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# Absolute temperature and the kelvin scale

## Video transcript

so all bodies and systems possess a property called temperature and most commonly temperatures used to refer to how hot or cold something is but the real ciyon see definition of temperature is that it's a measure of the average kinetic energy of the particles in a system so I've got a system and I'm I'm filling it with little individual particles and if we think about this microscopically each little particle in the system is moving in some way whether in rotation or in a straight line or curving but or about by kind of a combination of these means all of these little particles are moving and that energy of motion is called the kinetic energy so all of these moving particles have kinetic energy and so the faster those little particles are moving the greater their kinetic energy and if each of those little particles in the system has greater kinetic energy that means the system as a whole has a larger amount of total energy and we would say that it has a greater temperature because again temperature is a measure of the average kinetic energy of those particles and because knowing the amount of energy in a system can be really useful in chemistry and in physics we've developed temperature scales to help us quantify or measure the amount of this value this value of energy so the three scales most widely used are the Kelvin scale the Celsius scale and the Fahrenheit scale so Ferren Fahrenheit scale and for all of these scales I'm going to draw a little thermometer so one for Kelvin then we have a thermometer for Celsius and then another thermometer for the the Fahrenheit scale and the two scales used most in the physical sciences are probably the Celsius scale and the Kelvin scale so as a point of comparison here on these thermometers the freezing point of water occurs at zero degrees Celsius so we have zero degrees Celsius that's where water freezes and then the boiling point of water occurs at a hundred degree Celsius so the boiling point of water occurs at 100 degrees Celsius that's where water turns into steam and I'm going to write h2o here real quick just so we don't get confused that we're talking about the freezing and boiling point of water now when we use the Kelvin scale we find that water's freezing point is 273 0.15 Kelvin and then we find that water boils at 373 0.15 Kelvin so the differ fundamentally in the zero point the Celsius and Kelvin scales differ in the zero points that they use but between water's freezing point and and and water's boiling point we have a span of 100 temperature units for both scales so although they differ in the in the zero points that they use they use the same size unit or the same magnitude of unit to measure the temperature so converting then between the two scales only really requires that we make an adjustment for the two different zero points and and this is what I mean if we want to know the temperature in Kelvin all we need to do is take the temperature in Celsius and add 273.15 degree you Mnet's to it so if we want to know the temperature in Kelvin for the freezing point of water we take the temperature in Celsius which would be zero and we add 273 point one five units to it and that would give us 273.15 Kelvin now if we want to flip that and if we want to find the temperature in Celsius from Kelvin all we have to do is take the Kelvin figure and subtract 273.15 to it or to subtract 273.15 from it excuse me and so we would see that 373 point 1 5 Kelvin minus 273.15 would give us 100 degrees Celsius so just as another example let's convert 300 Kelvin to Celsius and to start since we're looking for Celsius we'll take that Kelvin value and we'll subtract 273 0.15 from it and that's going to give us 26.8 five degrees Celsius so 26.8 five degrees Celsius is the same thing as 300 Kelvin and I just want to point out really quickly that I'm only using the degree symbol here for for Celsius and I'm doing that intentionally we don't need this symbol with Kelvin scale because instead of calling the temperature units degrees we just call them Kelvin so the only thing we need is an uppercase K now converting between the Celsius and Fahrenheit scales is a little bit more complicated you see in Fahrenheit water freezes at 32 degrees Fahrenheit so 32 degrees Fahrenheit and water boils at 212 degrees Fahrenheit so 212 and this gives us a span between the freezing point and the boiling point of water of a hundred and eighty degree units so we're going to need to consider two different adjustments here one for degrees size because the units have a different magnitude the same value or the same span of temperature is 100 units in Celsius and 180 units in Fahrenheit and we're also going to need to account for the two different zero points zero degrees Celsius for freezing and 32 degrees Fahrenheit for the freezing point of water so first we can say that 180 degrees Fahrenheit is equal to 100 degrees Celsius and again we can say this because both of these magnitudes refer to the same change in total energy and so if we write this as a ratio we have 180 over a hundred which just reduces down to 9 over 5 so the ratio of Fahrenheit to Celsius is 9 to 5 now we need to think about the two different zero points and because 32 degrees Fahrenheit is equal to zero degrees Celsius we can find the Celsius temperature if we take the the temperature in Fahrenheit and we subtract 32 degrees from it and this makes sense because 32 degrees Fahrenheit minus 32 degrees Fahrenheit would give us zero degree use Celsius and now we just need to apply the unit ratio so just like any dimensional analysis problem we need to cancel out the degrees Fahrenheit so if we put the degrees Fahrenheit on the bottom here so nine degrees Fahrenheit we can cancel out the Fahrenheit leaving us with just degrees Celsius so to find the temperature in Celsius we take the temperature in Fahrenheit subtract 32 from it and multiply it by a ratio of five to nine and then we can also manipulate this formula if we want to start with Celsius so all we have to do is solve for the the temperature in Fahrenheit and so to start we would divide both sides by a five over nine or that's the same thing as multiplying by the reciprocal set and then to finish it off we would just add 32 so plus 32 is equal to the temperature in Fahrenheit so now if we want to start with temperature in Celsius we can move to temperature in Fahrenheit or we could start with temperature in Fahrenheit and move to temperature in Celsius and so to practice this let's go from let's go from Celsius to Fahrenheit and it turns out that these temperature scales actually cross paths at a temperature which is kind of kind of a fun fact so if we plug in negative forty let's let's go from negative 40 degrees Celsius to Fahrenheit we'll find that T F is equal to negative 40 times nine fifths plus 32 and so we can reduce this term here so five and negative eight five and negative forty reduces to negative eight so negative eight times nine plus 32 that's negative 72 plus 32 so the temperature in Fahrenheit would equal negative 40 as well so negative forty degrees Celsius is the same thing as saying negative forty degrees Fahrenheit that's kind of just a fun fact and another observation from this little factoid is that Celsius and Fahrenheit scales can both have negative or positive values we see that both can be negative 40 so these can both have negative values and that's actually a point where they differ from the Kelvin scale the Kelvin scale can only have a positive value it turns out that the absolute coldest temperature is zero Kelvin so zero Kelvin is absolute absolute zero and the reason we can't get any colder is that at this point no particles would have any kinetic energy and so that means no motion at all we said that temperature is a measure of the kinetic energy and the coldest that you can get is no no kinetic energy whatsoever and it turns out that the laws of physics specifically the uncertainty principle just don't allow for this so we can get close like within a billionth of a Kelvin but we can't get all the way there and because Kelvin scale always has a positive value it becomes a little handier in various formulas and so it's used as the standard or the standard the SI unit for temperature so I'll show you in future videos why absolute zero happens at negative 273.15 degrees Celsius but I'm starting to run out of timing this one so I'm going to have to save it for later and I'll talk about that with Charles law in the future