**Heating and Cooling Curves** represent amount of heat (q) absorbed or released by a substance during phase changes.

Heating & Cooling Curves

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concept

## Heating and Cooling Curves Concept 1

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in these next series of videos, we're gonna 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. Remember heat uses the variable Q. Here we have a heating curve versus a cooling curve. In a heating curve, our substance is absorbing heat. It's if it's absorbing heat, that means that it is an endo thermic 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 Excel thermic process. Or if you 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 is no change in heat. It's plateau. That's because the substances 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. I remember going from solid to liquid is melting or fusion. So we can say melting slash fusion can happen here once all of these solid ice is melted into liquid water, it then starts to climb again in terms of temperature and here is where 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 gashes 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 gasses, 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 can 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 at this point that the gasses water is condensing down into a liquid. So here we have compensation here, it's already a liquid, so it's gonna 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 can 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 degrees Celsius and melting slash fusion can occur at zero degrees Celsius, just like freezing, kat, 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 you can continue to move up or down in terms of temperature change. Right? So now that we get the basic idea of what the heating and cooling curve is, we'll continue onward with additional calculations.

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## Heating and Cooling Curves Concept 2

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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 equals M cap que represents our heat em can either be grams or moles and it depends on the units for our specific heat capacity which is C delta T. Is just changing 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 courage, we saw that the temperature plateau, it didn't change. That's because he 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 are average kinetic energy is constant and temperature is constant. That's not changing. With a phase change. We use our new entropy formula which is cute equals M. Which again can either be in grams or moles, times our change in entropy. So delta H. So keep this in mind. When temperature changes, we use our heat capacity formula but with phase changes where temperature is remaining constant, we have our entropy formula here

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example

## Heating and Cooling Curves Example 1

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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 degrees Celsius. We exist in the gashes phase. Remember we're looking for liquid water once we reach 100 degrees Celsius, 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 when we finally have only liquid water. D. D. E would be us going from a liquid to a solid. Another phase change and then from E to F would be our sod. For now if you look here on line segment CD Since we're undergoing a temperature change because we're going from 100-0, we use Q equals and cat here we're here are specifically capacity C would be the specifically capacity of liquid water. If we're dealing with a gas, we'd still use two equals N CAC would be the specific heat of gasses, 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

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## Heating and Cooling Curves Concept 3

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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 be Q equals and cap where see our specific heat capacity is based on the substance existing as a gas, a liquid or solid. Now at phase changes, our temperature is constant. A plateaus. At this point we utilize the entropy formula, which is Q times M. Q equals M times delta H. M. Here could either be grams or moles. The units depend on what the value of delta H is. Now we're gonna use these two formulas to calculate our total energy involved in a heating and cooling curve. So basically we add up each of the line segments from either the heating or cooling curve and add them all together. So Q one plus Q two plus Q. Three and so on if necessary. And that will help us find out the total heat or total energy involved.

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example

## Heating and Cooling Curves Example 2

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how much total energy in joules is required to convert 55.8 g of ice at negative five degrees Celsius to a gas at 100 degrees Celsius. 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 negative five degrees Celsius is here And we're gonna 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 start 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 are a solid here we're transitioning from a solid to a liquid. Here were 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 equals M times delta H. Here going from a liquid to a gas is vaporization. So we use delta H. Vape here we're going from a solid to a liquid. So here it would be Q equals M times delta H. Going from a solid to a liquid is melting or fusion. And then here what the temperature changes, we're gonna use em cat. So here Q equals M. Cat and here Q equals M. Cap. We need to add up all the cues together. So we calculate all the heat Q. Involved using appropriate specific heats and M. Papi's of a substance involved. Now here since this is a heating curve, it's endo thermic. So all the signs would be positive for specific heats and for entry piece if we're undergoing a cooling curve we'll be releasing heat. So they would have a negative sign. They would have a negative sign in terms of our entropy of fusion and our entropy of vaporization. Alright, so now we're going to add all these up together. So let's say this is Q. One where we started Q. Two, Q three and Q four. We're gonna 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. So she won has to do with us going from negative five degrees Celsius 200. Re Celsius, Q two has to do what I do with us being at 0°C or phase change occurs. Q three has to do with us going along and increasing temperature as a liquid. So Q equals M. Cat again. Well actually it's uh more specifically we're gonna say it's from 0°C to 100°C and then Q four is at 100°C. So remember as the temperature is changing those become cuticles. And castle Q equals M. Cat here, Q. Equals and cat here top at zero degrees Celsius. And at 100 degrees Celsius, these are phase changes. So Q. Equals M. Times delta H. Ad zero degrees Celsius. It's delta H. Infusion. Because we're melting and at 100 were being vaporized. So Q. Equals M. Times delta H of vaporization. Alright, so now we're gonna plug in the numbers that we know we're dealing with. 558g of water. Here it is solid ice. Right? So the specifically devices this so 2.09 jules over g times degrees C. And Delta T. is final temperature minus initial temperature. So that's 0 -1 -5. Which is a positive five. So this comes out to 583.11 jewels. For here we're dealing with 55.8 g. Again, Delta HF fusion is 3 30 for jules over grants. So g cancel out. And we have 18637.2 jewels Here we're dealing with 0-100°C, which means we're dealing with liquid water. So we're gonna use the specific heat of liquid water which is 4.184. So cue here equals 55.8 g times 4.184 jewels over grams times degree Celsius. And then it's final temperature minus initial temperature. So this comes out to 23 346. jewels. And then finally At 100°C, we have to convert all of the liquid water into gas. So mass is 55 8 g. Entropy of vaporization is 2 to 60 jewels over grams. So here this comes out 1-6108 jewels. So all we have to do here is we have to add up each one of these cues that we got. So this plus this, plus this, plus this. So we'd say here talk, you total is us adding all of them together. When we add them all up together, we get 168, 03 jewels Here, let's do this in terms of 366. So this comes out to 1.69 times 10 to the five jewels. So this is the amount of heat energy that had to be absorbed for us to transition from ice and negative five degrees Celsius to gas at 100 degrees Celsius. So just keep in mind when we're undergoing a temperature change, we use Q equals end cap at phase changes, temperatures staying constantly becomes Q equals and times delta H.

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Problem

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

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Problem

If 53.2kJ of heat are added to a 15.5g ice cube at - 5.00 ** ^{o}**C, 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

Additional resources for Heating and Cooling Curves

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