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Sal says "degrees Kelvin" in this video, but he means "Kelvin". Temperature measured in Kelvin is not expressed as degrees.

Specific heat, heat of fusion and vaporization example

Video transcript

a couple of video goes we learned that if we started with solid water or I set a reasonably low temperature I don't know maybe this temperature right here is minus ten degrees Celsius and we could deal with Celsius when we're dealing with these phase changes because we really just care about the difference in temperature and not necessarily the absolute temperature so when you go from the different one degree in Celsius is the same thing as one degree in kelvins so the differences are the same whether you're dealing with Celsius or Kelvin so we're starting with minus 10 degree Celsius ice or solid solid water and we learned that as you heat it up as you add heat energy to the water the temperature goes up the the molecules at least while they're in that ice lattice Network they just start vibrating and their average Candida kinetic energy goes up until we get to zero degrees which is the melting point of water and at zero degrees we already learned something interesting happens the in created heat in the system does not increase the temperature of the ice anymore at least over that little period right here what's happening is that heat energy is being used to kind of break the lattice structure to add potential energy to the ice or it essentially melt it so for it here right here where ice right at this point where zero Degree ice and then as we add more and more heat we get to zero degree water so at zero degrees you can either have water or ice and if you have water to turn it into ice you have to take heat out of it and if you have ice and you want to turn into water you have to put heat into it and then the heat is used again to warm up the water at some rate and then at a hundred degrees which is the boiling point of water right here this a similar phase change happens where the increased heat is not used to increase the temperature of the water it's used to put potential energy into the system so the water molecules are are forced away from each other the same way that if I'm forced away from the planet Earth I have potential energy because I can fall back to the earth similarly the they have the potential energy of falling back to each other but this energy right here is the energy necessary to vaporize the water right here you have 100 degree water 100 degree liquid liquid and here you have 100 degree vapor water vapor and then as you add more and more heat and once again increases the temperature but you say Sal I've already I learned this few videos ago I I have the intuition but I want to deal with real numbers I want to know exactly how much heat is required for these different things to happen and for that we can get these numbers and these are specific to the different states of water if you looked up any other element or molecule you would have different values for these numbers we're going to be dealing with right now but this first number right here is the heat of fusion and this is the amount of heat is required to fuse 100 degree water 100 degree water into 100 degree ice or the amount of energy you have to take out of the water so this distance right here or along this axis is 333 joules if you're going in the leftward direction you have to take that much out of the system to turn into ice if you're going in the rightward direction you have to add that much to turn into water so heat of fusion and it's called a heat of fusion because when you fuse something together you make it solid so it could also be considered the heat of melting that's just two different words for the same thing depending on what direction you go in the important thing is the number 333 similarly you have the heat of vaporization 2257 joules per gram let me write that 2257 that's this distance along this axis right now here so if you had one gram of 100 degree liquid water and you wanted it to turn into one gram of 100 degree liquid vapor and we're in all of this we're assuming that that nothing silly is happening to the pressure that we're under constant pressure you would have to put 2257 joules into the system if you had 100 degree vapor and you wanted to condense it you would have to take that much energy out of the system okay fine you know how to how much energy is required for the phase changes but what about what about these parts right here how much energy is required to warm up let's say a gram of ice by one degree Celsius or Kelvin and for that we look at the look at the specific heat it takes to joules of energy to warm up one gram one degree Kelvin and when when water is in the solid state when it's in the liquid state it takes about double that it takes about four joules per gram to raise it one degree Kelvin and when you're in the vapor state it's actually more similar more similar to the solid state so given what we know now we can actually figure how out how much energy it would take to say go from minus 10 degree minus 10 degree ice to 110 degree vapor let's work this out so the first thing we're going to be doing is we're going to be going from minus 10 degree ice to zero Degree ice zero Degree ice so we're going to go 10 degrees so we have to figure out how much heat does it take to warm up hight ice by 10 degrees so the heat is going to be equal to our change in temperature so actually let me write the we could write the specific heat first so 2.05 joules per gram Kelvin let me write that down to 0.05 joules per gram Kelvin our specific heat times oh and I should tell you we can't you know we're gonna have different values for the amount of ice we're warming up to vapor so let's say we're dealing with 200 grams so it'll be the specific heat times the number of grams we're warming up of ice times the change in temperature that we're trying to get so times 10 degrees well this is Kelvin here so let's just say where it's 10 degrees Kelvin change it doesn't matter we're using Kelvin or Celsius I could have written a Celsius here too in the unit's let's put Celsius right there Celsius so what is that equal to get the calculator clear it out two point zero five times 200 times whoops let me do it over two point zero five times 200 times 10 is equal to 4100 Jules let me do this in a different color so radio this is 4,100 joules fair enough now so what we've done is just this part right here this this distance right here is 4,100 joules now we have to turn that zero Degree ice into zero degree water so now we have to go zero Degree ice to zero degree water and for that we use the heat of fusion we're adding that amount of heat so it's 330 3.5 Julz per gram so it's three so that's equal to three thirty five point five five joules per gram times we have 200 grams of ice that we're trying to melt so that is what so let me get the calculator out so I have three thirty five point five five times 200 is equal to sixty seven thousand 110 so we have so that's equal to let me do it in that color so it can sum up at the end sixty seven thousand one hundred and ten joules to melt the water now or take it from ice to water now we have to go from and this is the big one we have to go from zero degree water to 100 degree water to 100 degree water or liquid water right and this is in the liquid state so now we take the specific heat of water which was four point one eight one seven eight I for some reason I'm thinking it's four point one seven six but it doesn't matter let's say it's four point one seven eight I might be off a little bit on that number but it's a it's a digits not that significant joules per gram Celsius times 200 grams times let me write the unit's times 200 grams times 100 degrees Celsius and notice the Celsius and the Celsius cancels out the grams and the grams cancel out so we are left with joules which is what we want we want to know how much heat or how much energy we're adding to the system so let me get the calculator out so this stage the stage is going to be four point four point one seven eight times times 200 times 100 is equal to nope I did something wrong I think I press the negative oh I press the negative button instead of the times four point one seven eight times 200 times 100 is equal to eighty three thousand five hundred and sixty joules okay so we get eighty three thousand five hundred and sixty and does that look about right let's see four times two hundred eight hundred eight hundred times one hundred yeah that's about right Jules now we're dealing with 100 degree water vapor and we have to turn that 100 degree water vapor 100 degree vapor to 110 degree vapor so we use the specific heat of vapor one point eight nine joules per gram Kelvin one point eight nine joules per gram Kelvin multiplied by the amount of vapor we're dealing with 200 grams that obviously doesn't change we're not adding or taking away mass from the system times the temperature change times ten so what is that let me get the calculator out again so we're dealing with a 10 degree change 10 degree Celsius times 200 times one point eight nine times one point eight nine is equal to three thousand seven hundred and eighty three thousand seven hundred and eighty and I just realized I made a horrible mistake because look I just this over here I mean it's not a replicable it mistake otherwise I would rerecord the video but I just figured out the amount of energy to take it from zero degree water to 100 degree water which is this energy right here right and now I just calculated how much energy to go from 100 degree vapor to one ten degree vapor which is this right here that distance right here I forgot to figure out how much energy to turn that 100 degree water into 100 degree vapor so that's key so that I really should have done up here right before I calculated the vapor but I'll do it down here so to do 0 or 100 degree water to 100 degree vapor right that's this step right here this is the phase change I multiplied the heat of vaporization which is 2257 joules per gram times 200 grams and this is this is let's see clear it out 2257 times 200 is equal to 450 1400 during that blue color 450 1400 joules so this piece right here is 450 1000 for our exempt for our sample of 200 grams this piece right here went was 83,000 joules this piece right here was three thousand seven hundred eighty jewel jewels so to know the total amount of energy then with total amount of heat that we had to put in the system to go from minus 10 degree ice all the way to 110 degree vapor we just add up all of the energies we had to do to all of these steps let's see and I'll do them in order this time so to go from to go from minus 10 degree ice minus 10 degree ice to zero Degree ice and of course we have 200 grams of it it was 40 140 100 plus plus I'll just plus the 67,000 so plus I'm just doing this off the screen so plus 67,000 1 110 plus 83,000 that's to go from zero degree water to degree water plus eighty-three thousand five hundred and sixty so 154,000 right now to just to get to 100 degree water and then we need to turn that 100 degree water into 100 degree vapor so you add the four hundred and fifty one thousand so plus four hundred fifty one four hundred is equal to 606 and then finally we add it we're at 100 degree vapor and we want to convert convert that to 110 degree vapor so it's another thirty-seven hundred joules so plus three thousand seven hundred and eighty is equal to six hundred nine thousand nine hundred and fifty joules so this whole thing when we're dealing with two hundred grams when you're going from minus ten to 110 and remember this is for two hundred grams it took us six hundred and nine thousand nine hundred and fifty joules or 609 kilojoules to do this and before so that by itself is an interesting thing you might think oh wow this is a huge number but it actually turns out joules isn't a lot of work kilojoules starts to become a little bit interesting because you might realize two hundred grams of ice that's that's about half a pound of ice so to take half a pound of ice and to warm it up on your stove would take 609 kilojoules kilojoules of heat to do that so that's something that you probably could do on your stove at home
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