Heating and Cooling Curves: Videos & Practice Problems

Understanding heating and cooling curves is crucial for grasping how substances absorb or release heat during phase changes. As a substance heats up, it undergoes an endothermic process, indicated by a positive heat variable ($Q$), absorbing energy to break molecular bonds and transition from solid to liquid (melting or fusion) and eventually to gas (vaporization). Conversely, cooling is an exothermic process, with $Q$ being negative, as the substance releases energy, transitioning from gas to liquid (condensation) and finally to solid (freezing). These transitions are marked by plateaus on the curve where temperature remains constant, allowing complete phase conversion.

Temperature changes involve converting heat into kinetic energy, with the relationship:

$Q=mc\Delta T$

where 'm' is mass, 'c' is specific heat capacity, and '$\Delta T$' is the change in temperature. For phase changes, heat converts into potential energy, maintaining constant average kinetic energy and temperature, using the enthalpy formula:

$Q=m\Delta H$

where '$\Delta H$' is the change in enthalpy. Calculating total energy involves summing the heat calculated at different segments of the curve, using the appropriate formula for temperature or phase changes.

Introduction to Heating and Cooling Curves

In these next series of videos, we're going to take a look at heating and cooling curves, now realizing that heating and cooling curves represent the amount of heat absorbed or released by a substance during phase changes. Now remember, heat uses the variable Q. Here we have a heating curve versus a cooling curve and a heating curve. Our substance is absorbing heat. If it's absorbing heat, that means that it is an endothermic process. So that means Q would be positive. In a cooling curve we are releasing heat, the substance is cooling off. Releasing heat makes it an exothermic process or Q would be negative.

If we take a look here at our heating curve, we have a heating curve for water. Now water can exist as a solid, liquid or gas. Remember, at 0�C we can have the melting of ice, So if we add enough heat to solid ice, it gets to 0�C. At that point is where it undergoes a phase change. And notice that during a phase change there's no change in heat, it's plateaued. That's because a substance is using that heat that it's been absorbing in order to finally break its bonds, loosening up its molecules and transition from a solid phase to a liquid phase. Now remember, going from solid to liquid is melting or fusion, so we can say melting slash fusion can happen here.

Once all of the solid ice is melted into liquid water, it then starts to climb again in terms of temperature, and here is where it exists as a liquid now. Once it gets to 100�C, it's finally reached its next temperature change where it can undergo a phase change. So what 100�C. The liquid water has absorbed enough energy and it can use that energy to finally break itself even further apart into the gaseous phase. Remember, going from a liquid to a gas is a vaporization. If additional energy keeps getting added to the substance, it can go beyond. So at this point it's all changed into gaseous water or water vapor, and then keep climbing up having its temperature change and it exists as a gas. So that's how we look at a heating curve for water.

Now, conversely, if we're looking at cooling of water, we can say that water starts up here as a gas. It's at a temperature that's above 100�C. It could start to slowly release that energy and start to cool off. Once it reaches 100�C, we can say that it finally has released enough energy that it can undergo a phase change. Again, we've reached a plateau. There's no temperature change. It's at this point that the gaseous water is condensing down into a liquid. So here we have condensation. Here it's already a liquid, so it's going to keep releasing heat. And when we get to 100, it undergoes another phase change where temperature remains constant. It plateaus again. Here's where our liquid is becoming a solid. So here it is undergoing freezing and if it keeps releasing heat energy it could keep going and now it's a solid and temperatures changing again.

So think of these two things as mirror images of each other. We can see that vaporization and condensation both can occur at 100�C and melting fusion can occur at 0�C, just like freezing can. Think of this, when you're looking at the temperature changes involved with any substance as it's going between these phase changes, we can see that the temperature plateaus so that it can convert fully into new new phase and before it can continue to move up or down in terms of temperature change, right. So now that we get the basic idea of what a heating and cooling curve is, we'll continue onward with additional calculations.

Temperature Changes vs PhaseChanges

Now realize that with heating and cooling curves, there are significant differences between temperature and phase changes. Now taking a look at some of the key differences here with temperature changes we have heat being converted into kinetic energy, so the energy of motion and realize that the higher our temperature gets, the higher kinetic energy will be as well.

With temperature changes we have our specific heat capacity formula where Q=MCΔT. Q represents our heat. M can either be grams or moles and it depends on the units. For our specific heat capacity, which is C ΔT is just change in temperature, which is final temperature minus initial temperature.

Now with a phase change, we're going to say that if we look at our heating and cooling curves, we saw that the temperature plateaued. It didn't change. That's because heat is being converted into potential energy and we know that there's a connection between temperature and kinetic energy. So if your temperature is not changing, then your kinetic energy also would not change.

So here our average kinetic energy is constant and temperature is constant. It's not changing with a phase change. We use our new enthalpy formula which is Q=m×ΔH which again can either be in grams or moles times our change in enthalpy, so ΔH. So keep this in mind what temperature changes. We use our heat capacity formula but with phase changes where temperature is remaining constant. We have our enthalpy formula here.

Cooling Curve Example

Identify the line segment on the diagram where specific heat of liquid water is used to calculate energy flow. So remember here this is a cooling curve above 100�C. We exist in the gaseous phase. Remember, we're looking for liquid water. Once we reach 100�C, that's where we undergo our first phase change. Here we're going from a transition of a gas to a liquid.

Now we want only the liquid form of water and that starts to occur at Point C. Going down from C to D is where we finally have only liquid water. D to E would be us going from a liquid to a solid, another phase change, and then from E to F would be our solid form.

Now if we look here on line segment CD, since we're undergoing a temperature change, because we're going from 100 to 0, we'd use Q=MCΔT here, where here our specific heat capacity C would be the specific heat capacity of liquid water. If we're dealing with the gas, we'd still use Q=MCΔT, which would be the specific heat of gaseous water. And then here it would be the specific heat of ice.

Now again going back to the question, we're looking for liquid water. So that would mean the answer is option C. Line segment CD would have the specific heat of liquid water.

Calculations with Heating and Cooling Curves

So at this point we're thinking conceptually when it comes to heating and cooling curves. Now recall there's two formulas used to calculate heat at different parts of the curves. If we're undergoing temperature changes, then we have to utilize the specific heat capacity formula. Here it would be Q=mcΔT, where c (specific heat capacity) is based on the substance existing as a gas, a liquid or solid.

Now at phase changes, our temperature is constant, it plateaus. At this point we've utilized the enthalpy formula, which is Q=m∗ΔH. Here m could either be grams or moles. The units depend on what the value of ΔH is. Now we're going to use these two formulas to calculate our total energy involved in a heating and cooling curve.

So basically we'd add up each of the line segments from either the heating or cooling curve and add them all together, so Q1+Q2+Q3 and so on if necessary. And that'll help us find out the total heat or total energy involved.

Energy Calculation Example

How much total energy in Joules is required to convert five 5.8 grams of ice at -5�C to a gas at 100�C? All right, so step one is we draw the necessary curve and label all the changes. We're starting off at ice because we are starting out below freezing point. So let's say five degrees -5�C is here and we're going to climb until we hit 100�C and undergo a phase change. This is where our ice starts to melt into a liquid. Once it's fully melted, it becomes a liquid and it continues to climb up until we hit 100�C. At this point our liquid starts to become vaporized into a gas.

Now we don't go beyond 100�C because we're stopping exactly there, so these would this would be our curve that we're dealing with in terms of this question. Now here we have to identify all the heats involved along with the necessary formulas. So here we're a solid, here we're transitioning from a solid to a liquid, here we're a liquid, and here we're transitioning from a liquid to a gas. Remember what the phase changes, no temperature change is occurring. So for them we'd say Q=M⁢ΔH here going from a liquid to a gases vaporization, so we'd use delta H vape. Here we're going from a solid tool liquid. So here it would be Q=M⁢ΔH Going from a solid to a liquid is melting or fusion.

And then here what the temperature changes we're going to use MCAT. So here Q=M⁢C⁢ΔT and here Q=M⁢C⁢ΔT. We need to add up all the queues together, so we calculate all the heats Q involved using appropriate specific heats and enthalpies of a substance involved. Now here, since this is a heating curve, it's endothermic, so all the signs would be positive for specific heats. And for enthalpies, if we're undergoing a cooling curve, we'd be releasing heat. So they all would have a negative sign. They would have a negative sign in terms of our enthalpy of fusion and our enthalpy of vaporization.

All right. So now we're going to Add all these up together. So let's say this is Q1 where we started, Q2Q3 and Q4, we're going to do the math here. And once we do that, we go to step four. We add them all together to get our total energy or total heat involved, All right. So Q1 has to do with us going from -5�C to 100�C. Q2 has to do with DO with us being at 0�C where a phase change occurs. Q3 has to do with us going along and increasing temperature as a liquid. So Q=M⁢C⁢ΔT again. Oh, actually it's more specific. We're going to say it's from 0�C to 100�C and then Q4 is at 100�C.

So remember, as the temperature is changing, those become Q=M⁢C⁢ΔT, so Q=M⁢C⁢ΔT here. Q=M⁢C⁢ΔT here at 0�C and at 100�C. These are phase changes. So Q=M⁢ΔH Add 0�C. It's delta H of fusion because we're melting and at 100 we're being vaporized. So Q=M⁢ΔH of vaporization. All right, so now we're going to plug in the numbers that we know. We're dealing with 55.8g of water here. It is solid ice, right? So the specific heat of ice is this. So 2.09 Joules over grams times degrees Celsius. And delta T is final temperature minus initial temperature, so that's 0 minus, or -5 which is a +5. So this comes out to 583.11 Joules.

For here we're dealing with 55.8g. Again, delta H of fusion is 334 Joules over grams, so grams cancel out and we have 18637.2 Joules. Here we're dealing with zero to 100�C, which means we're dealing with liquid water. So we're going to use the specific heat of liquid water, which is 4.184. So Q here equals 55.8g * 4.184 Joules over grams times degree Celsius, and then it's final temperature minus initial temperature. So this comes out to 23346.72 Joules and then finally add 100�C. We have to convert all of the liquid water into gas. South mass is 55.8g. Enthalpy of vaporization is 2260 Joules over grams. So here this comes out to 126108 Joules.

So all we have to do here is we have to add up each one of these queues that we got. So this plus this, plus this plus this. So we'd say here Q total is US adding all of them together. When we add the mall together we get one six 8675.03 Joules. Here let's do this in terms of three sig fix. So this comes out to 1.69 * 10 to the five joules. So this is the amount of heat energy that had to be absorbed for us to transition from ice at -5�C to gas at 100�C. So just keep in mind when we're undergoing a temperature change, we use Q=M⁢C⁢ΔT. Hase changes temperatures, staying constant, so it becomes Q=M⁢ΔH.

How much energy (kJ) is required to convert a 76.4 g acetone (MM = 58.08 g/mol) as a liquid at -30°C to a solid at -115.0°C?

• A. -11.406 kJ
• B. -39.820 kJ
• C. -22.811 kJ
• D. -82.592 kJ

Answer: (C)

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

Answer: (A)

Here’s what students ask on this topic:

What characteristics are shared by both heating and cooling curves?

Heating and cooling curves are graphical representations that show how the temperature of a substance changes as heat is added or removed. Both types of curves share several key characteristics:

1. Plateaus (or flat parts of the curve): These occur at points where the substance is undergoing a phase change. During these periods, the temperature remains constant because the energy added or removed is used for the phase transition, such as melting, freezing, boiling, or condensation, rather than for changing the temperature.
2. Sloped sections: These represent periods where the substance is either heating up or cooling down in a single phase (solid, liquid, or gas). The temperature changes at a rate dependent on the specific heat capacity of the substance in that phase.
3. Temperature axis: Both curves have a temperature axis (usually the y-axis) that indicates the temperature of the substance.
4. Heat energy axis: Both curves have an axis (usually the x-axis) that represents the amount of heat energy added or removed from the substance.
5. Phase change identification: Both curves allow you to identify the different phases of a substance (solid, liquid, gas) and the transitions between these phases based on the temperature plateaus.

By analyzing these curves, you can determine the temperatures at which a substance will melt, freeze, boil, or condense, and how much energy is involved in each.

Why do heating and cooling curves have plateaus instead of being a single straight line?

Heating and cooling curves have plateaus because they represent the phase changes of a substance, during which temperature remains constant despite the continuous input or removal of heat. This happens because the energy added or removed is used for breaking or forming intermolecular bonds rather than increasing the kinetic energy of the particles, which would raise the temperature.

For example, when ice is heated, it absorbs heat energy as it warms up to its melting point. Upon reaching this temperature, the curve plateaus because all the heat energy goes into breaking the hydrogen bonds between the water molecules, transitioning the ice from a solid to a liquid. The temperature does not increase during this phase change. Only after all the ice has melted will the temperature of the water start to rise again as the added energy increases the kinetic energy of the water molecules. The same concept applies to cooling curves when a substance transitions from a gas to a liquid or a liquid to a solid.