# Heat of Phase Changes

by Jared Rovny

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00:01 Our second topic in this final lecture is pertaining to how a substance changes its phase.

00:07 So, for example if we have a cup of liquid water and we could heat up that water so it begins to boil, some of that water will become a vapor, so it's water in a different phase of matter.

00:18 It's a gas phase instead of a liquid phase.

00:21 It turns out that while the temperature of the water right at the boiling point which we already know to be 100 degrees Celsius or 212 degrees Fahrenheit, is different [amounts] of heat for the liquid water than the gaseous water even though they're at the exact same temperatures.

00:40 So this is again, one of these somewhat confusing ideas that the temperature can be one thing, the same for the liquid water right at the boiling point and for the vaporous gas right at the same boiling point while the energies can be different.

00:53 So again, keep in your head the idea of heat as a unit of energy being added to a system separate from the idea of the temperature of that system.

01:01 We can also see this in a different way just by looking at a graph.

01:04 So what we see here in this is graph is a horizontal axis which is the temperature of a system, in this case, water.

01:10 And then on the vertical axis we can see our plotted heat added.

01:14 So looking at this graph you can see that for example, just for the solid water which would be ice, its temperature would go up and up as we slowly add some heat to it.

01:25 But a very interesting thing happens when we get to the boundary of the change of the phase from the solid to the liquid or from the liquid to the gas.

01:33 Notice that right at those boundaries, the temperature doesn't change.

01:37 We are either at the freezing point or at the boiling point of water, but we do have to add much more heat.

01:43 We have to give the substance more energy and this energy just goes into the change of the phase of the substance.

01:49 So for example, to go from the a solid to a liquid we would stay at zero degrees Celsius, but we do have to add a certain amount of heat to get the solid to turn into its new phase of liquid.

02:01 This amount of heat required simply to melt the solid is called the heat of fusion.

02:06 Similarly, we have a heat which is required to get the liquid into a gaseous phase to boil the water, and that is that heat of vaporization because we have to turn it into a vapor.

02:17 So again, notice the somewhat confusing idea here when you first hear it, that at a particular temperature like particularly zero degrees or just at 100 degrees, you can have different amounts of energy in your substance and those different amounts of energy will correspond to the phase of that substance whether it's on one side of that change or the other.

02:37 The way this is measured, this amount of heat going into a substance, this heat of vaporization or the heat of fusion, is usually measured per quantity of material.

02:46 So instead of joules the amount of energy you would need, it would usually be measured in something like joules per mole or joules per gram of substance that you have.

02:55 And so we have this written here that the heat you would have to add is in joules per mole.

02:58 Meaning that on our graph we have this little letter "n" here because we're multiplying by the number of moles or the number of grams if it was measured in grams in order to get the actual heat, the actual energy that we have to add in order to get the substance to change its phase.

03:16 Also don't forget that now that we know how to go from the solid to the liquid phase at a particular temperature, We also already learned how if we are changing our temperatures without changing our phase, we know how the heat in the temperature are related because we already talked about the specific heat and the heat capacity.

03:35 So now what you'll be able to do is how find how much heat you would have to add to water to go from zero degrees in the liquid phase all the way up to 100 degrees at the liquid phase just by using variable C that we found.

03:50 So you could use the heat added is equal to the amount which would be, again, moles or grams times the specific heat capacity C times the change in temperature which for the example I just gave would be equal to 100 degrees or 100 Kelvin depending on which units you have that C, that specific heat capacity in.

04:11 This is a very useful effect especially biologically because for example, when your are using evaporative cooling which is sometimes just called sweating, you have water or liquid on the surface of your skin.

04:22 And for that water to change phase and to go out into the atmosphere, what it has to do even if it's at the right temperature to boil up into the atmosphere which again doesn't have to be the actual boiling point of the water necessarily.

04:35 it depends on the pressure and a number of variables about your environment, so the water can leave your skin and evaporate even if it's not boiling, but for it to leave your skin, it still will have to change phase from a liquid to a gas to become a vapor out in the air.

04:51 In order to change this phase it has to take that energy from your body.

04:55 It has to take that n times the heat of evaporation where we have the amount of material measured in 'n'.

05:02 So when the sweat trying to leave your body it will sap a lot of energy from your body making a very efficient cooling method as it takes all that energy from your skin.

05:12 This is also in effect, you might notice with ice cubes in a drink.

05:16 For ice in a liquid, not only does that ice have to go from the very cold temperature of maybe your freezer where your got it from and go up to the temperature of the liquid that your put it in, it also has to change phase and become from a solid which is ice into a liquid which is the material that it's in.

05:33 In this process of going from the solid ice to the liquid water in your drink it actually uses a huge amount of energy from the drink itself cooling the drink as the ice cube melts.

05:45 You might notice this if you've ever tried to use ice cubes that are made of a different material like some sort of marble or stone, they might have the same heat capacity.

05:52 So as they change temperature from the cold temperature of your freezer to the temperature of your drink, they might take the same amount of energy as the ice cube did but they don't get this melting effect.

06:02 They dont get the heat of evaporization to be taken from the drink And so they might not be as effective, even again, if they have the same total heat capacity.

The lecture Heat of Phase Changes by Jared Rovny is from the course Thermodynamics and Thermochemistry.

### Included Quiz Questions

1. The measurement of change in heat of fusion is measured per quality
2. The temperature of a substance is the same on either side of the phase change, but the energies are different
3. At the phase of transitions, heat is added without change in temperatures
4. The heat required to melt is the heat of fusion
5. The heat required to vaporize is the heat of vaporization
1. Joules/mol
2. Joules/Pascal
3. Joules/Kelvin
4. Joules/sec
5. Joules/meter
1. Heat added = n x specific heat x change in temperature
2. Heat added = n x specific heat / change in temperature
3. Heat added = n / specific heat and temperature
4. Heat added = n - specific heat + temperature
5. Heat added = temperature / specific heat x n

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