1 00:00:05,220 --> 00:00:11,450 Here's a pan on a stove top. The pan's body and handle are made out of the same material. 2 00:00:11,450 --> 00:00:15,139 The burner has been turned on for a little while, and the pan body is hot enough to cook 3 00:00:15,139 --> 00:00:20,730 this egg. But what about the handle? Is it too hot to touch? Or is it cool enough to 4 00:00:20,730 --> 00:00:24,759 hold? Let's find out. 5 00:00:24,759 --> 00:00:29,529 This video is part of the Equilibrium video series. It is often important to determine 6 00:00:29,529 --> 00:00:34,060 whether or not a system is at equilibrium, to do this we must understand how a system's 7 00:00:34,060 --> 00:00:38,660 equilibrium state is constrained by its boundary and surroundings. 8 00:00:38,660 --> 00:00:44,620 Hi, my name is John Lienhard, and I am a professor of Mechanical Engineering at MIT. 9 00:00:44,620 --> 00:00:51,310 Today, I am going to talk to you about Equilibrium and Steady State. It's a common misconception 10 00:00:51,310 --> 00:00:56,540 that Equilibrium and Steady State are the same. In this video, we'll take a closer look 11 00:00:56,540 --> 00:01:02,690 at these concepts and see how they differ. In order to understand this video, you should 12 00:01:02,690 --> 00:01:06,970 be familiar with the First and Second Laws of Thermodynamics, the meaning of thermal 13 00:01:06,970 --> 00:01:13,800 equilibrium, and the concept of heat flow rate, which is heat transfer per unit time. 14 00:01:13,800 --> 00:01:17,960 After watching this video, you will be able to identify whether a system is at equilibrium 15 00:01:17,960 --> 00:01:24,960 or at steady state, and to describe the difference between Thermal Equilibrium and Steady State. 16 00:01:29,350 --> 00:01:34,780 This metal bar has been sitting in a large room for a long period of time. In this example, 17 00:01:34,780 --> 00:01:39,190 we can assume that the room, which acts as the surroundings, is very large, much larger 18 00:01:39,190 --> 00:01:45,250 than the bar, which acts as our system. Heat transfer from the bar to the room acts as 19 00:01:45,250 --> 00:01:50,710 energy transfer across the system boundary. We'll assume that the volume of the bar and 20 00:01:50,710 --> 00:01:57,658 pressure of the room are constant. In other words, no mechanical work is done. 21 00:01:57,658 --> 00:02:04,659 The temperature of the bar is 25°C and the temperature of the room is also 25°C. Even 22 00:02:05,310 --> 00:02:09,449 though the molecules in the air are colliding with the atoms on the surface of the bar, 23 00:02:09,449 --> 00:02:14,700 there is no net transfer of energy between the room and the bar. The temperature of both 24 00:02:14,700 --> 00:02:21,700 the bar and the room remain constant at 25°C. In thermodynamic terms, we say that the bar 25 00:02:22,450 --> 00:02:29,450 and the room are in thermal equilibrium. Because there is no difference in temperature, 26 00:02:29,480 --> 00:02:35,290 there is no heat transfer between the bar and the room. What if we wanted the temperature 27 00:02:35,290 --> 00:02:40,230 of the bar to be larger than that of the room, and we wanted it to remain that way? Pause 28 00:02:40,230 --> 00:02:47,230 the video and think about how we might do this. 29 00:02:50,610 --> 00:02:57,170 Of course, if we simply place a bar at 45°C in the room, the small bar will lose energy 30 00:02:57,170 --> 00:03:02,440 to the large room until both the bar and room are once again at thermal equilibrium at a 31 00:03:02,440 --> 00:03:09,440 temperature approximately equal to but ever so slightly higher than 25°C. 32 00:03:10,800 --> 00:03:15,690 You might have suggested connecting some sort of heating element to the bar. Let's try this 33 00:03:15,690 --> 00:03:22,569 and see what happens. Here's the bar after it has been left on a heater for a long time. 34 00:03:22,569 --> 00:03:27,030 As you might have expected, the bar is hottest where it's touching the heater, and coolest 35 00:03:27,030 --> 00:03:32,319 at the opposite end. There is a temperature gradient between these two points, but this 36 00:03:32,319 --> 00:03:37,920 gradient doesn't change over time. In this case, would you say the bar is at 37 00:03:37,920 --> 00:03:43,329 thermal equilibrium with the room? Why or why not? Pause the video here and discuss 38 00:03:43,329 --> 00:03:50,329 this with a partner. We know that energy is being continuously 39 00:03:54,440 --> 00:03:59,400 transferred from the heater to the metal bar. And we also know that the temperature profile 40 00:03:59,400 --> 00:04:05,959 of the bar is not changing; in other words, it's not getting any hotter or cooler. That 41 00:04:05,959 --> 00:04:10,459 means the bar must be transferring the energy it's gaining from the heater to the air in 42 00:04:10,459 --> 00:04:17,060 the room. And that means it cannot be in thermal equilibrium with the room. 43 00:04:17,060 --> 00:04:23,060 Now, in order for the temperature profile to be constant in time, the heat flow rate 44 00:04:23,060 --> 00:04:28,970 from the heater into the bar must be constant and equal to the heat flow rate from the bar 45 00:04:28,970 --> 00:04:35,240 to the room. We could use a new term to describe these conditions -- we could say that the 46 00:04:35,240 --> 00:04:42,050 bar is at steady state. A quantity is at Steady State when it is constant 47 00:04:42,050 --> 00:04:47,870 with respect to time. In other words, the partial derivative of the quantity with respect 48 00:04:47,870 --> 00:04:54,310 to time is zero. The metal bar is at steady state because the time derivative of its temperature 49 00:04:54,310 --> 00:04:59,870 at any point is zero. This happens when the heat flow rate into the bar and out of the 50 00:04:59,870 --> 00:05:06,870 bar are equal and constant. 51 00:05:07,320 --> 00:05:11,750 Let's go back to the heated pan which was left on the stove for a long time. Do you 52 00:05:11,750 --> 00:05:17,160 think the pan handle will be too hot to touch, or cool enough to hold? 53 00:05:17,160 --> 00:05:21,550 Use the concepts of thermal equilibrium and steady state temperature to think of circumstances 54 00:05:21,550 --> 00:05:27,340 in which the handle might be too hot, or cool enough, to hold. You might consider how the 55 00:05:27,340 --> 00:05:32,880 handle is attached to the pan, or how well the handle transfers heat to the room. Pause 56 00:05:32,880 --> 00:05:39,880 the video here and discuss. 57 00:05:42,570 --> 00:05:47,630 How many scenarios did you come up with? There are many, but let's start with two extreme 58 00:05:47,630 --> 00:05:49,500 cases. 59 00:05:49,500 --> 00:05:53,680 What would happen if the handle and pan were in perfect thermal contact, and both were 60 00:05:53,680 --> 00:05:59,270 completely isolated from the room? Eventually, the handle would reach the same temperature 61 00:05:59,270 --> 00:06:04,610 as the pan. This is what that would look like: the temperature of the pan and handle are 62 00:06:04,610 --> 00:06:11,610 identical and constant. So, the handle is in thermal equilibrium with the pan. What 63 00:06:12,919 --> 00:06:17,100 can you say about the transfer of heat from the pan to the handle once the pan and handle 64 00:06:17,100 --> 00:06:24,100 are in this situation? Pause the video and discuss. The rate of heat transfer must be 65 00:06:30,880 --> 00:06:36,250 zero -- if it wasn't, the handle would keep getting hotter, which is impossible, assuming 66 00:06:36,250 --> 00:06:41,150 that the temperature of the pan is constant. The heat flow rate from the handle to the 67 00:06:41,150 --> 00:06:47,530 room is also zero, because we assumed the handle is isolated from the room. 68 00:06:47,530 --> 00:06:54,530 So, the heat flow rates into and out of the handle are exactly the same - zero and constant. 69 00:06:56,479 --> 00:07:00,919 And steady state occurs when the flow rate in equals the flow rate out, even if they're 70 00:07:00,919 --> 00:07:07,919 both zero. So this scenario, which we've been describing as "equilibrium," is really just 71 00:07:08,819 --> 00:07:14,699 a limiting case of steady state. And that's true for all systems at thermal equilibrium: 72 00:07:14,699 --> 00:07:21,389 they are all at steady state with respect to temperature. But the opposite is not true: 73 00:07:21,389 --> 00:07:27,270 not all systems at steady state are in thermal equilibrium. In this case, the handle will 74 00:07:27,270 --> 00:07:33,169 obviously be too hot to hold, since it's the same temperature as the pan. 75 00:07:33,169 --> 00:07:38,199 Now let's consider the opposite case. What would happen if the handle were completely 76 00:07:38,199 --> 00:07:44,909 insulated from the pan? The handle would be at thermal equilibrium with the room, and 77 00:07:44,909 --> 00:07:49,849 would stay that way no matter how hot the pan got. The temperature of the handle would 78 00:07:49,849 --> 00:07:56,849 be exactly the same as that of the air. Just as in our first case, both the heat flow rate 79 00:07:58,099 --> 00:08:04,520 from the pan to the handle and from the handle to the air are zero and constant. Thus, this 80 00:08:04,520 --> 00:08:09,910 case of "thermal equilibrium" is really just another limiting case of steady-state temperature, 81 00:08:09,910 --> 00:08:16,349 except, of course, the handle will be cool enough to hold. Both of these cases are great 82 00:08:16,349 --> 00:08:21,030 thought experiments. But they could never happen in real life, because it's impossible 83 00:08:21,030 --> 00:08:27,160 to completely isolate one component of a system from another. In case 1, it would be impossible 84 00:08:27,160 --> 00:08:33,179 to isolate the pan and handle from the room; and in case 2, it would be impossible to isolate 85 00:08:33,179 --> 00:08:38,219 the handle from the pan. So are we any closer to figuring out whether we can pick up this 86 00:08:38,219 --> 00:08:42,499 pan or not? Let's keep going... 87 00:08:42,499 --> 00:08:47,319 Let's go back to our first case and refine our thinking. We originally assumed that the 88 00:08:47,319 --> 00:08:52,670 pan and handle were in perfect thermal contact, and that the pan and handle were totally isolated 89 00:08:52,670 --> 00:08:59,209 from the room. Let's keep the first assumption, but change the second assumption. In other 90 00:08:59,209 --> 00:09:05,850 words, we will allow for some flow of heat from the handle to the room. Now what happens 91 00:09:05,850 --> 00:09:11,019 as we heat up the pan? We can assume that the heat flow rate from the pan to the handle 92 00:09:11,019 --> 00:09:16,899 is initially larger than the heat flow rate from the handle to the room. This is reasonable 93 00:09:16,899 --> 00:09:21,459 because the pan is initially much hotter than the handle. 94 00:09:21,459 --> 00:09:27,489 So the handle will definitely heat up, just like our metal bar from before. As long as 95 00:09:27,489 --> 00:09:30,899 the flow of heat from the pan to the handle is greater than the flow of heat from the 96 00:09:30,899 --> 00:09:37,050 handle to the room, the handle will get hotter. And also just like our metal bar, it will 97 00:09:37,050 --> 00:09:42,509 be hottest closest to the pan, and coolest far away from it. 98 00:09:42,509 --> 00:09:46,699 As the temperature of the handle rises, the heat flow rate from the handle to the room 99 00:09:46,699 --> 00:09:53,480 will also rise. And eventually, it will equal the heat flow rate from the pan to the handle. 100 00:09:53,480 --> 00:09:58,050 In other words, after some length of time the handle will be losing energy to the room 101 00:09:58,050 --> 00:10:05,050 at exactly the same rate as it's gaining energy from the pan. When this happens, the temperature 102 00:10:05,199 --> 00:10:10,379 gradient along the handle will stop changing, and the system will be at steady state with 103 00:10:10,379 --> 00:10:17,379 respect to temperature. But, remember: it will not be in thermal equilibrium. So, can 104 00:10:19,369 --> 00:10:25,329 we say whether the handle is too hot to hold? No! That depends on the exact temperature 105 00:10:25,329 --> 00:10:30,779 distribution when the system reaches steady state. Take a moment to sketch a temperature 106 00:10:30,779 --> 00:10:36,449 profile that describes a steady-state situation wherein all or part of the handle is too hot 107 00:10:36,449 --> 00:10:43,449 to touch. What values of the heat flow rate from the pan to the handle could result in 108 00:10:43,470 --> 00:10:49,350 a handle that is too hot to touch. What characteristics of the pan, handle and/or room could produce 109 00:10:49,350 --> 00:10:56,350 this profile? Pause the video and discuss this with a partner. 110 00:10:58,269 --> 00:11:05,269 Okay, we're at our final scenario. Let's review the previous cases. 111 00:11:08,309 --> 00:11:13,689 In case 1, we assumed the pan and handle were in perfect thermal contact and that the system 112 00:11:13,689 --> 00:11:19,459 was completely isolated from the room. In case 2, the handle was completely isolated 113 00:11:19,459 --> 00:11:21,559 from the pan. 114 00:11:21,559 --> 00:11:27,049 In both case 1 and case 2, the handle was in thermal equilibrium -- there was no transfer 115 00:11:27,049 --> 00:11:32,709 of heat into or out of the system. The handle was also at steady state with respect to temperature. 116 00:11:32,709 --> 00:11:37,100 Make sure that you can explain why this is true. 117 00:11:37,100 --> 00:11:41,249 In case 3, we went back to our assumption of perfect thermal contact between the pan 118 00:11:41,249 --> 00:11:48,009 and the handle, but we allowed for some heat transfer from the handle to the room. For 119 00:11:48,009 --> 00:11:52,999 this final case, let's pick and choose the most reasonable assumptions from our previous 120 00:11:52,999 --> 00:11:58,689 cases and build from there. We'll assume that the handle can exchange heat with the room. 121 00:11:58,689 --> 00:12:04,970 We'll also assume that the pan and handle are insulated from each other. This is reasonable, 122 00:12:04,970 --> 00:12:11,220 because if you're a pan designer, you don't want your customers burning their hands! But 123 00:12:11,220 --> 00:12:17,029 of course, there is no such thing as perfect insulation, so we have to allow for at least 124 00:12:17,029 --> 00:12:23,139 some heat transfer between the pan and handle. If the rate of heat flow from the pan to the 125 00:12:23,139 --> 00:12:28,170 handle is extremely small, what can you say about the temperature profile across the handle 126 00:12:28,170 --> 00:12:33,949 once the system reaches steady state? Pause the video and sketch a possible steady state 127 00:12:33,949 --> 00:12:37,470 temperature profile in the handle. 128 00:12:37,470 --> 00:12:44,470 Here's one. If the rate of heat flow from the pan to the handle is very low, the system 129 00:12:46,279 --> 00:12:51,959 will reach a steady state temperature well before the majority of the handle gets hot. 130 00:12:51,959 --> 00:12:56,739 There will be a very small region near the pan where the handle is hotter than the room, 131 00:12:56,739 --> 00:13:03,420 but most of the handle will be close to the temperature of the room. So let's answer our 132 00:13:03,420 --> 00:13:08,569 original question. Will the pan handle be too hot to hold or will it be comfortable 133 00:13:08,569 --> 00:13:14,949 to touch? Let's look at a thermal image of the pan after it has been left on the stove 134 00:13:14,949 --> 00:13:21,949 for 30 minutes. It looks like we predicted in case 4! A very small portion of the handle 135 00:13:21,949 --> 00:13:28,389 is warmer than the room, but most of the handle is at room temperature. Remember, this does 136 00:13:28,389 --> 00:13:33,929 not mean that the handle is in thermal equilibrium with the room. There is a constant but small 137 00:13:33,929 --> 00:13:39,239 rate of heat flow from the pan to the handle, and an equal rate of heat flow from the handle 138 00:13:39,239 --> 00:13:41,259 to the room. 139 00:13:41,259 --> 00:13:45,109 The handle was designed to reach a steady-state temperature that is comfortable to hold without 140 00:13:45,109 --> 00:13:52,109 a glove. This is a well-designed pan! 141 00:13:53,589 --> 00:13:57,989 You now have the tools to understand that Thermal Equilibrium and Steady State temperature 142 00:13:57,989 --> 00:14:03,589 are different. We saw that if the temperatures of all parts of a system do not change with 143 00:14:03,589 --> 00:14:10,199 time, the system can either be at steady state or at thermal equilibrium. If the net heat 144 00:14:10,199 --> 00:14:15,790 flow is constant and nonzero as for our metal bar on the heater, the system will have a 145 00:14:15,790 --> 00:14:22,790 steady temperature profile. If it is constant and zero, as for our metal bar at room temperature, 146 00:14:22,839 --> 00:14:29,569 the system is at thermal equilibrium. So, equilibrium is just a special case of steady 147 00:14:29,569 --> 00:14:35,889 state. We were able to apply our understanding of thermal equilibrium and steady state temperature 148 00:14:35,889 --> 00:14:41,499 to describe the temperature profile of a pan left on the stove for a long time and to understand 149 00:14:41,499 --> 00:14:48,339 the design elements that led to that profile. I hope you enjoyed this video. 150 00:14:48,339 --> 00:14:54,579 Good luck in your studies.