 The first new thing that we're going to talk about is how much energy it takes to melt something. Where you can think of it in reverse, how much energy is released when you freeze something. They're going to be the same thing, but for the most part I'm going to think about it and I'm going to talk about it in terms of how much energy it takes to melt some solid things. So we're going to be talking about this flat area here. The concept behind how much energy it takes to melt something that's solid is called heat of fusion and the concept is sort of illustrated with another thought experiment. Imagine that I have one gram of ice cubes at zero degrees Celsius. So they're just about to melt, the zero degrees Celsius is the temperature the ice melts at. And let's pretend that it takes one candle's worth of energy. I have to burn one candle to melt my one gram of ice cubes completely. If that's true, then if I have two grams of ice at zero degrees Celsius, and it's important that it's at zero degrees Celsius, because this has to be done just at the point where the solid material is about to melt. If I have twice as much ice at the same temperature, then it's reasonable to assume that it's going to take twice as much energy. So it's going to cost me two candles worth of energy to melt twice as much ice. This idea of it takes a certain amount of energy to melt a certain amount of material is called heat of fusion. The slightly more formal definition of heat of fusion is how much heat or energy do I have to add to one gram of some solid in order to melt it. And I want to change one thing, one solid that's just about to melt. In other words, write the melting temperature. It has to be at that point, otherwise you're going to have to do a specific heat calculation too, because you're going to have to raise the temperature of the material. So heat of fusion only works when the temperature of the stuff doesn't change. We are going from ice cubes, so this is an ice cube that is at zero degrees Celsius, and we are turning it into liquid water that is also at zero degrees Celsius, and as you can see the temperature is not changing. Heat of fusion, again just to emphasize if you got lost in all of this, is how much energy do I need to add to one gram of some solid that's just about to melt in order to melt it. And it will be a different amount of energy for different somethings. For water it's a certain amount of energy for every one gram of solid water that's just about to melt. For aluminum it will be a different amount of energy. For gold it will be something different. You can think of it in reverse, you can think of it down here, in reverse how much energy do I have to remove from one gram of a liquid that's just about to freeze in order to freeze it. And if you're doing things very carefully the amount of energy that it takes to melt something is, one gram of something is going to equal the amount of energy that gets released when you take one gram of a liquid and freeze it. So the energies will be the same, you're just going in different directions. Again, there are different numbers for different materials. For water the heat of fusion of water is about 80 calories per gram of water. In other words, I'm going to write it as maybe a more proper fraction, I'm not sure if that's the correct term, but if you have 80, if you have one gram of water of let's say ice at zero degrees Celsius, it's going to cost you 80 calories of energy in order to melt that one gram of ice and this is called the heat of fusion of water. And so heat of fusions are usually going to be written as some number, I'm just going to call it x calories or joules. So the total is another unit for measuring energy per one gram of my material, right at the melting temperature. So in this x it's going to be a different number for different somethings. For water it happens, x happens to be 80 calories and so it's going to cost you 80 calories to melt a gram of ice. For different substances it will be a different number. Again, don't memorize these numbers, I would give them to you on a quiz or a test but you should understand that heat of fusion numbers tell you how easy it is to melt something or how easy it is to freeze something and it's more specifically how much energy it's going to take you to do to do the melting or the freezing and it's usually written as energy per one gram of whatever material you're talking about. So here's an example, you have 26 grams of ice cubes at zero degrees Celsius. Again, what's special about this? This is the melting temperature for water. And so we have 26 grams of ice cubes, you add them to your Coca-Cola or whatever and first question is how much energy is needed to melt all of the ice and I tell you that the heat of fusion of water is 80 calories per gram. So and the second question is what happens to the temperature of the Coca-Cola and why? You can pause and work through this if you want and when you unpause I'll go through it. So what I would say is I'm going to write this as a fraction, I'm going to say 80 calories is how much energy I need to melt one gram of ice and just to be formal at zero degrees Celsius. The nice thing is the question tells us we are at zero degrees Celsius but this is how much how much energy it takes to melt one gram. Do we have one gram? No, we have 26 grams so I'm going to make an equal fraction over here and instead of one gram I'm going to write 26 grams of ice at zero degrees Celsius in the denominator and then I'm going to put an X here for calories because I don't know how much it's going to take and so if we want to solve for X we can cross multiply again. We can do 80 calories times 26 grams is equal to one gram times X calories. One gram times X calories and we need to get the X all alone so to get rid of the one gram to get the X all alone we'll divide both sides by one gram divide the left side by one gram as well on the right side the one grams cancel out on the left side the gram units cancel out the only unit that I'm left with is calorie which is what we wanted we wanted to know how much energy it's going to take and so X calories is equal to 80 times 26 calories which is 2,080 calories again I don't really care about significant digits I care that you know how to do the calculation so if you had a gram of ice that was just about to melt it would only cost you 80 calories but we don't we have 26 times as much so it's going to cost us 26 times as much energy or roughly 2,080 calories worth of energy to melt our 26 grams of ice cubes so that's the answer to the first question 2,080 calories second question is more general it says what happens to the temperature of the Coca-Cola the answer is the temperature of the Coca-Cola goes down it drops the reason is the energy that was used to melt our 26 grams of ice those 2,080 calories that was used to melt it they had to come from somewhere and what that where they came from is where the ice cubes got dropped into they got dropped into the Coca-Cola so basically there was energy in the Coca-Cola that was used to melt the ice and if energy got used from the Coca-Cola that basically means energy or heat left your Coca-Cola and because energy or heat left the temperature of your coke of your liquid coke went down and that's basically how ice cubes work to cool things down there there's when you drop ice cubes into some liquid drink energy is taken from the liquid and used to melt the ice and as that energy is being used to melt the ice it leaves the liquid and it basically makes the liquid get cooler so that's a reasonable way of thinking about how ice cools things down but what we have done here is called a heat of fusion calculation we figured out how much energy it took to melt 26 grams of ice cubes and again don't memorize 80 calories per gram of water it's a colossal waste of time to do that but you should be able to use that information if it shows up on a quiz or a test the other flat area that we were going to talk about we go back is this flat area here this was when we vaporize or or condense a liquid or when we vaporize a liquid into a gas or we condense a gas back into a liquid the same concept works in that flat area as worked in the heat of fusion calculation but it just deals with boiling so let's go here the concept of how much energy it takes to boil away one gram of something is called heat of vaporization the concept is again still the same imagine I have very hot liquid and I have one gram of it it's just about to boil away and pretend that it takes one candle's worth of energy to boil it away I have one gram of it if I have twice as much very hot liquid then it's going to take two grams two candles worth of energy to boil it all away and this idea of how easy or difficult it is to vaporize or boil away something is called heat of vaporization more formally it's how much energy heat or energy do I have to add to one gram of a liquid that's just about to boil away about to boil away in other words it has to be right at the boiling temperature to vaporize it into a gas and it will be a different amount of energy for different some things for water it will be a certain number if it was gasoline which is a liquid it would be a different number it would be a different amount of energy you can think of it in reverse how much heat or energy do I have to remove from one gram of a gas in in order to turn it or condense it back into a liquid and again the gas has to be right at the point that's just about to condense for you to do these calculations and so as an example the heat of vaporization of water is about 540 calories per gram of water what that means in English is if I have one gram of liquid water at 100 degrees Celsius which is the temperature that water boils at it's going to cost me 540 calories to boil it all the way so and this is called the heat of vaporization of water and again whenever you write heat of vaporization it'll be something x energy units could be calories could be joules there are other units for energy too but those are the most common ones per one gram of something and this x over here it'll be a different number for different somethings for water it's 540 for gasoline I don't know what it is but it's something different and so don't memorize those numbers they will show up on a quiz or a test and you'll have to understand how to use them but again it's a waste of time to memorize the numbers themselves so I'm not going to do a heat of vaporization calculation because it's essentially identical as the heat of fusion calculation that we did for melting and freezing so that's it for heat of vaporization and heat of fusion