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Concept #1: Zeroth Law of Thermodynamics

Transcript

Hey guys, in this video we want to talk about the Zeroth law of thermodynamics. Alright let's get to it.Thermodynamics has a whole bunch of laws associated with them there are four common ones the zero well sorry there are three common ones and there's a fourth sometimes talked about there's the Zeroth the first and the second then there's also the third which is 50/50 probably a little bit less probability whether or not you would counter it in a course alright what temperature which we've been talking about is closely tied to is something called thermal equilibrium, thermal equilibrium gives us sort of like a conceptual definition for what temperature is. Thermal equilibrium exists when two substances are in contact with each other and are comfortable in their final state when they get comfortable so first two substances are in different states you put them together they fight back and forth eventually arriving at one state that they're both comfortable with. Heat is not being transferred between these two objects when they are in thermal equilibrium so we already talked about what happens when you put a hot object in contact with the cold objects that hot object is going to give that cold object heat and they're going to keep exchanging heat they're going to fight until they're comfortable with their common state until they've reached thermal equilibrium in which case heat is no longer going to be exchange if we consider two objects A and B. Which I've shown in the figure above me in contact with one another heat can transfer as long as the contact is conductive to heat, heat can transfer. Initially there temperatures don't have to be equal but when they're in thermal equilibrium by definition there temperatures have to equal so if one is hotter than the other that hot object is going to give heat and give heat and give heat to the colder object until their temperatures balance out remember that as the hot object is giving heat it's temperature is dropping as a cold object is gaining heat its temperature is rising so the hot object is going to keep giving heat until it stops giving heat when it stops giving heat you know that they have the same temperature and they're in thermal equilibrium but what if you have three objects A,B and C. as shown in this figure and they're arranged in a very specific way. A is in contact in thermal contact with C so heat is allowed to flow that way, B is in thermal contact with C so heat is allowed to fow this way but A and B are not in thermal contact they are insulated from one another so heat cannot flow between A and B, so the only way that heat is flowing is heat is flowing between A and C and between B and C. What the Zeroth law of thermodynamics says that if A and C are in equilibrium if there temperatures are the same and if B and C are in equilibrium so their temperatures are the same then the temperature of A must equal the temperature of B. They must be in equilibrium and this should make sense because if you look at the picture A and B are not isolated from one another they're still in thermal contact they're not in direct contact they're indirect contact but they're still in thermal contact with one another through C, if A is really really hot B is really really cold and C is kind of neutral then there's going to be a whole flow of the heat from A through C into B and so A can influence B so if A and C are in thermal equilibrium and B and C. are in thermal equilibrium the Zeroth law for thermodynamics says that A and B must be in thermal equilibrium with one another. Now the Zeroth law is important because its tied of the definition of temperature, temperature can only really be measured in equilibrium so whenever you stick a thermometer into something you see like a mercury thermometer you see that mercury growing that mercury lengthening right now it's not in thermal equilibrium you can't really measure the temperature until it stops growing once it stops growing it's reached thermal equilibrium with what it's touching in whatever its touching then you can measure temperature. It was found experimentally that when two gases are in equilibrium we have this equation where P is the pressure V is the volume and capital N is the number of particles in the gas this allowed temperature to be defined experimentally like so they just said oh this is equal to this in thermal equilibrium we know temperature is equal to temperature in thermal equilibrium so this thing here clearly has to be related to the temperature so what they did was they slapped on a constant R to the temperature and said it equals to P.V over N. R serves two purposes first P.V over N doesn't have the same units as temperature so R has to convert the units to Kelvin the units of temperature, that gives T the proper units the other thing is that R was experimentally derived to make this inequality, otherwise they would just be related to one another but you need R to make it inequality. Alright because when you multiply P.V over N maybe you get 3 but your temperature is 1 so R needs to multiply that 1 into a 3 so that you get 3 equals 3 so you get that equality and that R by the way is called the ideal gas constant sometimes called the gas constant sometimes called a universal gas constant and it's going to appear throughout our discussion of thermodynamics let's do an example hot coffee at 75 degrees Celsius is poured into a ceramic mug at 27 degrees Celsius are these two systems the coffee and the mug in thermal equilibrium I'll call that question A what if after a long time the coffee's temperature dropped to 55 degrees Celsius what is a reasonable temperature to guess the mug is at ? I'll call this question B. So A what's the temperature of the coffee? 75 degrees Celsius, what's the temperature of the mug? 27 degrees Celsius, 75 does not equal 25 so they are not in equilibrium. Very very simple what is thermal equilibrium say that temperatures have to be equal to one another you were told specifically that the temperatures are not equal to one another so they're not in thermal equilibrium reaching equilibrium takes time, think about if you have a mug at room temperature and you have piping hot coffee and you pour that coffee into the mug are they instantly going to be in equilibrium no their states are going to be in flux they're going to be exchanging heat until eventually they do reach equilibrium. Part B after a long time what do you think is going to be the status of their equilibrium after a long time they should be in equilibrium. So if the coffee's temperature is at 55 degrees Celsius what's a reasonable temperature to guess the mugs sorry what's a reasonable guess as to the mug's temperature? 55 degrees Celsius why because after a long time they should be in thermal equilibrium which means the their temperature should be the same so a reasonable guess is that they are in thermal equilibrium and their temperatures are the same so if the coffee is 55 the mug is 55 thermal equilibrium takes time to reach alright and if you give it enough time eventually the mug will be just as hot as the coffee. Alright guys that wraps up our discussion on the Zeroth law of Thermodynamics. Thanks for watching.