1 00:00:03,520 --> 00:00:08,460 You have probably heard entropy defined or described as "disorder." The usual example 2 00:00:08,460 --> 00:00:13,280 is that of a college dorm room, which, without regular tidying, becomes "messier" or "less 3 00:00:13,280 --> 00:00:18,100 ordered" over time. Supposedly the entropy of the messy room is higher than that of the 4 00:00:18,100 --> 00:00:24,340 tidy room. This analogy is easy to picture, but it's misleading. In this video, you'll 5 00:00:24,340 --> 00:00:27,380 learn a more accurate description of entropy and understand how it relates to the concept 6 00:00:27,380 --> 00:00:27,550 of spontaneity. 7 00:00:27,550 --> 00:00:31,880 This video is part of the Governing Rules video series. A small number of rules describe 8 00:00:31,880 --> 00:00:36,040 the physical and chemical interactions that are possible in our universe. 9 00:00:36,040 --> 00:00:41,390 Hi. My name is John Lienhard and I am a professor in the Department of Mechanical Engineering 10 00:00:41,390 --> 00:00:42,660 at MIT. 11 00:00:42,660 --> 00:00:49,660 Today, I'm going to talk to you about entropy, a fascinating, but often confusing topic. 12 00:00:51,180 --> 00:00:55,520 In order to understand the topic of this video, you should be familiar with the idea that 13 00:00:55,520 --> 00:01:02,320 energy is quantized and the thermodynamic definition of a system and its surroundings. 14 00:01:02,320 --> 00:01:06,950 After watching this video, you should be able to describe, at a basic level, the concept 15 00:01:06,950 --> 00:01:11,899 of a microstate. You should also be able to discuss what entropy measures in a conceptual 16 00:01:11,899 --> 00:01:13,240 way. 17 00:01:13,240 --> 00:01:20,240 First, what do we mean by a spontaneous process? In thermodynamics, a spontaneous process is 18 00:01:20,880 --> 00:01:25,810 one that will occur without any outside intervention given enough time. 19 00:01:25,810 --> 00:01:31,279 In the world around us, many everyday events proceed in a particular manner. We would call 20 00:01:31,279 --> 00:01:37,020 them spontaneous. You have observed spontaneous processes yourself, but because they seem 21 00:01:37,020 --> 00:01:41,450 so natural, you may not have taken particular note of them. 22 00:01:41,450 --> 00:01:45,630 For example, think of an inflated balloon that hasn't been tied and is simply pinched 23 00:01:45,630 --> 00:01:52,630 between someone's fingers. Once the person releases the balloon, what is going to happen? 24 00:01:53,729 --> 00:01:58,840 Experience tells us that the gas inside the balloon will rapidly escape from the opening, 25 00:01:58,840 --> 00:02:03,639 moving from high pressure to low pressure. This will propel the balloon through the air, 26 00:02:03,639 --> 00:02:08,910 until finally, we are left with a deflated balloon. The gas that was once in the balloon 27 00:02:08,910 --> 00:02:12,970 is now dispersed throughout the surroundings. 28 00:02:12,970 --> 00:02:18,800 You have probably also seen food coloring or hydrophilic dye dropped into water. What 29 00:02:18,800 --> 00:02:25,390 happens? From experience, you may know that the dye disperses. 30 00:02:25,390 --> 00:02:30,730 You may also have had some experience removing hot pans from the stovetop. While they come 31 00:02:30,730 --> 00:02:37,020 off of the stovetop hot, we know they will eventually cool. Here, we see a liquid crystal 32 00:02:37,020 --> 00:02:43,640 in the pan change color, first as the pan is heated, and then again, as the pan cools. 33 00:02:43,640 --> 00:02:47,829 Experience tells us in which direction these everyday events will proceed. But what about 34 00:02:47,829 --> 00:02:51,470 processes with which we don't have experience? 35 00:02:51,470 --> 00:02:56,120 For example, it would be nice if we had a way of knowing whether or not a given chemical 36 00:02:56,120 --> 00:02:59,940 reaction will happen at given conditions. 37 00:02:59,940 --> 00:03:04,300 The 2nd law of thermodynamics can help us with this. 38 00:03:04,300 --> 00:03:09,900 The 2nd law of thermodynamics states that during any spontaneous process, the total 39 00:03:09,900 --> 00:03:15,990 entropy change of a system and its surroundings is positive. In other words, the entropy of 40 00:03:15,990 --> 00:03:22,180 the "universe," that is, the system plus surroundings, can only increase. 41 00:03:22,180 --> 00:03:27,290 But what is entropy? Is entropy a magical force that overturns your furniture and creates 42 00:03:27,290 --> 00:03:30,600 havoc in your office or home? No. 43 00:03:30,600 --> 00:03:34,020 Entropy is a measure of the number of possible ways energy can be distributed in a system 44 00:03:34,020 --> 00:03:40,840 of molecules. Molecules in a system at equilibrium have the same average energy. However, at 45 00:03:40,840 --> 00:03:46,069 a given instant in time, it is highly unlikely that all of the molecules have the same exact 46 00:03:46,069 --> 00:03:48,350 energy. 47 00:03:48,350 --> 00:03:53,319 Molecules in a system are constantly interacting and transferring energy amongst each other. 48 00:03:53,319 --> 00:03:58,360 As a result, one molecule may have a certain amount of energy at one instant and at the 49 00:03:58,360 --> 00:04:03,640 next; it could have more or less. Depending on the energy the molecule has, it will be 50 00:04:03,640 --> 00:04:08,150 able to access different energy levels. 51 00:04:08,150 --> 00:04:11,900 The total energy of the system, determines what energy levels will be accessible to the 52 00:04:11,900 --> 00:04:17,289 molecules. Higher energy levels will not be accessible because the energy required to 53 00:04:17,289 --> 00:04:21,189 reach them is not available. 54 00:04:21,189 --> 00:04:25,099 So when we say that entropy is a measure of the number of possible ways energy can be 55 00:04:25,099 --> 00:04:31,249 distributed in a system of molecules, we have to account for all of the possible combinations. 56 00:04:31,249 --> 00:04:35,580 And the way we do that is by considering the microstates available to the molecules in 57 00:04:35,580 --> 00:04:40,460 the system. Let's use an analogy to understand the term 58 00:04:40,460 --> 00:04:41,680 "microstate". 59 00:04:41,680 --> 00:04:48,069 Let's say that you have two dice. What are all of the possible sums for a pair of dice? 60 00:04:48,069 --> 00:04:55,069 Pause the video here and take a moment to jot them down. 61 00:04:55,439 --> 00:05:02,080 Okay, you should have a list that looks something like this. We would call these sums possible 62 00:05:02,080 --> 00:05:08,199 macrostates of our system -- the macrostate doesn't tell us what each individual die reads 63 00:05:08,199 --> 00:05:13,569 when we roll them, just the total, or "macroscopic view" if you will. 64 00:05:13,569 --> 00:05:18,300 What are all of the possible dice combinations that will produce each of those sums? For 65 00:05:18,300 --> 00:05:23,240 example, we can produce the sum of three by rolling a one on the first die and a two on 66 00:05:23,240 --> 00:05:28,900 the 2nd die. Or, we can roll a 2 on the first die and a one on the 2nd die. So there are 67 00:05:28,900 --> 00:05:32,558 two combinations that will produce the sum of 3. 68 00:05:32,558 --> 00:05:37,219 The dice combinations that produce the remaining sums are shown here. 69 00:05:37,219 --> 00:05:43,759 We would call each of these combinations "microstates" that correspond to each macrostate. The microstate 70 00:05:43,759 --> 00:05:47,669 gives us information about the individual conditions of each die. 71 00:05:47,669 --> 00:05:52,669 We see that the most likely macrostate, a sum of 7, has the greatest number of possible 72 00:05:52,669 --> 00:05:53,139 microstates. 73 00:05:53,139 --> 00:05:57,849 Do you think that the entropy change for the system (the cold bar) was positive, negative, 74 00:05:57,849 --> 00:05:58,969 or equal to zero? 75 00:05:58,969 --> 00:06:05,189 Please pause the video here and discuss your reasoning with a classmate. 76 00:06:05,189 --> 00:06:12,189 Let's start with the system first. The transfer of energy to the cold bar will allow the molecules 77 00:06:43,339 --> 00:06:50,339 in the cold bar to access new energy levels that they could not reach before, increasing 78 00:08:34,229 --> 00:08:40,309 the number of possible microstates for that system. So we would suspect that the entropy 79 00:08:40,309 --> 00:08:43,179 change for the system is positive. 80 00:08:43,179 --> 00:08:45,620 But what about the surroundings? 81 00:08:45,620 --> 00:08:52,140 The total entropy of a system and its surroundings has to increase if the process is spontaneous. 82 00:08:52,140 --> 00:08:57,200 Let's use a very simplified diagram to think about the heat diffusion demo. We have two 83 00:08:57,200 --> 00:09:04,140 bars made of the same material. One bar is hot and one is cold. We'll look at 4 atoms 84 00:09:04,140 --> 00:09:10,490 making up each bar. The hot bar has more energy than the cold bar -- its atoms are moving 85 00:09:10,490 --> 00:09:14,640 more than the atoms in the cold bar, which seem barely to move. 86 00:09:14,640 --> 00:09:19,890 Now, before we put the cold bar in contact with the hot bar, let's think about each bar 87 00:09:19,890 --> 00:09:25,100 separately. In our simplified drawing of the cold bar, let's say that three of the atoms 88 00:09:25,100 --> 00:09:30,520 have no energy and one atom has one quantum of energy and is at a slightly higher energy 89 00:09:30,520 --> 00:09:35,930 level, symbolized by the set of curved lines representing its motion. How many different 90 00:09:35,930 --> 00:09:40,660 microstates can this system exhibit? If we think about the different ways we can 91 00:09:40,660 --> 00:09:45,890 distribute the quantum of energy amongst the 4 atoms, we see that there are 4 possible 92 00:09:45,890 --> 00:09:51,010 microstates. If we do the same for our hot bar, where we 93 00:09:51,010 --> 00:09:56,560 have 5 quanta of energy that can be distributed in a variety of ways amongst the 4 atoms, 94 00:09:56,560 --> 00:10:02,360 we use some math to see that there are 56 possible microstates. 95 00:10:02,360 --> 00:10:06,570 When we brought the two bars in contact in our demonstration, we saw that they reached 96 00:10:06,570 --> 00:10:11,650 thermal equilibrium. Here, in our simplified example, we will bring 97 00:10:11,650 --> 00:10:17,780 the cold bar (defined as our system) and the hot bar (defined as our surroundings) together 98 00:10:17,780 --> 00:10:23,460 and divide the 6 quanta of energy equally between the two. The first law of thermodynamics 99 00:10:23,460 --> 00:10:27,520 tells us that the total of 6 quanta will be conserved. 100 00:10:27,520 --> 00:10:34,520 Now, how many microstates are now possible in each bar? 101 00:10:35,250 --> 00:10:39,880 As you might have expected, the number of possible microstates in what was originally 102 00:10:39,880 --> 00:10:44,930 our hot bar decreased, and the number of possible microstates in what was originally our cold 103 00:10:44,930 --> 00:10:48,400 bar increased. Let's see what this means for our total entropy 104 00:10:48,400 --> 00:10:55,400 change. We will use a relationship for entropy that was derived by Ludwig Boltzmann. It states 105 00:10:56,020 --> 00:11:00,810 that entropy is equal to a constant, called the Boltzmann constant, times the natural 106 00:11:00,810 --> 00:11:03,720 log of the number of microstates. 107 00:11:03,720 --> 00:11:09,040 When calculating entropy change, whether it be for the system or surroundings, delta S 108 00:11:09,040 --> 00:11:15,080 would be equal to Boltzmann's constant times the natural log of the ratio of the final 109 00:11:15,080 --> 00:11:19,630 number of microstates to the initial number of microstates. 110 00:11:19,630 --> 00:11:24,550 The entropy change in our cold bar was positive while the entropy change in our hot bar was 111 00:11:24,550 --> 00:11:30,970 negative. But remember, it's the total entropy change that matters. We see that our total 112 00:11:30,970 --> 00:11:36,080 entropy change for this process is positive. The spontaneous transfer of heat from our 113 00:11:36,080 --> 00:11:42,690 hot bar to our cold bar is consistent with the 2nd law of thermodynamics. 114 00:11:42,690 --> 00:11:47,240 If you did a similar calculation for the reverse process, that of heat transferring from the 115 00:11:47,240 --> 00:11:52,130 cold bar to the hot bar, the total entropy change would be negative indicating that it 116 00:11:52,130 --> 00:11:57,110 is not spontaneous. As we hinted earlier and as you may have guessed 117 00:11:57,110 --> 00:12:02,240 by our very simplified scenario, calculating the number of microstates in a real system 118 00:12:02,240 --> 00:12:07,940 can be very challenging. Generally speaking, you will be calculating entropy in terms of 119 00:12:07,940 --> 00:12:14,740 measurable macroscopic quantities such as heat capacity or enthalpy of phase change. 120 00:12:14,740 --> 00:12:19,940 However, having a qualitative understanding of the physical meaning of entropy will help 121 00:12:19,940 --> 00:12:24,930 you properly interpret the entropy changes caused by various processes. 122 00:12:24,930 --> 00:12:31,760 To Review, for a process to proceed spontaneously, the total entropy change for a system and 123 00:12:31,760 --> 00:12:37,070 its surroundings must be positive. Entropy measures the number of possible ways energy 124 00:12:37,070 --> 00:12:43,920 can be distributed in a system of molecules. A microstate is an instantaneous catalog that 125 00:12:43,920 --> 00:12:49,870 describes the energy of each molecule in a system. Because molecules are constantly interacting 126 00:12:49,870 --> 00:12:56,870 and exchanging energy, this description constantly needs to be revised. A given system has a 127 00:12:56,950 --> 00:13:03,060 large number of possible microstates. As we saw with the Boltzmann equation, entropy is 128 00:13:03,060 --> 00:13:10,060 proportional to the number of microstates.