:21:35.120 align:middle line:90% C is path dependent. 00:21:35.120 --> 00:21:43.250 align:middle line:90% 00:21:43.250 --> 00:21:53.440 align:middle line:90% Dq is a process variable. 00:21:53.440 --> 00:22:05.150 align:middle line:84% So it's useful to define common processes. 00:22:05.150 --> 00:22:09.820 align:middle line:90% 00:22:09.820 --> 00:22:12.670 align:middle line:84% I should say define for common processes. 00:22:12.670 --> 00:22:14.860 align:middle line:84% And the ones that we encounter in this class 00:22:14.860 --> 00:22:33.590 align:middle line:84% are CV equals dq/dt at fixed volume and CP, which 00:22:33.590 --> 00:22:39.035 align:middle line:90% is dq/dt at fixed pressure. 00:22:39.035 --> 00:22:45.548 align:middle line:90% 00:22:45.548 --> 00:22:47.340 align:middle line:84% And the reason these are what you encounter 00:22:47.340 --> 00:22:50.438 align:middle line:84% is because these are the most useful. 00:22:50.438 --> 00:22:52.230 align:middle line:84% How do you keep a system at fixed pressure? 00:22:52.230 --> 00:22:54.840 align:middle line:84% Let's say, you want to keep a system at atmospheric pressure. 00:22:54.840 --> 00:22:56.257 align:middle line:84% What's the easiest way to do that? 00:22:56.257 --> 00:22:58.780 align:middle line:90% 00:22:58.780 --> 00:23:01.160 align:middle line:90% STUDENT: Use it like a piston. 00:23:01.160 --> 00:23:03.660 align:middle line:84% RAFAEL JARAMILLO: It's actually, I would think the opposite. 00:23:03.660 --> 00:23:07.710 align:middle line:84% Expose it to the atmosphere, remove the piston. 00:23:07.710 --> 00:23:10.500 align:middle line:84% Because if a system is exposed to the atmosphere, 00:23:10.500 --> 00:23:12.660 align:middle line:84% it can exchange volume with the atmosphere. 00:23:12.660 --> 00:23:14.490 align:middle line:84% It can get bigger or get smaller. 00:23:14.490 --> 00:23:16.410 align:middle line:84% If it's higher pressure in atmosphere, 00:23:16.410 --> 00:23:18.390 align:middle line:84% it'll push against the atmosphere 00:23:18.390 --> 00:23:20.380 align:middle line:84% and return back to atmospheric pressure. 00:23:20.380 --> 00:23:21.960 align:middle line:84% If it's at lower pressure, it will 00:23:21.960 --> 00:23:24.390 align:middle line:84% get compressed by the atmosphere and return back 00:23:24.390 --> 00:23:25.870 align:middle line:90% to atmospheric pressure. 00:23:25.870 --> 00:23:30.910 align:middle line:84% So the existence of a free surface regulates the pressure. 00:23:30.910 --> 00:23:33.700 align:middle line:84% Cost in volume, that would be a case like a piston, where 00:23:33.700 --> 00:23:36.850 align:middle line:84% you have something rigid, a really rigid container. 00:23:36.850 --> 00:23:39.618 align:middle line:84% You can fix the volume and then run the process. 00:23:39.618 --> 00:23:41.035 align:middle line:84% The volume is not going to change. 00:23:41.035 --> 00:23:43.650 align:middle line:90% 00:23:43.650 --> 00:23:45.792 align:middle line:90% Which one of these is bigger? 00:23:45.792 --> 00:23:47.292 align:middle line:84% That requires a little more thought. 00:23:47.292 --> 00:23:49.292 align:middle line:84% We're going to increase the energy of the system 00:23:49.292 --> 00:23:49.930 align:middle line:90% by heating it. 00:23:49.930 --> 00:23:53.120 align:middle line:90% 00:23:53.120 --> 00:23:56.920 align:middle line:84% We're going to increase the energy by heating it. 00:23:56.920 --> 00:24:00.060 align:middle line:84% For a given increase in temperature, 00:24:00.060 --> 00:24:02.310 align:middle line:84% do I need to hear it more of a fixed volume or a fixed 00:24:02.310 --> 00:24:03.572 align:middle line:90% pressure? 00:24:03.572 --> 00:24:05.030 align:middle line:84% We haven't really gotten there yet. 00:24:05.030 --> 00:24:08.360 align:middle line:84% But I'm wondering if somebody wants to venture 00:24:08.360 --> 00:24:09.800 align:middle line:90% a guess with an explanation. 00:24:09.800 --> 00:24:16.360 align:middle line:90% 00:24:16.360 --> 00:24:19.656 align:middle line:84% STUDENT: Maybe for fixed pressure. 00:24:19.656 --> 00:24:22.660 align:middle line:84% RAFAEL JARAMILLO: Fixed pressure, how do you figure? 00:24:22.660 --> 00:24:25.420 align:middle line:84% STUDENT: I mean, I think if the system is like half fixed 00:24:25.420 --> 00:24:31.090 align:middle line:84% volume, it wouldn't be able to use the heat as work. 00:24:31.090 --> 00:24:33.790 align:middle line:84% But with fixed pressure, it can expand. 00:24:33.790 --> 00:24:35.860 align:middle line:90% RAFAEL JARAMILLO: Yeah. 00:24:35.860 --> 00:24:38.290 align:middle line:84% So your reasoning is right, but your answer is wrong. 00:24:38.290 --> 00:24:40.000 align:middle line:84% So I'm glad-- the reason there is 00:24:40.000 --> 00:24:42.160 align:middle line:84% when you have a system that's at fixed volume, 00:24:42.160 --> 00:24:44.620 align:middle line:84% it can't do any work on the surroundings. 00:24:44.620 --> 00:24:46.270 align:middle line:90% It's hemmed in. 00:24:46.270 --> 00:24:48.580 align:middle line:84% So all of these thermal energy you put in 00:24:48.580 --> 00:24:51.520 align:middle line:84% will go into a change in the internal energy of the system, 00:24:51.520 --> 00:24:53.710 align:middle line:90% increase in temperature. 00:24:53.710 --> 00:24:57.550 align:middle line:84% Whereas if you have a system that's fixed pressure, 00:24:57.550 --> 00:24:58.360 align:middle line:90% it can do work. 00:24:58.360 --> 00:25:01.160 align:middle line:84% It can expand against its surroundings. 00:25:01.160 --> 00:25:04.210 align:middle line:84% So as you pour energy in the form of heat, 00:25:04.210 --> 00:25:07.010 align:middle line:84% it can lose energy in the form of doing work. 00:25:07.010 --> 00:25:08.820 align:middle line:84% So it's like filling up a leaky cup. 00:25:08.820 --> 00:25:11.320 align:middle line:84% You have to pour more water in because there's stuff leaking 00:25:11.320 --> 00:25:12.528 align:middle line:90% out at the bottom of the cup. 00:25:12.528 --> 00:25:14.560 align:middle line:84% In this case, the stuff leaking out 00:25:14.560 --> 00:25:18.160 align:middle line:84% is energy in the form of work on the surroundings. 00:25:18.160 --> 00:25:20.355 align:middle line:90% So CV is smaller. 00:25:20.355 --> 00:25:21.280 align:middle line:90% CP is larger. 00:25:21.280 --> 00:25:24.520 align:middle line:84% But your thinking about work was correct. 00:25:24.520 --> 00:25:27.880 align:middle line:90% 00:25:27.880 --> 00:25:41.190 align:middle line:84% C is an empirical observable recorded in devices. 00:25:41.190 --> 00:25:48.850 align:middle line:90% 00:25:48.850 --> 00:25:50.540 align:middle line:90% That's really important. 00:25:50.540 --> 00:25:52.570 align:middle line:84% Maybe you know that, maybe you don't. 00:25:52.570 --> 00:25:55.990 align:middle line:84% But the heat capacity of a system 00:25:55.990 --> 00:25:59.335 align:middle line:84% tells you so much about that system. 00:25:59.335 --> 00:26:01.210 align:middle line:84% But most of those things, you can't calculate 00:26:01.210 --> 00:26:03.280 align:middle line:90% from first principles. 00:26:03.280 --> 00:26:06.410 align:middle line:84% They need to be measured and then reported. 00:26:06.410 --> 00:26:08.545 align:middle line:84% So for example, what has larger-- 00:26:08.545 --> 00:26:16.220 align:middle line:90% 00:26:16.220 --> 00:26:29.710 align:middle line:84% here's some, here's-- entry level, 00:26:29.710 --> 00:26:32.540 align:middle line:84% what has a bigger capacity, a big pot of water or a small pot 00:26:32.540 --> 00:26:33.040 align:middle line:90% of water? 00:26:33.040 --> 00:26:36.421 align:middle line:90% 00:26:36.421 --> 00:26:37.932 align:middle line:90% STUDENT: They have the same. 00:26:37.932 --> 00:26:39.640 align:middle line:84% RAFAEL JARAMILLO: Well, yeah, it depends. 00:26:39.640 --> 00:26:43.260 align:middle line:84% Heat capacity could be extensive or intensive. 00:26:43.260 --> 00:26:46.030 align:middle line:84% So I think I know what you're saying, water is water. 00:26:46.030 --> 00:26:49.110 align:middle line:84% But when we want to regulate the temperature of something, 00:26:49.110 --> 00:26:51.360 align:middle line:84% we want to prevent a temperature change, 00:26:51.360 --> 00:26:57.630 align:middle line:84% it helps to have a large heat capacity object nearby, 00:26:57.630 --> 00:27:00.217 align:middle line:90% a large thermal reservoir. 00:27:00.217 --> 00:27:01.800 align:middle line:84% That's one reason why the temperatures 00:27:01.800 --> 00:27:05.400 align:middle line:84% are more moderate on the coasts of continents than inland. 00:27:05.400 --> 00:27:07.890 align:middle line:84% Our temperature in Boston doesn't swing nearly 00:27:07.890 --> 00:27:11.030 align:middle line:90% as much as it does in Iowa. 00:27:11.030 --> 00:27:14.090 align:middle line:84% You could say the same about any inland versus coastal community 00:27:14.090 --> 00:27:14.880 align:middle line:90% in the world. 00:27:14.880 --> 00:27:16.490 align:middle line:84% And the reason is that the oceans 00:27:16.490 --> 00:27:18.080 align:middle line:90% are a big thermal reservoir. 00:27:18.080 --> 00:27:21.830 align:middle line:84% They have a larger heat capacity than the Great Lakes do. 00:27:21.830 --> 00:27:23.750 align:middle line:84% So our temperature swings are less. 00:27:23.750 --> 00:27:26.590 align:middle line:90% What about bread or cheese? 00:27:26.590 --> 00:27:29.500 align:middle line:90% 00:27:29.500 --> 00:27:33.113 align:middle line:84% Same quantity, now, same mass, bread or cheese? 00:27:33.113 --> 00:27:36.360 align:middle line:90% 00:27:36.360 --> 00:27:38.410 align:middle line:90% STUDENT: Bread? 00:27:38.410 --> 00:27:39.730 align:middle line:90% STUDENT: Cheese, maybe. 00:27:39.730 --> 00:27:40.450 align:middle line:84% RAFAEL JARAMILLO: I think it's cheese. 00:27:40.450 --> 00:27:42.040 align:middle line:84% When you eat pizza, the bread is not 00:27:42.040 --> 00:27:43.520 align:middle line:84% the one that burns the top of your mouth. 00:27:43.520 --> 00:27:44.187 align:middle line:90% It's the cheese. 00:27:44.187 --> 00:27:46.410 align:middle line:90% It has a larger capacity. 00:27:46.410 --> 00:27:47.808 align:middle line:90% Cheese has a larger capacity. 00:27:47.808 --> 00:27:49.725 align:middle line:84% That has to do with, of course, the chemistry. 00:27:49.725 --> 00:27:51.930 align:middle line:84% A big pot of water has a larger heat capacity. 00:27:51.930 --> 00:27:55.155 align:middle line:84% What about aluminum foil or a potato? 00:27:55.155 --> 00:28:01.350 align:middle line:90% 00:28:01.350 --> 00:28:03.470 align:middle line:84% STUDENT: Isn't a larger heat capacity and ability 00:28:03.470 --> 00:28:06.800 align:middle line:84% to absorb more thermal energy without changing temperature, 00:28:06.800 --> 00:28:07.460 align:middle line:90% though? 00:28:07.460 --> 00:28:09.860 align:middle line:90% RAFAEL JARAMILLO: Yes, exactly. 00:28:09.860 --> 00:28:14.120 align:middle line:84% STUDENT: So isn't the cheese changing more in temperature 00:28:14.120 --> 00:28:15.075 align:middle line:90% than the bread? 00:28:15.075 --> 00:28:15.950 align:middle line:90% RAFAEL JARAMILLO: No. 00:28:15.950 --> 00:28:17.750 align:middle line:84% What it means is that you have to put 00:28:17.750 --> 00:28:20.030 align:middle line:84% in more energy from your mouth to cool down 00:28:20.030 --> 00:28:23.105 align:middle line:84% the cheese than you do to cool down the bread. 00:28:23.105 --> 00:28:24.980 align:middle line:84% So here's another example, which should help. 00:28:24.980 --> 00:28:26.528 align:middle line:84% Aluminum foil versus potato-- you 00:28:26.528 --> 00:28:28.070 align:middle line:84% bake a potato that's wrapped in foil. 00:28:28.070 --> 00:28:30.980 align:middle line:90% 00:28:30.980 --> 00:28:32.210 align:middle line:90% STUDENT: Potato. 00:28:32.210 --> 00:28:34.127 align:middle line:84% RAFAEL JARAMILLO: You take it out of the oven. 00:28:34.127 --> 00:28:37.180 align:middle line:90% 00:28:37.180 --> 00:28:38.110 align:middle line:90% Someone said potato. 00:28:38.110 --> 00:28:39.460 align:middle line:84% The answer is going to be the foil. 00:28:39.460 --> 00:28:42.043 align:middle line:84% When you take something out of the oven, it's wrapped in foil. 00:28:42.043 --> 00:28:43.630 align:middle line:90% You can often open the foil. 00:28:43.630 --> 00:28:45.460 align:middle line:84% Even if the oven was at 400 degrees, 00:28:45.460 --> 00:28:48.100 align:middle line:84% you can open the foil without burning your fingers. 00:28:48.100 --> 00:28:49.660 align:middle line:90% You have to avoid the steam. 00:28:49.660 --> 00:28:53.770 align:middle line:84% But you could grab that foil and very quickly bring that foil 00:28:53.770 --> 00:28:58.440 align:middle line:84% down to room temperature without burning your fingers. 00:28:58.440 --> 00:29:00.170 align:middle line:84% But if you grab the potato, you're 00:29:00.170 --> 00:29:02.230 align:middle line:90% going to burn your hands. 00:29:02.230 --> 00:29:05.140 align:middle line:84% Because it takes more energy out of you, in this case, 00:29:05.140 --> 00:29:07.900 align:middle line:84% to cool the potato than it does to cool the foil. 00:29:07.900 --> 00:29:09.970 align:middle line:84% STUDENT: Doesn't that mean the potato is actually 00:29:09.970 --> 00:29:12.550 align:middle line:90% the one with a high C? 00:29:12.550 --> 00:29:15.160 align:middle line:84% RAFAEL JARAMILLO: Larger C, yeah, sorry, sorry. 00:29:15.160 --> 00:29:18.280 align:middle line:90% Everything I said, but reverse. 00:29:18.280 --> 00:29:21.310 align:middle line:84% Exactly, it's easier to bring down. 00:29:21.310 --> 00:29:22.720 align:middle line:84% And this is lots of examples here 00:29:22.720 --> 00:29:25.060 align:middle line:84% that are every day, why certain surfaces outside 00:29:25.060 --> 00:29:28.270 align:middle line:84% feel colder or hotter than other surfaces on a very cold or very 00:29:28.270 --> 00:29:31.840 align:middle line:84% hot day, lots of examples like this. 00:29:31.840 --> 00:29:37.510 align:middle line:90% So what do I mean to say here? 00:29:37.510 --> 00:29:41.650 align:middle line:90% 00:29:41.650 --> 00:29:52.510 align:middle line:84% C can be calculated for simple, we call toy problems. 00:29:52.510 --> 00:29:56.150 align:middle line:90% 00:29:56.150 --> 00:30:01.930 align:middle line:84% But in most cases, especially in cases 00:30:01.930 --> 00:30:07.360 align:middle line:84% that we rely on as engineers, measurements are necessary. 00:30:07.360 --> 00:30:14.937 align:middle line:90% 00:30:14.937 --> 00:30:16.770 align:middle line:84% And I actually did record some numbers here. 00:30:16.770 --> 00:30:22.340 align:middle line:84% So heat capacity in joules per gram Kelvin-- 00:30:22.340 --> 00:30:24.570 align:middle line:90% let's see, water. 00:30:24.570 --> 00:30:26.615 align:middle line:90% Water has a large capacity. 00:30:26.615 --> 00:30:29.810 align:middle line:84% It has to do with all of the vibrational degrees of freedom 00:30:29.810 --> 00:30:30.880 align:middle line:90% in water. 00:30:30.880 --> 00:30:35.050 align:middle line:90% Aluminum is very small, 0.897. 00:30:35.050 --> 00:30:37.510 align:middle line:84% So this right here is why you can touch the aluminum foil, 00:30:37.510 --> 00:30:40.960 align:middle line:84% but you have to avoid getting a steam burn when you open up 00:30:40.960 --> 00:30:43.090 align:middle line:90% the food you packed in foil. 00:30:43.090 --> 00:30:47.110 align:middle line:84% Potato is actually large, close to water. 00:30:47.110 --> 00:30:48.940 align:middle line:84% Because anything that's food-related, 00:30:48.940 --> 00:30:52.790 align:middle line:84% basically is set by the water content. 00:30:52.790 --> 00:30:57.620 align:middle line:84% Cheese has a lower water content than potato. 00:30:57.620 --> 00:30:59.210 align:middle line:90% I grabbed the number 3.15. 00:30:59.210 --> 00:31:01.460 align:middle line:84% If you are a gourmet chef, you have 00:31:01.460 --> 00:31:04.340 align:middle line:84% a table of capacities of things like cheese. 00:31:04.340 --> 00:31:09.020 align:middle line:90% And 3.15 is this one number. 00:31:09.020 --> 00:31:10.370 align:middle line:90% I mean, I don't know cheddar. 00:31:10.370 --> 00:31:14.857 align:middle line:90% But anyway, so let's move on. 00:31:14.857 --> 00:31:15.440 align:middle line:90% Let's move on. 00:31:15.440 --> 00:31:19.410 align:middle line:90% 00:31:19.410 --> 00:31:22.230 align:middle line:84% So, let's talk about something really important, 00:31:22.230 --> 00:31:24.080 align:middle line:90% the first law of thermodynamics. 00:31:24.080 --> 00:31:36.180 align:middle line:90% 00:31:36.180 --> 00:31:49.800 align:middle line:84% So here's the first law of thermodynamics, 00:31:49.800 --> 00:31:54.240 align:middle line:84% as you sometimes encounter it in a physics class. 00:31:54.240 --> 00:31:57.240 align:middle line:90% 00:31:57.240 --> 00:32:01.140 align:middle line:84% And I'm here to tell you this is totally useless. 00:32:01.140 --> 00:32:05.370 align:middle line:84% Because if this is all it were, who cares? 00:32:05.370 --> 00:32:10.730 align:middle line:84% I mean, it's interesting, but you can't use that. 00:32:10.730 --> 00:32:13.370 align:middle line:84% And that's not how we arrived at it. 00:32:13.370 --> 00:32:18.780 align:middle line:84% Intellectually, it's sort of intellectually being dishonest. 00:32:18.780 --> 00:32:24.490 align:middle line:84% Because this is very non-obvious, very non-obvious 00:32:24.490 --> 00:32:27.580 align:middle line:90% and rather hard to prove also. 00:32:27.580 --> 00:32:28.630 align:middle line:90% How is this useful? 00:32:28.630 --> 00:32:31.600 align:middle line:90% 00:32:31.600 --> 00:32:35.960 align:middle line:84% The answer is because it applies locally. 00:32:35.960 --> 00:32:40.420 align:middle line:84% And this is where the real intellectual thread comes from. 00:32:40.420 --> 00:32:52.250 align:middle line:90% 00:32:52.250 --> 00:33:02.320 align:middle line:84% So we talk about the energy of a system plus the surroundings. 00:33:02.320 --> 00:33:06.590 align:middle line:90% 00:33:06.590 --> 00:33:10.310 align:middle line:84% System plus surroundings, you could call universe. 00:33:10.310 --> 00:33:12.900 align:middle line:90% 00:33:12.900 --> 00:33:14.400 align:middle line:84% It's kind of highfalutin language. 00:33:14.400 --> 00:33:16.410 align:middle line:84% Sometimes I'll slip, and I'll say universe, 00:33:16.410 --> 00:33:18.810 align:middle line:90% but I don't mean to. 00:33:18.810 --> 00:33:21.240 align:middle line:84% Systems plus surroundings-- energy of system plus 00:33:21.240 --> 00:33:22.620 align:middle line:90% surroundings is constant. 00:33:22.620 --> 00:33:26.740 align:middle line:90% 00:33:26.740 --> 00:33:28.940 align:middle line:90% But here's where it gets useful. 00:33:28.940 --> 00:33:36.360 align:middle line:84% We use the boundary for bookkeeping. 00:33:36.360 --> 00:33:41.110 align:middle line:90% 00:33:41.110 --> 00:33:47.840 align:middle line:84% And like it or not, a lot of thermo is bookkeeping. 00:33:47.840 --> 00:33:59.160 align:middle line:84% So we have a system, we have a boundary, 00:33:59.160 --> 00:34:03.460 align:middle line:90% and we have flows of energy. 00:34:03.460 --> 00:34:05.230 align:middle line:84% I mean, you can keep track of them. 00:34:05.230 --> 00:34:08.219 align:middle line:84% And we can keep track of the forms that energy can flow. 00:34:08.219 --> 00:34:10.230 align:middle line:84% So there are three ways that energy 00:34:10.230 --> 00:34:14.840 align:middle line:84% can flow between a system and the surroundings in 3020. 00:34:14.840 --> 00:34:17.593 align:middle line:84% We have encountered two of them so far about 20 minutes ago. 00:34:17.593 --> 00:34:19.760 align:middle line:84% Somebody want to tell me what the three of them are, 00:34:19.760 --> 00:34:20.360 align:middle line:90% all three? 00:34:20.360 --> 00:34:25.050 align:middle line:90% 00:34:25.050 --> 00:34:28.830 align:middle line:84% STUDENT: Convection, radiation, and conduction. 00:34:28.830 --> 00:34:29.850 align:middle line:90% Nope. 00:34:29.850 --> 00:34:34.350 align:middle line:84% Sorry, so those are forms of heat transfer. 00:34:34.350 --> 00:34:40.090 align:middle line:84% But we are not going to talk about fluid dynamics 00:34:40.090 --> 00:34:44.710 align:middle line:84% or radiative processes in any detail in 020. 00:34:44.710 --> 00:34:47.050 align:middle line:84% So what you said was scientifically true. 00:34:47.050 --> 00:34:49.600 align:middle line:84% It's not specifically what the three forms are in 020. 00:34:49.600 --> 00:34:53.120 align:middle line:84% RAFAEL JARAMILLO: We've talked about two of them so far. 00:34:53.120 --> 00:34:56.572 align:middle line:84% One is heat, which is everything you just described. 00:34:56.572 --> 00:34:58.030 align:middle line:84% What's another way energy can flow? 00:34:58.030 --> 00:35:00.690 align:middle line:90% 00:35:00.690 --> 00:35:01.400 align:middle line:90% STUDENT: Work. 00:35:01.400 --> 00:35:04.880 align:middle line:84% RAFAEL JARAMILLO: Work, heat, work, mechanical work. 00:35:04.880 --> 00:35:08.082 align:middle line:84% And there's a third way that energy can flow. 00:35:08.082 --> 00:35:09.290 align:middle line:90% We haven't introduced it yet. 00:35:09.290 --> 00:35:11.840 align:middle line:84% Would anyone likes to venture a guess? 00:35:11.840 --> 00:35:12.975 align:middle line:90% STUDENT: Mass transfer. 00:35:12.975 --> 00:35:14.600 align:middle line:84% RAFAEL JARAMILLO: Mass transfer, right. 00:35:14.600 --> 00:35:16.260 align:middle line:90% Matter has energy. 00:35:16.260 --> 00:35:20.438 align:middle line:84% And so you can exchange matter and transfer energy that way. 00:35:20.438 --> 00:35:21.980 align:middle line:84% So this is the bookkeeping that we're 00:35:21.980 --> 00:35:23.940 align:middle line:90% going to do in this class. 00:35:23.940 --> 00:35:27.154 align:middle line:84% So this gets me to first law of bookkeeping. 00:35:27.154 --> 00:35:36.050 align:middle line:90% 00:35:36.050 --> 00:35:38.810 align:middle line:84% I wish I had a week to teach fluid dynamics 00:35:38.810 --> 00:35:43.910 align:middle line:84% and talk about convection and then talk about heat transfer, 00:35:43.910 --> 00:35:46.520 align:middle line:84% talk about conduction, and do radiative. 00:35:46.520 --> 00:35:49.538 align:middle line:84% But that goes well beyond this class. 00:35:49.538 --> 00:35:51.580 align:middle line:84% You'll learn about those things in other classes. 00:35:51.580 --> 00:35:54.490 align:middle line:84% Or come to office hours, we can talk about heat transfer. 00:35:54.490 --> 00:36:02.320 align:middle line:84% First law bookkeeping-- this is where we hopefully resolve some 00:36:02.320 --> 00:36:06.400 align:middle line:84% ambiguity about 020 with the other classes you've taken. 00:36:06.400 --> 00:36:17.050 align:middle line:84% So types of energy include kinetic, potential, 00:36:17.050 --> 00:36:24.340 align:middle line:90% and internal, which we u. 00:36:24.340 --> 00:36:31.330 align:middle line:84% So kinetic energy depends on how fast a system is moving. 00:36:31.330 --> 00:36:33.110 align:middle line:90% You know that. 00:36:33.110 --> 00:36:36.760 align:middle line:84% So if your system is a baseball, kinetic energy 00:36:36.760 --> 00:36:38.290 align:middle line:90% is how fast it's moving. 00:36:38.290 --> 00:36:43.870 align:middle line:84% Potential energy depends on where a system 00:36:43.870 --> 00:36:46.900 align:middle line:90% is in some reference frame. 00:36:46.900 --> 00:36:48.790 align:middle line:84% So again, if your system is a baseball, 00:36:48.790 --> 00:36:50.920 align:middle line:84% the potential energy depends on where 00:36:50.920 --> 00:36:53.500 align:middle line:84% it is, relative to the center of mass of the Earth. 00:36:53.500 --> 00:36:56.620 align:middle line:90% 00:36:56.620 --> 00:36:59.920 align:middle line:84% Internal energy is everything else. 00:36:59.920 --> 00:37:03.250 align:middle line:84% It's all of the energy which is independent of the velocity 00:37:03.250 --> 00:37:06.140 align:middle line:84% of the system and independent of the location of the system. 00:37:06.140 --> 00:37:08.200 align:middle line:84% So again, if your system is the baseball, 00:37:08.200 --> 00:37:11.170 align:middle line:84% the internal energy is all the molecular bonds 00:37:11.170 --> 00:37:17.760 align:middle line:84% that make up the baseball plus the binding energy 00:37:17.760 --> 00:37:21.370 align:middle line:90% of the electrons to the nuclei. 00:37:21.370 --> 00:37:24.510 align:middle line:84% So this is the one that we use in thermo. 00:37:24.510 --> 00:37:26.850 align:middle line:84% This is the last time we'll talk about kinetic energy 00:37:26.850 --> 00:37:29.460 align:middle line:84% in the last time we'll talk about potential energy. 00:37:29.460 --> 00:37:33.090 align:middle line:84% We might get to a 20 minutes of electrochemistry 00:37:33.090 --> 00:37:34.195 align:middle line:90% later in the term. 00:37:34.195 --> 00:37:35.820 align:middle line:84% And then potential might sneak back in. 00:37:35.820 --> 00:37:43.720 align:middle line:84% But basically, this is where we are for 3020. 00:37:43.720 --> 00:37:56.680 align:middle line:84% What about processes that exchange energy? 00:37:56.680 --> 00:37:58.560 align:middle line:84% That would just be, we just answered. 00:37:58.560 --> 00:38:07.845 align:middle line:84% There's heating, there's work, and there's mass transfer. 00:38:07.845 --> 00:38:16.502 align:middle line:90% 00:38:16.502 --> 00:38:18.210 align:middle line:84% So this is some first law of bookkeeping. 00:38:18.210 --> 00:38:23.970 align:middle line:84% I hope this helps a little bit as we try to recall what counts 00:38:23.970 --> 00:38:26.070 align:middle line:84% and what doesn't in equilibrium thermo. 00:38:26.070 --> 00:38:30.360 align:middle line:90% 00:38:30.360 --> 00:38:34.980 align:middle line:84% So we can do this mathematically. 00:38:34.980 --> 00:38:39.700 align:middle line:84% Energy is a state function, but it's changed by processes. 00:38:39.700 --> 00:38:48.550 align:middle line:84% So du equals change in heat energy 00:38:48.550 --> 00:39:00.265 align:middle line:84% plus change in mechanical work plus something new, 00:39:00.265 --> 00:39:03.165 align:middle line:84% a term which accounts for a change in mass. 00:39:03.165 --> 00:39:06.020 align:middle line:90% 00:39:06.020 --> 00:39:16.950 align:middle line:84% So dq equals heat applied to the system. 00:39:16.950 --> 00:39:18.730 align:middle line:90% There's a sign convention here. 00:39:18.730 --> 00:39:21.120 align:middle line:84% We're going to follow the sign convention in the DeHoff 00:39:21.120 --> 00:39:21.620 align:middle line:90% textbook. 00:39:21.620 --> 00:39:23.990 align:middle line:90% 00:39:23.990 --> 00:39:26.800 align:middle line:84% So if you're heating a system, let's say 00:39:26.800 --> 00:39:30.280 align:middle line:84% that's the endothermic reaction, the instant cold pack, 00:39:30.280 --> 00:39:34.150 align:middle line:90% then dq is positive. 00:39:34.150 --> 00:39:44.695 align:middle line:84% Dw is work performed on a system. 00:39:44.695 --> 00:39:47.680 align:middle line:90% 00:39:47.680 --> 00:39:50.190 align:middle line:84% So there's a consistent convention there. 00:39:50.190 --> 00:39:53.070 align:middle line:90% These have the same sign. 00:39:53.070 --> 00:39:55.320 align:middle line:84% Positive dq increases the energy of the system, 00:39:55.320 --> 00:39:57.495 align:middle line:84% positive dw increases the energy of the system. 00:39:57.495 --> 00:40:02.020 align:middle line:90% 00:40:02.020 --> 00:40:07.240 align:middle line:84% So for example, for mechanical work 00:40:07.240 --> 00:40:16.690 align:middle line:84% that we encounter in this class, dw equals P dV, and here I ask 00:40:16.690 --> 00:40:19.075 align:middle line:90% is it positive or minus? 00:40:19.075 --> 00:40:23.480 align:middle line:90% 00:40:23.480 --> 00:40:24.230 align:middle line:90% Which one is it? 00:40:24.230 --> 00:40:27.955 align:middle line:90% 00:40:27.955 --> 00:40:28.830 align:middle line:90% This is the pressure. 00:40:28.830 --> 00:40:32.880 align:middle line:84% This is the change in volume of a system. 00:40:32.880 --> 00:40:37.260 align:middle line:84% So a positive P dV means the system is doing work 00:40:37.260 --> 00:40:38.130 align:middle line:90% on the surroundings. 00:40:38.130 --> 00:40:41.500 align:middle line:84% It's expanding against the surroundings. 00:40:41.500 --> 00:40:43.200 align:middle line:84% So what should be the sign here to stick 00:40:43.200 --> 00:40:46.170 align:middle line:90% with our new convention? 00:40:46.170 --> 00:40:47.220 align:middle line:90% STUDENT: Negative. 00:40:47.220 --> 00:40:49.770 align:middle line:84% RAFAEL JARAMILLO: Negative right, it's negative. 00:40:49.770 --> 00:40:54.690 align:middle line:84% Because the system is losing energy as it expands, negative. 00:40:54.690 --> 00:40:58.670 align:middle line:90% So it equals minus P dV. 00:40:58.670 --> 00:41:02.860 align:middle line:90% 00:41:02.860 --> 00:41:04.940 align:middle line:84% A little mathematical note here-- 00:41:04.940 --> 00:41:08.120 align:middle line:90% this is a process variable. 00:41:08.120 --> 00:41:11.060 align:middle line:90% 00:41:11.060 --> 00:41:13.765 align:middle line:90% This is a state variable. 00:41:13.765 --> 00:41:17.205 align:middle line:90% 00:41:17.205 --> 00:41:18.580 align:middle line:84% This is not an equation of state. 00:41:18.580 --> 00:41:21.170 align:middle line:84% This is a differentiable form of an equation of state. 00:41:21.170 --> 00:41:23.450 align:middle line:90% So it's not the same thing. 00:41:23.450 --> 00:41:26.810 align:middle line:84% But it has this funny property, that you have on the one hand, 00:41:26.810 --> 00:41:29.300 align:middle line:84% process variable, on the other hand, is state variable. 00:41:29.300 --> 00:41:35.670 align:middle line:84% This could be considered an integration constant. 00:41:35.670 --> 00:41:40.793 align:middle line:90% 00:41:40.793 --> 00:41:43.210 align:middle line:84% If you don't care about that comment, ignore that comment. 00:41:43.210 --> 00:41:45.130 align:middle line:84% We don't really talk about integration concepts 00:41:45.130 --> 00:41:46.390 align:middle line:84% in this class, we don't have time. 00:41:46.390 --> 00:41:47.765 align:middle line:84% But they are kind of hidden there 00:41:47.765 --> 00:41:49.600 align:middle line:90% and the structure of thermo. 00:41:49.600 --> 00:42:05.350 align:middle line:84% All right so dq/dw and mu i dNi equals the energy 00:42:05.350 --> 00:42:18.976 align:middle line:84% of change dNi of moles of component i 00:42:18.976 --> 00:42:21.350 align:middle line:84% where i has to run over all the different components 00:42:21.350 --> 00:42:22.680 align:middle line:90% of the system. 00:42:22.680 --> 00:42:30.305 align:middle line:84% So N of i equals number moles of component i. 00:42:30.305 --> 00:42:34.250 align:middle line:90% 00:42:34.250 --> 00:42:44.070 align:middle line:84% And mu of i is defined as partial u, partial N of i, 00:42:44.070 --> 00:42:45.030 align:middle line:90% for a fixed-- 00:42:45.030 --> 00:42:46.440 align:middle line:90% and we'll get to this-- 00:42:46.440 --> 00:42:55.150 align:middle line:84% entropy, volume, and moles of j not equal to i. 00:42:55.150 --> 00:42:57.270 align:middle line:90% I is a component label. 00:42:57.270 --> 00:43:03.860 align:middle line:90% 00:43:03.860 --> 00:43:12.350 align:middle line:84% And this whole thing is called the chemical potential, 00:43:12.350 --> 00:43:15.760 align:middle line:84% which is a really central concept for material science 00:43:15.760 --> 00:43:18.250 align:middle line:90% and chemical engineering. 00:43:18.250 --> 00:43:23.650 align:middle line:84% So we will be spending an entire term on the chemical potential. 00:43:23.650 --> 00:43:27.570 align:middle line:84% That's where I wanted to get to today. 00:43:27.570 --> 00:43:30.000 align:middle line:90%