About this video
Using two vessels of water heated on similar burners, the video shows that the same thermal energy raises the temperature of a smaller mass more, because the energy is shared among fewer molecules. It defines heat capacity (energy needed to raise the temperature by one degree celsius), which depends on mass and so is extrinsic, and specific heat capacity (energy to raise one gram by one degree celsius), which is intrinsic and lets us compare materials like water, wood and copper.
You'll be able to
- explain why a smaller mass of water heats up faster than a larger mass with the same energy.
- define heat capacity and explain why it is an extrinsic property.
- define specific heat capacity and explain why it is an intrinsic property.
- use how quickly materials heat up to compare their specific heat capacities.
Key words
- heat capacity
- The amount of energy needed to raise the temperature of an object by one degree celsius.
- specific heat capacity
- The amount of energy needed to raise the temperature of one gram of a substance by one degree celsius.
- temperature
- A measure of the average kinetic energy of the molecules.
- extrinsic property
- A property that depends on how much stuff there is, like mass or heat capacity.
- intrinsic property
- A property that stays the same for a material whatever the amount, like density or specific heat capacity.
Transcript
- [Instructor] We have two vessels of water both at room temperature, and we're gonna start heating them up on very similar burners, so they're gonna provide very similar amounts of heat, okay? The question is which one will start boiling first? I have fast forwarded over here.
Well, it's no surprise, from our daily experience, we can guess that the one with less water will start boiling first. But the question is why? Why does that happen? Well, let's find out. So we have the two vessels of water, and they're initially at the same temperature, the room temperature.
The first big question for us is what exactly is temperature? Remember, temperature is the measure of average kinetic energy of the molecules over here. Since initially the temperature is the same, on average, they have the same kinetic energy. Now, let's heat them up.
Since we're using similar burners, if we wait for some time, we're gonna provide the same amount of thermal energy. And the big question now is what happens to the average kinetic energy? Let's first look over here. That energy that we supply will be distributed among lots and lots of molecules.
Just like how when you take a cake and distribute it amongst lots and lots of kids, each kid will get a tiny share, over here, each molecule will get a tiny share of that extra thermal energy. As a result, the kinetic energy over here does not increase much. But what about over here?
That same thermal energy over here is distributed among less number of molecules. So just like how if you were to take that same cake and distribute it among less number of kids, only very few kids, then each kid will get a big piece. Similarly over here, each molecule on average gets a big share of that thermal energy.
As a result, what happens to the average kinetic energy over here? It'll be a lot more than over here, right? So the average kinetic energy over here ends up becoming a lot more compared to over here, because there are fewer molecules, so each one gets, on average, a bigger share.
That's why the temperature over here, look! Becomes much more than the temperature over here. And that's why the temperature here shoots faster, and therefore, this one boils first. Here, to raise the temperature, it'll take a lot of heat energy. But here, because there are only fewer molecules, to raise the temperature, it takes very little amount of heat energy.
And this helps us now to define something called the heat capacity. We define heat capacity as the amount of energy needed to raise the temperature by one degree celsius. So just from this definition, can you think about which of these two will have a higher heat capacity?
Pause and think about this. All right. Well we just saw that here, it takes a lot of energy to raise the temperature by one degree celsius, because there are a lot of molecules over here. And therefore, this has a higher heat capacity. Over here, well since there are very few molecules, it takes a little bit of energy to raise the temperature by one degree celsius, so you have a lower heat capacity over here.
In other words, if you have a bigger mass, you have a higher heat capacity. And if you have a smaller mass, you have a lower heat capacity. So this brings up another question now. Do you think heat capacity is an intrinsic or an extrinsic property? Again, pause and think about this.
Well, we just saw heat capacity depends on the mass. If you have more mass, it takes more energy to raise the temperature by one degree celsius. I mean, think about if you had a swimming pool. Oh, it will take a lot more energy to raise its temperature by one degree celsius.
So clearly, heat capacity depends on the amount of stuff, and therefore, it's an extrinsic quantity. Okay, heat capacity's awesome when we're comparing samples of the same material. But what if we are comparing samples of different material? For example, consider if we have a glass of water, we have some wood, and we have a copper rod.
Let's say that they have the same mass, and they have the same temperature to begin with. Now, we're gonna heat them up just by keeping it in sunlight. So again, we're pretty much heating them up equally. Now whose temperature will rise faster? Will it be the same or not?
Remember, they have the same mass. What do you think? Well, turns out copper's temperature will shoot the fastest, then comes the wood, and then finally comes the water. But why did that happen? They have the same mass, isn't it? Well, it turns out that different materials absorb heat in different ways.
Water absorbs heat in such a way that its temperature does not increase that quickly compared to wood. But copper absorbs heat in such a way that its temperature increases a lot compared to wood. So to tackle these differences, we're gonna introduce a new quantity called specific heat capacity, and we define that as the amount of energy needed to raise the temperature of one gram of substance by one degree celsius.
You see the difference between this and the heat capacity we defined earlier? Earlier, we defined heat capacity as the amount of energy needed to raise the temperature by one degree celsius. We didn't care about this part. The mass did not matter. But when we think about specific heat capacity, we're specifically considering one gram of substance.
If you take one gram of substance, and then calculated the amount of energy needed to raise the temperature by one degree celsius, that would be specific heat capacity. So just from this definition, can you pause and think about which of these three will have the highest specific heat capacity?
Can you pause and try? Well let's see. Copper's temperature increased the fastest. So I'm thinking that it's very easy to increase the temperature of one gram of copper, which means it should take the lowest amount of energy to raise its temperature by one degree celsius.
So among the three, copper should have the lowest specific heat capacity. On the other hand, water's temperature increased the least, so I'm thinking hey, it must be very hard to increase the temperature of one gram of water by one degree celsius, meaning it should take the highest amount of energy to increase its temperature by one degree celsius, so again, among these three, water should have the highest specific heat capacity.
And of course, wood will have the specific heat capacity somewhere in between, so it will have an intermediate value. All right, so the final question is is specific heat capacity an intrinsic or an extrinsic quantity? What do you think? Okay, this one's a little tricky.
So let's remember that extrinsic properties like mass depend on how much stuff is there, how much substance is present. Intrinsic properties like densities are consistent for a given material. So again, if you go back to heat capacity that we talked about earlier, is it consistent for water?
No. It depends on how much water is there. We've talked about that. And therefore, heat capacity is an extrinsic quantity. But what about specific heat capacity? Is that consistent for water? Yes, because by definition, we'll always measure specific heat capacity for one gram of the substance, so whether you take a little bit of water or you take a lot of water, its specific heat capacity will stay consistent, it'll be the same.
Similarly, if you take a little bit of copper, or you take a lot of copper, it'll have a specific value for a specific heat capacity. Specific heat capacity, like density, does not depend about the amount of substance, it's consistent for a given material, and therefore, it's an intrinsic quantity.
It's defined this way so that we can make comparisons between water, wood, and copper, or any other material we want. So to put it all together, heat capacity is the amount of energy needed to raise a temperature by one degree celsius. Specific heat capacity is the amount of energy needed to raise temperature of specifically one gram of substance by one degree celsius.
Heat capacity depends on mass and the material, making it an extrinsic property. So if I ask you, what is the heat capacity of water, that has no meaning, because it depends on how much water you take, whereas specific heat capacity only depends on the material.
It is consistent for a given material, so it's an intrinsic quantity. So if I ask you, what specific heat capacity of water, or any material for that matter, it has a specific value. And that's why specific capacity can be used to make comparison between different materials.
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