Specific heat capacity

- [Instructor] Hello everyones. Today we are going to be talking about heat capacity, also known as thermal capacity. Now this is just the amount of heat required to change the temperature of a material. So given this definition, what units would you expect heat capacity to have? Heat is a form of energy and we're describing how much of that is needed to change the temperature, so the units for heat capacity are energy per temperature, in SI would be Joules per Kelvin. Now, remember, in SI we use Kelvin for temperature, which is the same in magnitude as Celsius. So a difference of 1 degree Celsius is equal to a difference of 1 Kelvin, however, Kelvin does not have any negative numbers, and so 0 Kelvin is as low as you can get. Now, you probably already have an intuitive understanding of heat capacity even if you haven't heard it phrased exactly like this before. Imagine you have two pots of water over the same burner, but one of the pots is full of water and the other is only about half full. You would probably expect the one with less water in it to boil faster, and this is actually because of the heat capacity. The pot with the less water in it has a lower heat capacity. And this is because one of the things that heat capacity depends on is the mass of the object or system. Less water is less mass xis a lower heat capacity. The other thing that the heat capacity depends on is the material. This is also something you are probably already intuitively familiar with. Imagine you go to a barbecue on a hot day and there are two folding chairs left open for you to choose between. One is made of metal, the other of plastic, and they've both been sitting out in the sun. You'd probably choose the plastic one to save yourself some discomfort. The reason that the metal chair would be hotter despite both chairs having been sitting out in the sun is because metal and plastic are different materials and have different heat capacities. So we know that the heat capacity of an object or system depends on both the mass and the material it is made of. We can actually combine these then into something called specific heat capacity. Now the specific heat capacity is just the heat capacity per mass. This means that the specific heat capacity is independent of the mass of the system because we're measuring it per mass. Therefore, this is constant for a given material. This means it will take the same amount of energy to raise the temperature of 1 kilogram of any given material, but then for a different material, it will take a different amount of energy. Given this, what do you expect the units of specific heat capacity to be? Well, just like heat capacity, we have an energy per temperature, but now we also have a per mass. In SI this is going to be Joules per Kelvin per kilogram. This means that the heat capacity and the specific heat capacity are related by mass. so, if you have a specific heat capacity and you want to get the total heat capacity for the object or system, then you need to multiply by the object or system's mass. Conversely, if you have the heat capacity and the mass and you want to figure out what the heat capacity of a material is, you can divide the heat capacity by the mass. However, because specific heat capacity is a constant property of a given material, we can usually just go ahead and look up what that value is because scientists have already measured the specific heat capacities of lots of materials. Let's consider the water in those pots we talked about. Pure liquid water has a specific heat capacity of 4,184 Joules per Kelvin per kilogram, but different materials have different specific heat capacities. So let's think back to our chairs at a barbecue example and how the metal chair is hotter than the plastic chair. Now metal folding chairs are typically made of aluminum, which has a specific heat capacity of 897 Joules per Kelvin per kilogram. Solid plastic, however, has a specific heat capacity of 1,670 Joules per Kelvin per kilogram. So you can see from the specific heat capacities that since the sun is providing the same amount of energy to both chairs, the temperature of the metal chair is getting much more increased because it needs less energy to increase its temperature because it has a lower specific heat capacity. Now that we see how the material changes the heat capacity, let's talk a bit more about the mass and go back to our example of the pots. So in these pots, we have pure liquid water, which we know now has a specific heat capacity of 4,184 Joules per Kelvin per kilogram. Now the pots themselves also have a heat capacity, but we're going to ignore that to simplify the problem. If this pot has 2 kilograms of water in it, we can calculate how much energy it will take to change the temperature of this water. Let's say that the initial temperature of the water is about 300 Kelvin, which is approximately room temperature. And suppose we want to use this water to make some white tea, which has made best with water that's at about 355 Kelvin. Based off our understanding of heat capacity now, we can figure out how many joules it is going to take to raise the water from 300 Kelvin to 355 Kelvin. We have the specific heat capacity and a mass, and we know we can multiply those to get a total heat capacity. And we know that by definition, heat capacity is the energy required per temperature, which means that if we multiply the heat capacity by the change in temperature, we'll find out what the energy required is. In fact, this relationship is an important thermodynamic equation. Lower case c is commonly used for specific heat capacity and Q for heat. So this is exactly what we've just worked out. The heat or energy required equals the specific heat capacity times the mass, times the change in temperature. Let's go ahead and put our values in here. The mass, specific heat capacity, and the change in temperature. As always, we can use our units to guide us. Specific heat capacity has a unit of Joules per Kelvin per kilogram, we're multiplying mass that has a unit of kilograms, so those kilograms will cancel out. We're also multiplying by a change in temperature, which is measured Kelvin. And so that will also cancel out, leaving us just with joules which is an energy, just like we want. In this case, if we multiply this together, we would find that the energy required would be 460.24 kilojoules. Now, let's consider the other pot. If this pot has 1 kilogram of water, how would that change our calculation? Pause the video and think about what its heat capacity would be. So because we still have the same material and therefore the same specific heat capacity, the total heat capacity is going to decrease by half because of the mass is half. And since we still want to raise the water's temperature, the same amount, this means that the energy required is going to decrease by half as well, now requiring 230.12 kilojoules. So now we can see how the mass, as well as the material affect heat capacity. Today we talked about heat capacity. We learned that it is the amount of heat required to change the temperature of a material and that it is measured in Joules per Kelvin, and that it depends on both the mass of the system and the materials that the system is made up. We did a couple of examples to help us quantify this intuitive understanding we have of the world around us. And I encourage you to think about the ways he capacity pops up in your everyday life. For example, why are some things drier than other things when you unload the dishwasher? Have a think about that. Thank you so much for joining us. I hope you learned a little bit of something, and we'll see you again next time. Bye.