In our discussion of the heating curve, we learned a few things. Now, let's apply what we learned to the cooling curve. From the name, we know that it is going the opposite way. But actually before we begin talking about the cooling curve, let's go back to the heating curve. Let’s talk about we talked about all the different portions of the heating curve but I neglected to tell you why the lengths of things are different. Notice that the basic phase change from a solid to a liquid is smaller than from a liquid to a gas. That's because when you're going from a solid to a liquid, you're basically freeing the molecules from being completely stuck together. But even in a liquid, they're still pretty close to one another. You didn't separate them by that much of a distance. Therefore, the basic melting time is not going to be that big. But if we're going from a liquid to a gas, you actually have to separate the molecules very far apart because in gases, the molecules are great distances away from each other. And to go from being sliding on top of each other, being close together to being very separated, that requires a good amount of time, a good amount of energy. That's why the size of this line here is much larger. Oops, and it just disappeared. That's why that line there is much larger because it takes way more energy to be absorbed in order to go from a liquid to a gas because you're trying to spread the molecules even farther apart. Remember, in all this process, we're taking in heat. That means our q will be positive. This is an endothermic process where heat is being absorbed by the water so that we can break bonds.

In a cooling curve, we're releasing heat because remember if you're releasing heat, molecules are very energetic. They're bouncing everywhere and you're trying to cool them off. How do you do that? You give them time to release their excess energy and they move slower, move slow enough and it'll start to stick together. In a cooling curve, we're releasing heat. q is negative which will mean that we're exothermic. And the whole point of an exothermic process is to form bonds.

Now, if we take a look here, we can still think of this in terms of water. At 100 degrees Celsius, water can either become vaporized where it's going from a liquid to a gas or it could start to condense. Here, remember we have an equilibrium between liquid and gas. It's a liquid gas mixture. Here that would mean that our ΔH of vaporization would equal the ΔH of condensation. Remember, condensation means you're going from a gas to a liquid so you're forming bonds so it's an exothermic process so it's negative. This would be negative. They're related to each other. Say they're equal. I'm going to say they're directly related to each other. Then, here at 0 degrees Celsius, water can either start to melt or it can start to freeze. Here we can say when we're talking about ΔH of fusion which deals with melting, we could connect that to ΔH of freezing. Why am I telling you this? Because I want you to realize here that I gave you ΔH of fusion here and ΔH of vaporization. We could change this to freezing. All we have to do is make the sign negative because freezing means we're making bonds to your exothermic so the sign will become negative. Here, vaporization is related, is connected to condensation. And here that would mean the sign is negative.

Okay. We'd still have at these parts, q=m⋅ΔH. But now this would be ΔH of condensation. And then here this would be q=m⋅ΔH of freezing. And then here we'd have these temperatures changing. So those would be q=mcΔT. Here, remember we're a gas completely, which would mean that this c is for gases, for the gas form. Here, we are all liquid. This c would be for the liquid version of water. Here we're solid. So c here would be for the solid form of water. As we start to look at examples and questions and the calculations that are involved, keep in mind some of the key features we've talked about in terms of heating curves and cooling curves. Heating curves, we have to absorb energy in order to go from one phase to another. Absorbing energy means that we're endothermic so our values would be positive. If you're in a cooling curve, you're releasing heat in order to form bonds so you're exothermic. So your variables, your values will be negative. You'll get q's that are negative at the end. So keep in mind these fundamentals and as we look at questions, apply what we learned here to answer those questions.