WEBVTT 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. 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 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 00:00:20.730 --> 00:00:24.759 hold? Let's find out. 00:00:24.759 --> 00:00:29.529 This video is part of the Equilibrium video series. It is often important to determine 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 00:00:34.060 --> 00:00:38.660 equilibrium state is constrained by its boundary and surroundings. 00:00:38.660 --> 00:00:44.620 Hi, my name is John Lienhard, and I am a professor of Mechanical Engineering at MIT. 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 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 00:00:56.540 --> 00:01:02.690 at these concepts and see how they differ. In order to understand this video, you should 00:01:02.690 --> 00:01:06.970 be familiar with the First and Second Laws of Thermodynamics, the meaning of thermal 00:01:06.970 --> 00:01:13.800 equilibrium, and the concept of heat flow rate, which is heat transfer per unit time. 00:01:13.800 --> 00:01:17.960 After watching this video, you will be able to identify whether a system is at equilibrium 00:01:17.960 --> 00:01:24.960 or at steady state, and to describe the difference between Thermal Equilibrium and Steady State. 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, 00:01:34.780 --> 00:01:39.190 we can assume that the room, which acts as the surroundings, is very large, much larger 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 00:01:45.250 --> 00:01:50.710 energy transfer across the system boundary. We'll assume that the volume of the bar and 00:01:50.710 --> 00:01:57.658 pressure of the room are constant. In other words, no mechanical work is done. 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 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, 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 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 00:02:22.450 --> 00:02:29.450 and the room are in thermal equilibrium. Because there is no difference in temperature, 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 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 00:02:40.230 --> 00:02:47.230 the video and think about how we might do this. 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 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 00:03:02.440 --> 00:03:09.440 temperature approximately equal to but ever so slightly higher than 25°C. 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 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. 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 00:03:27.030 --> 00:03:32.319 at the opposite end. There is a temperature gradient between these two points, but this 00:03:32.319 --> 00:03:37.920 gradient doesn't change over time. In this case, would you say the bar is at 00:03:37.920 --> 00:03:43.329 thermal equilibrium with the room? Why or why not? Pause the video here and discuss 00:03:43.329 --> 00:03:50.329 this with a partner. We know that energy is being continuously 00:03:54.440 --> 00:03:59.400 transferred from the heater to the metal bar. And we also know that the temperature profile 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 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 00:04:10.459 --> 00:04:17.060 the room. And that means it cannot be in thermal equilibrium with the room. 00:04:17.060 --> 00:04:23.060 Now, in order for the temperature profile to be constant in time, the heat flow rate 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 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 00:04:35.240 --> 00:04:42.050 bar is at steady state. A quantity is at Steady State when it is constant 00:04:42.050 --> 00:04:47.870 with respect to time. In other words, the partial derivative of the quantity with respect 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 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 00:04:59.870 --> 00:05:06.870 bar are equal and constant. 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 00:05:11.750 --> 00:05:17.160 think the pan handle will be too hot to touch, or cool enough to hold? 00:05:17.160 --> 00:05:21.550 Use the concepts of thermal equilibrium and steady state temperature to think of circumstances 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 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 00:05:32.880 --> 00:05:39.880 the video here and discuss. 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 00:05:47.630 --> 00:05:49.500 cases. 00:05:49.500 --> 00:05:53.680 What would happen if the handle and pan were in perfect thermal contact, and both were 00:05:53.680 --> 00:05:59.270 completely isolated from the room? Eventually, the handle would reach the same temperature 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 00:06:04.610 --> 00:06:11.610 identical and constant. So, the handle is in thermal equilibrium with the pan. What 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 00:06:17.100 --> 00:06:24.100 are in this situation? Pause the video and discuss. The rate of heat transfer must be 00:06:30.880 --> 00:06:36.250 zero -- if it wasn't, the handle would keep getting hotter, which is impossible, assuming 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 00:06:41.150 --> 00:06:47.530 room is also zero, because we assumed the handle is isolated from the room. 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. 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 00:07:00.919 --> 00:07:07.919 both zero. So this scenario, which we've been describing as "equilibrium," is really just 00:07:08.819 --> 00:07:14.699 a limiting case of steady state. And that's true for all systems at thermal equilibrium: 00:07:14.699 --> 00:07:21.389 they are all at steady state with respect to temperature. But the opposite is not true: 00:07:21.389 --> 00:07:27.270 not all systems at steady state are in thermal equilibrium. In this case, the handle will 00:07:27.270 --> 00:07:33.169 obviously be too hot to hold, since it's the same temperature as the pan. 00:07:33.169 --> 00:07:38.199 Now let's consider the opposite case. What would happen if the handle were completely 00:07:38.199 --> 00:07:44.909 insulated from the pan? The handle would be at thermal equilibrium with the room, and 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 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 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 00:08:04.520 --> 00:08:09.910 case of "thermal equilibrium" is really just another limiting case of steady-state temperature, 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 00:08:16.349 --> 00:08:21.030 thought experiments. But they could never happen in real life, because it's impossible 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 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 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 00:08:38.219 --> 00:08:42.499 pan or not? Let's keep going... 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 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 00:08:52.670 --> 00:08:59.209 from the room. Let's keep the first assumption, but change the second assumption. In other 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 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 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 00:09:16.899 --> 00:09:21.459 because the pan is initially much hotter than the handle. 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 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 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 00:09:37.050 --> 00:09:42.509 be hottest closest to the pan, and coolest far away from it. 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 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. 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 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 00:10:05.199 --> 00:10:10.379 gradient along the handle will stop changing, and the system will be at steady state with 00:10:10.379 --> 00:10:17.379 respect to temperature. But, remember: it will not be in thermal equilibrium. So, can 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 00:10:25.329 --> 00:10:30.779 distribution when the system reaches steady state. Take a moment to sketch a temperature 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 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 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 00:10:49.350 --> 00:10:56.350 this profile? Pause the video and discuss this with a partner. 00:10:58.269 --> 00:11:05.269 Okay, we're at our final scenario. Let's review the previous cases. 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 00:11:13.689 --> 00:11:19.459 was completely isolated from the room. In case 2, the handle was completely isolated 00:11:19.459 --> 00:11:21.559 from the pan. 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 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. 00:11:32.709 --> 00:11:37.100 Make sure that you can explain why this is true. 00:11:37.100 --> 00:11:41.249 In case 3, we went back to our assumption of perfect thermal contact between the pan 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 00:11:48.009 --> 00:11:52.999 this final case, let's pick and choose the most reasonable assumptions from our previous 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. 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, 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 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 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 00:12:23.139 --> 00:12:28.170 handle is extremely small, what can you say about the temperature profile across the handle 00:12:28.170 --> 00:12:33.949 once the system reaches steady state? Pause the video and sketch a possible steady state 00:12:33.949 --> 00:12:37.470 temperature profile in the handle. 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 00:12:46.279 --> 00:12:51.959 will reach a steady state temperature well before the majority of the handle gets hot. 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, 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 00:13:03.420 --> 00:13:08.569 original question. Will the pan handle be too hot to hold or will it be comfortable 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 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 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 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 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 00:13:39.239 --> 00:13:41.259 to the room. 00:13:41.259 --> 00:13:45.109 The handle was designed to reach a steady-state temperature that is comfortable to hold without 00:13:45.109 --> 00:13:52.109 a glove. This is a well-designed pan! 00:13:53.589 --> 00:13:57.989 You now have the tools to understand that Thermal Equilibrium and Steady State temperature 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 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 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 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, 00:14:22.839 --> 00:14:29.569 the system is at thermal equilibrium. So, equilibrium is just a special case of steady 00:14:29.569 --> 00:14:35.889 state. We were able to apply our understanding of thermal equilibrium and steady state temperature 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 00:14:41.499 --> 00:14:48.339 the design elements that led to that profile. I hope you enjoyed this video. 00:14:48.339 --> 00:14:54.579 Good luck in your studies.