About this video
More water needs more heat to warm by the same amount because the energy must be shared among more molecules, and even equal masses of different substances, like water and oil, need different amounts of heat. Specific heat capacity, c, is the heat needed to raise 1 kg (or 1 g) of a substance by 1 °C; for water it is 4,180 J/kg°C or 4.18 J/g°C. This gives q = mcΔT, used to find heat or final temperature, and differences in c come from how much energy goes into kinetic versus other forms like potential energy.
You'll be able to
- explain why a larger mass needs more heat for the same temperature rise.
- define specific heat capacity and interpret its units.
- use q = mcΔT to calculate heat energy or a final temperature.
- explain why different materials have different specific heat capacities.
Key words
- heat energy (q)
- The thermal energy supplied to or removed from a substance.
- specific heat capacity (c)
- The energy needed to raise the temperature of 1 kg (or 1 g) of a substance by 1 °C.
- ΔT (delta T)
- The change in temperature: final temperature minus initial temperature.
- average kinetic energy
- The average energy of motion of the particles, which temperature measures.
- potential energy
- Stored energy, here from electric forces between molecules, which doesn't raise temperature.
Transcript
- [Instructor] Pop quiz, we have two pots of water at same temperature, say room temperature, of about 30 degrees Celsius. We want to increase this temperature to say 40 degrees Celsius. The question is which of the two will require more heat energy? What do you think?
Well, from our daily experience, you can probably guess that the one where there is a lot of water, that would require more heat energy, right? But what's the physics behind it? Well, we know that the temperature is a measure of the average kinetic energy of the molecules.
I mean, different molecules are moving at different speeds so they have different kinetic energy, but the average, if you take the average value, that represents the temperature. So initially the average kinetic energy must be the same because they have the same temperature.
Now if you want to increase the temperature, we need to increase the average kinetic energy and that's what happens when you heat. When you supply heat energy, that heat gets distributed to all the molecules and as a result, the average energy increases. But over here you have so many more molecules and so if you want to increase the average energy here as well by the same amount, well, you've got to supply more energy mainly because there are so many more molecules compared to over here.
That makes sense, right? So here, because there is more stuff, it took more energy, more heat energy to raise the temperature, right? But now let's make things interesting. What if I took the same amount of stuff but instead of water, I took oil? I take the same mass of water and oil at same initial temperature and now I want to increase the temperature to say 40 degrees Celsius again.
Now which one's gonna require more heat energy? Okay, they have the same mass, all right? So do you think it's gonna be the same amount of heat energy or what will require more or oil would require more? What's your guess now? All right, well my intuition says that now that we have the same amount of stuff and again, we are increasing the temperature by the same amount, 30 to 40 degrees Celsius let's say, will probably require the same amount of heat energy, right?
Well, it turns out not to be. So water still requires a lot more heat energy compared to oil, even if I take the same mass of them. And that is true in general. Even if I had some other substance, same mass and had to increase the temperature from 30 to 40 degrees Celsius, same amount, it would require a different amount of heat energy.
Different materials would require different amount of heat energy to raise their temperatures, but why is that the case? Well, we'll try to answer that question in this video, but before we do that, let's quantify this, okay? Let's take the example of water and oil and let's ask ourselves how much heat energy do you need to raise the temperature of water and raise the temperature of oil?
We can actually measure this, right? We can actually calculate this. We've done that, we've done a lot of measurements, and it turns out when it comes to water, if you take one kilogram of water, if this was one kilogram, then you would need to supply 4,180 joules.
This is an experimental value, okay? 80 joules of energy to raise the temperature by just one degree Celsius. If you take a kilogram of water, you wanna raise this temperature by just one degree Celsius, you need this much amount of energy. So I can actually write this as 4,180 joules is needed per kilogram of water per degree Celsius rise, okay?
That units will help us understand what this number is saying. What about oil, well, for oil, it depends on which oil you're talking about, but it will be much lower actually. It will be somewhere around say 1,900, 2,000, 2,200, so we can put about 2,000. So 2,000 joules of energy would be needed for a kilogram of oil, so per kilogram, to raise its temperature by one degree Celsius.
And these numbers are important because these numbers tells us how much energy is needed to raise the temperature, right? And therefore we give a name to these numbers, we call them specific heat capacity, or just specific heat and the letter we use to represent that is small c.
The value is different for water. It's different for oil. It'll be different for say copper. And just from the units, hopefully we understand what the numbers is. The number tells you how much energy you need to supply to increase the temperature of one kilogram of that substance by one degree Celsius.
Now you can also write this in slightly different units. For example, a kilogram is 1,000 grams. So if I were to convert this into grams, then I would get 4,180 joules by 1,000 grams per degrees Celsius and that would turn out to be 4.18 joules per grams per degrees celsius.
So you can represent a different units. What would this number tell you? This number says if you take one gram of water, to raise this temperature by one degree Celsius, you would require 4.18 joules of energy. And this is an important number for us because we can use this number to predict a lot of stuff, so let me just take an example.
So if you had to calculate how much heat energy is needed to raise a temperature of say five kilograms of water, okay? From 30 degrees Celsius to 40 degrees Celsius, why don't you pause the video. No equations as of now. Just try to intuitively use this number and try to answer this question.
Okay, here's how I'm thinking. I know that I need to supply a heat energy of 4,180 joules if I had one kilogram of water and to raise temperature by one degree Celsius, but I have five kilograms of water. Since I have five kilograms of water, well, the amount of heat energy will be five times as much, so I'll multiply this number by five, okay?
But again, this would be to raise the temperature by one degree Celsius, but how much are we raising it? We're going from 30 to 40. so we are raising it by 10 degrees Celsius. So this would be the number for one degree Celsius. So if I would raise it by 10 degrees Celsius, well, I have to multiply it by 10.
So I'll multiply it by 10. Actually let me write that out as 10.0 because we have three significant figures over here. Anyways if I simplify this, the Celsius cancels out, the kilograms cancels out, and I could just multiply this and that will give me 209,000 jewels.
So you see, I can do pretty cool calculations by knowing this number, okay? And so we can now even generalize. We can write an equation just based on this intuition that we have now, all right? So we can say in general, the amount of heat energy that is supplied, q is what we use for heat.
We can use small q. Some people use capital Q, but anyways this is the heat energy that we supplied. What is that equal to in general? Well, that equals c. This represents the heat energy per kilogram per degree Celsius. But if I have m kilograms, we'll have to multiply it by m like I did over here.
And if I'm not increasing by one degree Celsius but if I'm increasing it by delta T degree Celsius, that's the change in temperature, well, then I'm multiplied by delta T. Does that make sense? It's an important equation to do a lot of cool calculations, so hopefully it makes intuitive sense.
c represents the heat energy per kilogram per degree Celsius. So if you have m kilograms, you multiply it by m and if you are raising the temperature by delta T degrees Celsius, well, you multiply it by delta T. With that in mind, let's solve a couple of numerical.
Here's the first one. Calculate the amount of heat energy required to raise the temperature of 20 grams of aluminum from 25 degrees Celsius to 75 degrees Celsius. The specific heat capacity of the aluminum is given to be this much. So let's look at what's given and what's asked of us.
We are asked to calculate the amount of heat energy or q that is necessary. We are given the mass m. We know the initial and the final temperature so we can figure out what delta T is and we are given the specific heat capacity. So we are given all these three and we need to figure out what the q is, so we can just substitute and find out the amount of heat energy required.
So great idea to pause the video and see if you can try this yourself first before we do it together. All right, so let's plug in. I know the value of c. I know the value of m. How do I calculate delta T? Well, delta T is a change in temperature, it's the final temperature minus the initial temperature.
So if I plug in, this is what it looks like. Here's the specific heat capacity, here's the mass, and here's delta T final minus the initial temperature. And if I simplify this, 75 minus 25 is 50. So if I simplify, I get this and if you look at the units, the gram cancels out over here, the degree Celsius cancels out over here, and I'm left out with joules.
That's exactly what we want. q should be our answer should be in terms of joules and now I can plug these numbers into the calculator. Actually I don't have to because 20 times 50 is 1,000 and a thousand times .897 will be 897. So because we had simple numbers, our answer is going to be 897 joules and we have to make sure this is in three significant figures because everything else is in three significant figures and yes, it is.
So this is how much energy is needed to raise the temperature of our aluminum from 25 to 75 degrees Celsius. Okay, let's try one more. Pause the video and see if you can try this yourself first. All right, so we are given that there is a copper of mass .25 kilograms, so we know the mass.
It's initially at a temperature of 25 degrees Celsius, so we know the initial temperature. It's heated with 5,210 joules of energy, so we know q and if the specific heat capacity of copper is 385 joules per kilogram degrees Celsius which means c is given to us, we need to find the final temperature of the copper.
So look at what's given. We are given q, we are given c, we are given m, and we are also given the initial temperature. I just need to figure out the final temperature of the copper. So how do we do this? Well, before substituting, I'm going to rearrange this to get delta to isolate delta T because that's what I'm interested in.
I'm interested in figuring out final temperature. So if I rearrange this, I just divide by cm on both sides. I will now get delta T to be q divide by cm, and now I can plug in everything, right? Delta T is T final minus T initial and I know the T initial, so T initial is 25 and then I plug in all the other stuff.
And again, I'm just going to cancel out all the units just to make sure that I'm on the right track, so the joules cancels out. The kilogram cancels out. If one of them was in grams, then we would have to convert to make sure the units are the same. So it's always a good idea to make sure that you write down your units when you're simplifying and you have one over degrees Celsius that will go in the numerator, so you'll get degrees celsius.
This will have a unit of degrees Celsius which makes sense because our temperature should be in degrees Celsius. Anyways now we'll plug this into our calculator. 5,210 divide by 385 divide by .25 and that gives me this. So it's 54.12987 let's say. So that is my right-hand side and I usually like round off after having the final answer, okay?
So the final step would be to calculate Tf. I need to add 25 on both sides. So TF will be this plus 25 which will be 79.129 and now I can round it off to 79.1. And there you have it. That's my final answer. That will be the final temperature of the copper. But that now finally brings up the question why do different materials have different specific heat capacities in the first place?
In other words, if you had two objects of exactly the same mass and let's say you apply, so we supply the exact same amount of heat energy, then the temperatures will not increase by the same amount, why? Well, to answer that question, we need to look at stuff at the atomic level or the molecular level.
Each atom or molecule will have different kinetic energy in that material, but the average kinetic energy is what represents the temperature of the material. But here is the important point. There are other forms of energies which I'm gonna show in green over here, okay?
There are other forms of energies that do not contribute to the temperature. For example, there is potential energy that is due to the electric forces or you can think of it as due to the intermolecular bonds or in certain gases, molecules can even rotate in certain ways that again, do not contribute to temperature.
So this means over here when I supply 100 units of energy, it's possible that only 30 units is used up in increasing the kinetic energy and the rest, 70, is used up in increasing the other forms of energy like potential energy. But in this case, it's possible that say 60 of that 100 is used up in increasing the kinetic energy and the rest, 40, is used up in increasing the other forms.
Now if you're wondering what decides how much portion of this heat energy is used up in increasing the kinetic energy? Well, that completely depends upon the material. It depends upon the molecules, the structure, and all that stuff. But anyways you can now immediately see because of this difference, the increase in the average kinetic energy here and here will be very different.
Another reason for the difference is one kilogram of this material will have different number of molecules compared to one kilogram of this material. But whatever it is, you can clearly see when you supply the same amount of heat energy for the same amount of stuff, the average kinetic energy increase would be different.
And that's why the temperature change would be different and that's why the specific heat capacities of different materials would be different.
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