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Zeroth law of thermodynamics

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Video transcript

- [Voiceover] Let's talk about the 0th Law of Thermodynamics. Now the 0th law, it's a strange one. For one, it's called the 0th law and that's kind of weird. We'll talk about why in a minute. And for two, when you hear the actual statement of the 0th law, it sounds so obvious and trivial, you think it's kind of stupid to have a law for it. In fact, when I first heard it, I thought it was pretty dumb, but now that I know a little more, it's not quite as trivial as I thought it was and I'll try to explain why it might not be as trivial as you might think it is. So what is the 0th law? It has to do with thermal equilibrium. And to demonstrate thermal equilibrium, let's say you had a piece of pie, mmmmm key lime pie, and you also had a steel sphere and we're going to take this steel sphere and I'm going to place this in thermal contact with the pie, which is to say they can exchange heat and which way is the heat going to flow? We know the heat will flow from the hotter object to the cooler object. Let's say our pie was in the freezer, it's nice and cold and our sphere was sitting at room temperature, so it's the relatively hotter object, and we know heat will flow from the hot object to the cool object, which is to say heat will flow from the steel sphere into the pie. But this net exchange of heat stops at some point. At some point the sphere heats up the pie enough that no net heat is transferred one way or the other and basically you just have a pie and a steel sphere sitting there and no net heat is transferred, and when that happens, when no net heat gets transferred between two objects, we say they're in thermal equilibrium. So that's all well and good, but what does this have to do with the 0th Law of Thermodynamics? Well, let's say you did this. You had your pie and your sphere and you waited until they came into thermal equilibrium and now you insert a third object into the mix, some small amount of water or a large amount of water, it doesn't actually matter, but some water over here, and so after allowing the pie and sphere to come into thermal equilibrium, which is to say they don't exchange anymore heat, you bring this sphere over here, you put it in contact with the water and for the sake of argument, this doesn't usually happen this way. For the sake of argument, let's say no heat is transferred either way over here, so two is also in thermal equilibrium with this water, with three. Usually you'd have water at some different thermal state and they would exchange heat, but for the sake of argument, let's say that no heat is exchanged over here, that begs a question. You say to yourself wait. So two is in thermal equilibrium with one, no heat transferred. Two is in thermal equilibrium with three, no heat transferred. What if, now you start thinking, and you ask what if I put three in contact with one, will there be any heat transferred? That's the crux, that's the question that the 0th Law of Thermodynamics addresses and the answer is no. No heat is going to get transferred here either. So the 0th law says, that if object one is in thermal equilibrium with object two, and object two is in thermal equilibrium with object three, then object one is also in thermal equilibrium with object three. This is the 0th Law of Thermodynamics and you can see, some of you out there are probably thinking well duh, how could it ever not be like that? If one is in equilibrium with two, and two is in equilibrium with three, then one has to be in equilibrium with three. Well yeah, I mean it is like that. Our universe is like that, but think about it a little harder, you could probably think of a universe where it might not be like that. Imagine a case where, let's take this water, separate these all again. Imagine a crazy universe which is not ours where for some reason steel and pie, thermal equilibrium, no heat transferred. Steel and water, thermal equilibrium, no heat transferred, but water and pie, well not thermal equilibrium. Heat does get transferred. This would be terrible. This would be a horrible universe to do physics in because now you'd have to have some separate definition of temperature, depending on what type of material you have. There'd be a key lime pie to steel sphere temperature together and there'd be a steel sphere and water temperature, and there'd be a water and key lime pie temperature, it'd be horrible, but our universe does not behave that way. Our universe follows the 0th Law of Thermodynamics, and the best part is that this allows us to define a universal temperature scale, because temperature is defined to be the thing, that's the same between two objects when they're in thermal equilibrium. In other words, the 0th law makes it such that I could say this pie is at a temperature of 20 degrees Celsius and this sphere is at a temperature of 20 degrees Celsius and this water is at a temperature of 20 degrees Celsius. Regardless of me telling you beforehand which two I'm going to put in contact with each other. If I tell you these are all at the same temperature, you know, put any of them in contact, no net heat is going to transfer between them. If the 0th law didn't hold, you wouldn't be able to do this. You could say that, okay the pie and the sphere are at the same temperature, 20 degrees, and you could say that the sphere and the water was at the same temperature, call it 20 degrees if you want, but the water and pie would not be at the same temperature. You couldn't call these both 20 degrees. You'd have to have separate scales and that's why this would be horrible. That's why you should respect and love the 0th Law of Thermodynamics. But why is it called the 0th Law of Thermodynamics? Well, physicists had been working on the 1st Law of Thermodynamics for a long, long time. They got that pretty well nailed down. Only later did they realize, wait, this whole endeavor of thermodynamics is kind of relying on the ability of us to be able to define a universal temperature scale between all materials and objects and that's kind of more fundamental than even the 1st law is, so they realized we should give this a number previous to the 1st law, but the 1st law was already the 1st law, so we call this the 0th Law of Thermodynamics.