Heating and Cooling Curves: Study with Video Lessons, Practice Problems & Examples

Heating and cooling curves illustrate the heat absorbed or released during phase changes. For water, key temperatures are 0°C (melting) and 100°C (boiling). During phase changes, temperature remains constant while average kinetic energy does not change, as heat converts to potential energy. The equations used are $q=mc\mathrm{\Delta T}$ for temperature changes and $q=m\times \mathrm{\Delta H}$ for phase changes. Cooling curves represent exothermic processes where heat is released, forming bonds.

The Heating Curve

In this new video, we're going to take a look at heating and cooling curves. We're going to say here in heating and cooling curves, we have the representation of the amount of heat absorbed or released during phase changes. Now let's pretend that this heating curve represents that of water. We call it a heating curve because you can see that over time as our time increases going this way, our temperature is increasing. We're going to say here that we know that water either freezes or melts at 0 degrees Celsius. And then we should know that water either starts to condense or starts to boil at 100 degrees Celsius. These are key temperatures you need to know for water. If it were some other type of compound, like let's say methanol or hexane, you wouldn't know what their melting or boiling points were. So they would have to tell you those numbers. Okay. So just remember, for water, it's expected that you do know the values of 0 degrees Celsius and 100 degrees Celsius. But for other compounds, they would give it to you whether you're taking that as a quiz, homework, or an exam. Now we're going to notice that at these temperatures of 0 degrees Celsius and 100 degrees Celsius, our line is flat, meaning there is no change in our temperature. So here and here there's no change in our temperature. But then at temperatures that are not 0 degrees Celsius or 100 degrees Celsius, our temperature does change. Now we're going to need room guy. Let's talk about these different phases. We know that below 0 degrees Celsius, it's so cold that water will exist as a solid. We're going to say here that water exists as a solid up to 0 degrees Celsius. Once it hits 0 degrees Celsius, then we're undergoing a phase change. And what's happening here is that our solid water which is ice starts to melt. On this plateau on this line here that's not increasing, we're going to be a solid-liquid mix. The solid is slowly melting into a liquid. At this point here, all of it has melted and now it's completely a liquid. So this part here that's increasing is all liquid. Then when we get to 100 degrees Celsius, which is right here, our water starts to boil and again we're undergoing another phase change. On this line here, we have liquid as well as gas, sometimes called vapor. You can say a liquid-gas mix or liquid-vapor mix. And once we get to this end part here, all of the liquid has evaporated and now it's all gas. As we start to climb up again, it's all gas now. Now let's talk about what's happening at each one of these spots. So here we're going to say this is 135. This is 2 and 4. We're going to say here a few key things that we need to recognize in terms of this heating curve. We're going to say during phase changes. So during phase changes, that means we're talking about segments 24. We're going to say we can tell that temperature remains constant. That's pretty obvious. It's not increasing. It's flat. But here's some other things that are not as obvious. Because your temperature is staying constant, that means your average kinetic energy is remaining constant as well. Just remember, your average kinetic energy is connected to the temperature of your substance. If the temperature of the substance is not changing, your average kinetic energy for that substance won't change either. Now we're going to say here that during these phase changes because this is a heating curve, our particles are going to start to spread themselves out. Because if you think about it, in a solid, all the particles are tightly packed together. Then as we become a liquid, they're moving around more freely but they're still in pretty close vicinity to each other. They're just sliding on top of each other. Then as we become a gas, that's when they really spread themselves out. During our phase changes, again which are these blue parts where the temperature is remaining constant, we're going to say here the particles are spreading out and that's because the kinetic energy again is not changing. The average kinetic energy is staying the same and heat is being transferred into potential energy. During phase changes, heat is transferred into potential energy. Remember, potential energy is just the energy of your position, or in this case, the energy of your state. Solids have the lowest potential energy, liquids have the next highest, and then gases have the highest potential energy. Remember, during these phase changes we're going from one phase to another phase. Now, during temperature changes, what can we say? Here, during temperature changes, we're going to say that heat energy is converted into kinetic energy. Because this is a heating curve and the temperature is increasing, we're going to say increasing temperature would mean that we're going to have an increase in our average kinetic energy. Finally, the last thing we're going to talk about in terms of this heating curve is what type of equations do we use at each one of these positions. We're going to say here our temperature is changing for segment 1 here and so that's going to be q=mcΔT. M equals mass, c represents the specific heat of the substance, ΔT is the change in temperature. That's final minus initial temperature. Now here, water exists as a solid until it gets to 0 degree Celsius where it starts to melt. Here the specific heat will be for the solid. Now we're all accustomed to remembering the specific heat of water when it's a liquid but there's also specific heat of water when it's a solid, so it's ice, and when it is a gas or steam. We'll talk about the Delta H values in a moment. Remember, for line segment 1, because the temperature is changing, it's q=mcΔT. During phase changes, there is no change in temperature so that portion of the equation drops out. It then becomes q=m⋅Δh. M here could be either in grams or moles. How do we know which one it is? We look at the units for delta h. And here in these examples that I give to you, Delta H's have grams in them. So m in this case would represent grams. If it was joules per mole or kilojoules per mole, then m would represent moles. Now, here on this first phase change, we're going from a solid to a liquid. That means we're melting or fusion. Another name for melting is fusion. Then in line segment 3, temperature starts to change again so it's going back to q=mcΔT. On this part of the line, we're a liquid completely. Here this will be the specific heat for the liquid. Then on line segment 4 again, we're undergoing a phase change so there's no change in temperature. So q=m⋅ΔH. On this phase change, we're going from a liquid to a gas. That represents vaporization. We'll use delta H vape. Temperature is changing again. And the temperature is changing again. So q=mcΔT one more time. Here because it's a gas, we're going to use the specific heat for the gas. That's how we look in terms of this heating curve. Below we have the cooling curve. Check out the very next video where I go into looking at the cooling curve. But remember, if you know what the parts of the heating curve are, the cooling curve is just everything in the opposite direction.

The Cooling Curve

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.

Heating and Cooling Curves

How much energy in kilojoules is required to convert 76.4 grams of acetone, here given the molecular weight of it, as a liquid at negative 30 degrees Celsius to a solid at negative 115 degrees Celsius. Alright. So, in this question, we're going from -30 degrees Celsius to -115 degrees Celsius. From the information provided, we see that the melting temperature for acetone is negative 95 degrees Celsius. Now, remember that your melting temperature and your freezing point temperature occur at the same temperature. If we're going from solid to liquid, that represents melting. And if we're going from liquid to solid, that represents freezing. Both happen at the same temperature. So this melting could also be substituted in for our freezing temperature. When we think about this, we know that we're at negative 30 degrees Celsius, and all we're doing is getting colder. Here we have our freezing curve because the temperature is decreasing. We know at -95 degrees Celsius, that's when our liquid will transition into a solid. That's a phase change that's happening here. We are at a temperature higher up than that. So we must go from negative 30 degrees Celsius to negative 95 degrees Celsius, that's our change in temperature. That first portion will help us get our initial heat and because the temperature is changing, this q1=mc∆T. Once we reach negative 95 degrees Celsius, we're undergoing a phase change. And we must then go all the way down to -115, which brings us to our q3=mc∆T. So we have to calculate q1, q2, and q3. Add them all up together to get our qtotal.

Now, let's calculate q1. q1=mc∆T. As we're going from -30 degrees Celsius to negative 95 degrees Celsius, we remain in our liquid phase, getting colder until we start transitioning into a solid. So, bring down the 76.4 grams of acetone, multiply it by our specific heat, and then our change in temperature is final temperature minus initial temperature, so that's negative 95 degrees Celsius minus a negative 30 degrees Celsius. A minus of a minus really means plus. So, it's really negative 95 degrees Celsius plus 30 degrees Celsius. Look at how the units cancel out. At the end, our answer will be in joules. So when we work that out, we're going to get negative 10,726.6 joules, which, when changed into kilojoules, will give me negative 10.7266 kilojoules. That's just our q1. Here I changed it into kilojoules because when we find q2, it will also be in kilojoules, so I'll keep all the units consistent.

For q2, we're at this portion of my cooling curve. q2=m∆h, and the whole process is freezing. Remember freezing and melting occur at the same temperature. Notice the unit says 7.27 kilojoules per mole. We have 76.4 grams of acetone. To change it into moles, we use the molar mass of acetone as 58.08 grams per mole. This calculation gives us 1.31543 moles. This is important as fusion, also known as melting, involves breaking bonds, but here we're freezing, which is the formation of bonds. Formation of bonds is an exothermic process, so bond forming is exothermic with a negative delta H. So, don't forget the negative sign. The moles cancel out, giving us kilojoules, which will be negative, for q2.

Finally, we come to q3. In this part, we're going from negative 95 degrees Celsius

If 53.2kJ of heat are added to a 15.5g ice cube at - 5.00 ^oC, what will be the resulting state and temperature of the substance?

• A. 322.5°C, gas
• B. -3.70ºC, solid
• C. 98.82 ºC, liquid
• D. 222.5 ºC, gas

Here’s what students ask on this topic:

What are heating and cooling curves?

Heating and cooling curves are graphical representations that show how the temperature of a substance changes as heat is absorbed or released. In a heating curve, the temperature increases over time as heat is added, while in a cooling curve, the temperature decreases as heat is removed. These curves also illustrate phase changes, such as melting and boiling, where the temperature remains constant while the substance transitions between solid, liquid, and gas phases. For water, key temperatures are 0°C (melting/freezing) and 100°C (boiling/condensation).

Why does the temperature remain constant during phase changes in heating and cooling curves?

During phase changes, the temperature remains constant because the heat energy added or removed is used to change the phase of the substance rather than to increase or decrease its temperature. This energy is converted into potential energy, which alters the state of the substance (e.g., from solid to liquid or liquid to gas). The average kinetic energy, which is related to temperature, remains unchanged during these transitions.

What equations are used to calculate heat during temperature changes and phase changes?

For temperature changes, the equation used is $q=mc\Delta T$, where $q$ is the heat added or removed, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. For phase changes, the equation is $q=m\times \Delta H$, where $\Delta H$ is the enthalpy change of the phase transition (e.g., fusion or vaporization).

How do heating and cooling curves differ in terms of energy changes?

In heating curves, energy is absorbed by the substance, making the process endothermic. This absorbed energy is used to increase the temperature or to change the phase of the substance. In cooling curves, energy is released by the substance, making the process exothermic. This released energy allows the substance to decrease in temperature or to change its phase. The sign of $q$ is positive for heating (endothermic) and negative for cooling (exothermic).

What are the key temperatures for phase changes in water?

For water, the key temperatures for phase changes are 0°C and 100°C. At 0°C, water undergoes melting (solid to liquid) or freezing (liquid to solid). At 100°C, water undergoes boiling (liquid to gas) or condensation (gas to liquid). These temperatures are crucial for understanding the heating and cooling curves of water.