Hey, guys. So up until now, we've seen calorimetry problems that have only involved temperature changes. But you're going to need to know how to solve calorimetry problems where materials are not only just changing temperature but also phase. What I'm going to show you in this video is that we're going to combine what we know about calorimetry. We are going to use a lot of the same sequence of steps with just a couple of new ones, and we're going to combine it with what we know about latent heats and phase changes. We are going to be using these heat and temperature diagrams to visualize what's going on inside your calorimetry problems. Let's go ahead and check this out here. We're going to jump straight into our example. So, I have an insulated cup that combines 2 different materials. I've got some mass of water that's at 15 degrees Celsius, and then I'm going to put some ice in it to cool it down, and the ice is at negative 20 degrees Celsius. I want to combine these things, so two things happen. I want exactly half of the ice to melt, and I also want the final temperature of that mixture to be 0 degrees Celsius. Alright?

So we know we are going to have to use calorimetry equations, this QA is negative QB, but the very first thing I like to do, what I like to call step 0, is to actually draw the temperature versus q diagram and figure out what the initial temperatures are, so that I can sort of work backwards and find out what that final temperature is going to be. So let's go ahead and check this out. The water is at 15 degrees Celsius, which is going to be here in the water part of the diagram. So this is 15 degrees Celsius. The ice, on the other hand, is somewhere over here below the freezing points. So this is going to be negative 20 degrees Celsius. Now both of these things, right, are going to exchange heats, and they're going to meet somewhere in the middle. What we want is exactly half of the ice to melt, and we also want the temperature to be 0 degrees Celsius. So what that means is that the temperature is 0 degrees Celsius over here on this sort of dotted line but is going to be anywhere along this horizontal line here. Remember, the temperature is the same throughout this whole process. It's just that the phase is changing from ice to water. So what's going on here is if you kind of visualize as you input more heat, at this point, this is the freezing point, melting starts. So we have melting starts here. And then what happens is you input more heat, more ice gets converted to water. And then, basically, what happens over here is here is where you have complete melting. So this is complete melting over here. What we want is for this final mixture to exactly be half ice-melted. So what that means is that we're actually going to be looking here at this halfway point. We know the temperature that's final here is going to be 0 degrees Celsius because we're along this line, and we want exactly half the ice to melt. So we're going to go exactly halfway across this horizontal line. So that's really it. So let's go ahead and get to our first step, which is going to be writing out the calorimetry equation. So, we've got that q_{A} is equal to negative q_{B}. What we have here is we're going to have 1 q per change. What's going on here is if you think about it, we actually have 2 processes that are going on for the ice. The ice, in order for it to get from negative 20 degrees Celsius all the way to melted, has to do 2 things. The first thing ice has to do is actually get up to the freezing point of 0 degrees. I'm going to call this QA1. And the next part is it actually has to melt somewhat or possibly so that half the ice melts, so that's going to be QA2. The water on the other hand only actually has <<- HTML Error: Page break marked incorrectly in text processing: Fixed >>.