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# Thermodynamics part 3: Kelvin scale and Ideal gas law example

## Video transcript

so we just finished hopefully getting intuition for why you know my initial pressure times my initial volume / - room temperature it's going to equal you know if I change the volume or the pressure or the temperature or some combination of all of them is going to equal my new pressure times my new volume / my new temperature and and once again just remember all of this is you know pressure times volume is proportional to the amount of kinetic energy in the system what and and and temperature is proportional to the amount of kinetic energy per molecule so if we don't change the number of molecules well the amount and since by conservation of energy the amount of kinetic energy isn't going to change unless we you know do some work or get some potential energy or something these quantities this relationship won't change and watch the last video and hopefully you'll get some intuition if if it's still confusing I'll make another video for you guys now before I apply this before I apply this equation which which is really this is going to get you pretty far in thermodynamics just knowing this and even more just having the intuition of what it means I want to clarify something about temperature so there's a lot of different ways to measure temperature you know we we know that in Fahrenheit what's freezing of water it's 32 degrees Fahrenheit is freezing well that's also zero degrees Celsius right and actually that's how the Celsius scale was determined they said okay where does water free zero and then where does water boil 100 degrees Celsius is boiling and then that's that's how they they rated it and of course you could be colder than the freezing of water and you'd have to go negative in that situation Fahrenheit I'm actually not sure how far did I need to look that up in Wikipedia or that might be something for you to do in and tell me how it came out you know I think boiling of water in Fahrenheit 212 degrees so it's a little arbitrary I think Fahrenheit might be somehow related to human body temperature but I'm just guessing but anyway you could have different scales in this situation and they were all kind of a bit arbitrary when they were designed kind of to just have some type of relative to scale you know you could say well when things are boiling they're definitely hotter they have a higher temperature than when things are freezing but it's not clear to say that it has that you know you have well you can't divide 100 by zero but if something is one degree is it necessarily the case that's something that is 100 degrees Celsius is a hundred times hotter or has a hundred times the kinetic energy well actually we'll see that no it's actually not the case you don't have a hundred times the kinetic energy so this is a bit of an arbitrary scale so the actual interval might you know the intervals arbitrary you could pick the one degree as being one hundredth of the distance between 0 and 100 but where you start at least in the Celsius scale is a bit arbitrary they pick the freezing of water so later on people figured out that there is an absolute point to start at and that absolute point to start at is the temperature at which a molecule or an atom has absolutely no kinetic energy at because we said we said temperature is equal to you know the average kinetic energy of the system or the total kinetic energy of the system divided by the number of molecules or we could say the average kinetic energy per molecule right so the only way to really say that the temperature is zero is if and this is proportional I should say it's proportional because the temperature scales are still a little bit arbitrary it's proportional it's not exactly it's related to but the only way to get to a temperature of zero should be when the kinetic energy of each and every molecule is zero or the average gain so they're not they're not moving they're not vibrating they're not even blinking these molecules are stationary and the point at which that occurs is called absolute zero absolute zero and that actually occurs absolute zero and that's also called zero Kelvin zero Kelvin and that is the same thing as minus 273 degrees Celsius so nowhere in the universe at least that I'm aware of it is it colder than minus 207 three degrees Celsius at that temperature nothing moves even at the atomic scale I mean I'm talking the electrons collapse into the nucleus I mean nothing everything is completely completely stationary at zero Kelvin and it's it's a it's a theoretical absolute limit people and maybe we'll do a bunch of videos on how you can get close to that but in laboratory environments or maybe in deep space it gets really really close to this but I'm not I'm not sure I'm pretty sure nowhere in the universe is do we have absolutely zero Kelvin at least in any place where we actually have particles but I might be wrong there but we that's a little bit out of the scope of what we're talking about so anyway so the true way to measure temperature is in Kelvin and then when you're measuring in Kelvin if I say I have something that is one Kelvin versus something that is five Kelvin since we kind of nailed down the bottom at a point at which we really do not have kinetic energy I can I can't make the statement that this has five times the energy of this something that's at five Kelvin versus welke at one Kelvin so that whole long explanation about Kelvin that's just to make the point that whenever we use this formula or really any formula in thermodynamics that involve temperature we should convert to Kelvin unless we're just doing change in temperature then you could you could probably keep it Celsius but when you're doing proportionality or using it multiplying or dividing by temperature you have to use Kelvin and hopefully I've made a little bit clearer of why that is so let's do an example so let's let me let me erase and you'd be surprised how far this takes you and really the main trick is just to remember to convert things to Kelvin that's what that's that's the number one reason why people miss questions on thermodynamics exams is that they didn't convert to Kelvin so I'm gonna get a problem this problem and this is very typical of most of what you'll see this is from the baron's AP physics be on page 226 and it says see a confined gas is a temperature of 27 degrees so its initial initial temperature is 27 degrees Celsius when it has a pressure and volume so it's pressure it's pressure is 1,000 Pascal's or Newton's per meter squared and the volume volume is 30 meters cubed I think in one of the earlier videos I think I said Newtons per meter cubed know it's Newtons per meter squared I just want to make sure I didn't confuse people previously so that's the initial volume and then it says the volume is decreased so then we go to this state where my new volume is going to be 20 meters cubed the new temperature it's it's increased so the new temperature is now 50 degrees Celsius and they want to know they want to know what is my new pressure so before we just substitute into the equation and solve for the impression remember if they gave it to you in Celsius convert to kelvins and if they gave it to you in Fahrenheit which they seldom do then convert into Celsius and then convert it into Kelvin well we already know that you know zero Kelvin is equal to 273 sorry minus 273 Celsius or another way you could say it is X Kelvin Kelvin X Kelvin is equal to well essentially whatever degree you get in Celsius you just add 273 to it does that make sense because think of it this way zero Kalp if you're at zero degree Celsius if your zero degree Celsius you're at you're already at your 273 degrees above zero Kelvin right think about that hopefully that makes sense maybe you want to draw a number line just to make sure so whatever Celsius degree you have just add 273 to it and you'll get Kelvin so this is equal to one this is equal to let me do it in new color add 273 to 27 degrees Celsius that's 300 Kelvin and then 50 degrees Celsius is 1 add 273 to it so 50 plus 273 is 323 right so now we can substitute into this formula so p1 1,000 1,000 Pascal's times v1 times 30 divided by the first temperature remember doing kelvins 300 is equal to p2 that we don't know what that is p2 times v1 sorry times v2 this should be a 2 here times v2 times 20 divided by our new temperature 323 let's see we could simplify this we could take 2 zeros off of here take 2 zeros off of here and then we could take a 3 out of here and take a 3 out of here and we're left with 100 all right this is equal to hundred right that was three thousand divided by I'm sorry that's 30,000 divided by 300 and so that's 100 on the left hand side so we have a hundred is equal to P times 20 over 323 and then let me do it up here I'm running out of time and so if I were to just solve for it 323 times 100 equals divided by 20 equals so my new pressure is 16 15 16 15 Pascal's and I just solved this equation and the hard part was converting to Kelvin see in the next video