States of matter
-
States of Matter
-
States of Matter Follow-Up
-
Specific Heat, Heat of Fusion and Vaporization
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Chilling Water Problem
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Phase Diagrams
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Van Der Waals Forces
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Covalent Networks, Metallic, and Ionic Crystals
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Vapor Pressure
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Suspensions, Colloids and Solutions
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Solubility
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Boiling Point Elevation and Freezing Point Suppression
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Change of State Example
Specific Heat, Heat of Fusion and Vaporization Specifict heat and phase changes: Calculating how much heat is needed to convert 200g of ice at -10C to 110 degree steam.
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- A couple of videos ago, we learned that if we started
- with solid water or ice at a reasonably low temperature--
- maybe this temperature right here is
- minus 10 degrees Celsius.
- And we can deal with Celsius when we're dealing with these
- phase changes, because we really just care about the
- difference in temperature, and not necessarily the absolute
- temperature.
- So one degree in Celsius is the same thing is one degree
- in Kelvin so the differences are the same whether you're
- dealing with Celsius or Kelvin.
- So we're starting with minus 10 degree Celsius
- ice or solid water.
- And we learned that as you heat it up, as you add heat
- energy to the water, the temperature goes up.
- The molecules, at least while they're in that ice lattice
- network, they just start vibrating.
- And their average kinetic energy goes up until we get to
- zero degrees.
- Which is the melting point of water.
- And at zero degrees, we already learned something
- interesting happens.
- The added heat in the system does not increase the
- temperature of the ice anymore.
- At least over that little period right here.
- What's happening is that heat energy is being used to kind
- of break the lattice structure.
- To add potential energy to the ice.
- Or essentially melt it.
- So for it here, right here, we're ice.
- Right at this point, we're zero degree ice.
- And then as we add more and more heat we get to zero
- degree water.
- So at zero degrees, you can either have water or ice.
- And if you have water, to turn it into ice, you have to take
- heat out of it.
- And if you have ice, and you want to turn it into water,
- you have to put heat into it.
- And then the heat is used again to warm up the
- water at some rate.
- And then at 100 degrees, which is the boiling point of water,
- right here, a similar phase change happens.
- Where the increased heat is not used to increase the
- temperature of the water, it's used to put potential energy
- into the system.
- So the water molecules are forced away from each other.
- The same way that if I'm forced away from the planet
- Earth, I have potential energy because I can
- fall back to the earth.
- Similarly, they have the potential energy of falling
- back to each other.
- But this energy, right here is the energy necessary to
- vaporize the water.
- Right here you have 100 degree water, 100 degree liquid.
- And here you have 100 degree vapor, water vapor.
- And then as you add more and more heat, once again it
- increases the temperature.
- But you, Sal, I already learned this a few videos ago,
- I have the intuition.
- But I want to deal with real numbers.
- I want to know exactly how much heat is required for
- these different things to happen.
- And for that, we can get these numbers.
- And these are specific to the different states of water.
- If you looked up any other element or molecule, you would
- have different values for these numbers we're going to
- be dealing with right now.
- But this first number right here is the heat of fusion.
- And this is the amount of heat that's required to fuse 100
- degree water into 100 degree ice.
- Or the amount of energy you have to take out of the water.
- So this distance right here, or along this
- axis, is 333 joules.
- If you're going in the the leftward direction, you have
- to take that much out of the system to turn into ice.
- If you're going in the rightward direction, you have
- to add that much to turn into water.
- So heat of fusion.
- It's called the heat of fusion because when you fuse
- something together you make it solid.
- So it could also be considered the heat of melting.
- Just two different words for the same, thing depending on
- what direction you going.
- The important thing is the number, 333.
- Similarly, you have the heat of vaporization.
- 2257 joules per gram.
- That's this distance along this axis right here.
- So if you had one gram of 100 degree liquid water and you
- wanted to turn it into one gram of 100
- degree liquid vapor.
- And in all of this, we're assuming that nothing silly is
- happening to the pressure, that we're
- under constant pressure.
- You would have to put 2257 joules into the system.
- If you had 100 degree vapor and you wanted to condense it,
- you would have to take that much energy out of the system.
- OK, fine, you know how much energy is required for the
- phase changes.
- But what about these parts right here?
- How much energy is required to warm up a gram of ice by one
- degree Celsius or Kelvin?
- And for that we look at the specific heat.
- It takes 2 joules of energy to warm up 1
- gram 1 degree Kelvin.
- When water is in the solid state.
- When it's in the liquid state, it takes about double that.
- It takes about 4 joules per gram to
- raise it 1 degree Kelvin.
- And when you're in the vapor state, it's actually more
- similar to the solid state.
- So given what we know now, we can actually figure out how
- much energy it would take to go from minus 10 degree ice to
- 110 degree vapor.
- Let's work this out.
- So the first thing we're going to be doing is, we're going to
- be going from minus 10 degree ice to zero degree ice.
- So we're going to go 10 degrees.
- We have to figure out how much heat does it take to warm up
- ice by 10 degrees.
- So the heat is going to be equal to the change in
- temperature.
- So actually let me write the specific heat first. So 2.05
- joules per gram Kelvin.
- Oh, and I should tell you, we can't different values for the
- amount of ice we're warming up to vapor, so let's say we're
- dealing with 200 grams.
- So it'll be the specific heat times the number of grams
- we're warming up of ice times the change in temperature that
- we're trying to get.
- So, times 10 degrees Kelvin.
- Le'ts just say it's a 10 degrees Kelvin change, it
- doesn't matter if we're using Kelvin or Celsius.
- I could have written a Celsius here.
- Let's put Celsius right there.
- So what is that equal to?
- Get the calculator.
- Clear it out.
- 2.05 times 200 times times 10 is equal to 4,100 joules.
- Let me do this in a different color.
- This is 4,100 joules.
- Fair enough.
- Now, so what we've done is just this part right here.
- This distance right here is 4,100 joules.
- Now we have to turn that zero degree ice
- into zero degree water.
- And for that we use the heat of fusion.
- We're adding that amount of heat.
- It's 333.5 joules per gram.
- So that's equal to 335.55 joules per gram times, we have
- 200 grams of ice that we're trying to melt.
- So that is what?
- So let me get the calculator out.
- So I have 335.55 times 200 is equal to 67,110.
- Let me do it in that color so can sum them up at the end.
- 67,110 joules to melt the water.
- Or take it from ice to water.
- Now, we have to go from, and this is the big one.
- We have to go from zero degree water to 100 degree water.
- Or liquid water.
- This is in the liquid state.
- So now we take the specific heat of water which was 4.178.
- For some reason I'm thinking it's 4.176
- but it doesn't matter.
- So it's 4.178.
- I might off a little bit on that number, but that digit is
- not that significant.
- Joules per gram Celsius times 200 grams
- times 100 degrees Celsius.
- And notice, the Celsius and the Celsius cancel out.
- The grams and the grams cancel out.
- So we are left with joules, which is what we want.
- We want to know how much heat or how much energy we're
- adding to the system.
- Let me get the calculator out.
- So this stage is going to be 4.178 times 200 times 100 is
- equal to 83,560 joules.
- Does that look about right?
- Let's see.
- 4 times 200 is 800, 800 times 100; yeah, that's about right.
- Now, we're dealing with 100 degree water vapor, and we
- have to turn that 100 degree water vapor
- to 110 degree vapor.
- So we use the specific heat of vapor.
- 1.89 joules per gram Kelvin.
- Multiplied by the amount of vapor we're dealing with, 200
- grams. That obviously doesn't change.
- We're not adding or taking away mass from the system.
- Times the temperature change, times 10.
- So what is that?
- Let me get the calculator out again.
- So we're dealing with a 10 degree change.
- 10 degree Celsius times 200 times 1.89 is equal to 3,780.
- And I just realized, I made a horrible mistake.
- It's not an irrevocable mistake, otherwise I would
- rerecord the video.
- But I just figured out the amount of energy to take it
- from zero degree water to 100 degree water, which is this
- energy right here.
- And now I just calculated how much energy to go from 100
- degree vapor to 110 degree vapor.
- Which is this right here, that distance right here.
- I forgot to figure out how much energy to turn that 100
- degree water into 100 degree vapor.
- So that's key.
- So I really should have done that up here before I
- calculated the vapor.
- But I'll do it down here.
- So to do 100 degree water to 100 degree vapor.
- That's this step right here, this is the phase change.
- I multiply the heat of vaporization, which is 2,257
- joules per gram times 200 grams. And
- this is equal to 451,400.
- I'll do it in that blue color.
- 451,400 joules.
- So this piece right here is 451,000 for our sample of 200
- grams. This piece right here was 83,000 joules.
- This piece right here was 3,780 joules.
- So to know the total amount of energy, the total amount of
- heat that we had to put in the system to go from minus 10
- degree ice all the way to 110 degree vapor, we just add up
- all of the energies we had to do in all of these steps.
- Let's see.
- And I'll do them in order this time.
- So to go from minus 10 degree ice to zero degree ice.
- Of course we have 200 grams of it.
- It was 4,100.
- Plus the 67,000.
- I'm just doing this off the screen.
- So plus 67,110.
- Plus 83,000.
- That's to go from zero degree water to 100 degree water.
- Plus 83,560.
- So we're at 154,000 right now just to get
- to 100 degree water.
- And then we need to turn that 100 degree water into 100
- degree vapor.
- So you add the 451,000.
- So, plus 451,400 is equal to 606.
- And then finally, we're at 100 degree vapor, and we want to
- convert that to 110 degree vapor.
- So it's another 3,700 joules.
- So plus 3,780 is equal to 609,950 joules.
- So this whole thing when we're dealing with 200 grams, when
- you're going from minus 10 to 110.
- And remember, this is for 200 grams. It
- took us 609,950 joules.
- Or 609 kilojoules to do this.
- So that by itself is an interesting thing.
- You might think, wow, this is a huge number.
- But actually, it turns out joules isn't a lot of work.
- Kilojoules starts to become a little bit interesting.
- You might realize, 200 grams of ice, that's about half a
- pound of ice.
- So to take half a pound of ice and warm it up on your stove
- would take 609 kilojoules of heat to do that.
- So that's something that you probably could do on your
- stove at home.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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