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Zeroth law of thermodynamics

Video transcript

let's talk about the zeroth law of thermodynamics now the zeroth law it's a strange one for one it's called the zeroth 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 zeroth law it sounds so obvious in trivial you think it's kind of stupid to have a law for 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 zeroth law it has to do with thermal equilibrium and to demonstrate thermal equilibrium let's say you had a piece of pie mmm key lime pie and you also had a steel sphere 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 hot 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 then 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 zeroth 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 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 any more 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 heats exchange 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 zeroth law of thermodynamics addresses and the answer is no no heats going to get transferred here either so the zeroth 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 zeroth 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 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 in pi thermal equilibrium no heat transferred steel and water thermal equilibrium no heat transferred but water and pi well not thermal equilibrium he 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 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 zeroth law of thermodynamics in the best part is that this allows us to define a universal temperature scale because temperatures define to be the thing that's the same between two objects when they're in thermal equilibrium in other words the zeroth law makes it such that I could say this pi is at a temperature of 20 degrees Celsius and the sphere is at a temperature of 20 degrees Celsius and this waters 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 heats going to transfer between them if the zeroth law didn't hold you wouldn't be able to do this you could say that okay the PI and the sphere at the same temperature 20 degrees and you can say that the sphere and the water was at the same temperature call it 20 degrees if you want but the water and the PI would not be at the same temperature that 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 zeroth law of thermodynamics but why is it called the zeroth law of thermodynamics well physicists had been working on the first 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 first law is so they realized we should give this a number of previous two the first law the first law was already the first law so we call this the zeroth law of thermodynamics