Fluids and density

0:00- [Instructor] The Earth's core is mostly made of heavy metals like iron and nickel, whereas the crust, the outer thin crust, is made of the lighter silicates. Why is it like that? Why are the heavy stuff close to the center, whereas the lighter ones are closer to the surface?

0:13And if you consider extremely cold places like say, Antarctica, the average temperature over there is close to minus 50 degrees Celsius, which is way below the freezing point of water. And yet, for some reason, the oceans and lakes do not freeze over there, and that's why aquatic life survives.

0:31But, why don't they freeze? Well, to answer this question, we need to dig deeper into the idea of fluids and densities, and that's what we're gonna do in this video, so let's begin. So, what exactly are fluids? Fluids are substances that flow, and they do that because they don't have a fixed shape.

0:48So, think about liquids and gases. Collectively, we call them fluids. And if you consider our planet, the most of the surface of the planet is covered with liquid water. That is a fluid because water can flow, rivers and oceans all flow. And what about our atmosphere?

1:03Well, it's air, which is a gas, which is also a fluid, 'cause again, we know that it flows, giving us air currents, and breezes, and storms and whatnot. In contrast, if you consider the solid surfaces over here, they do not flow because they have a fixed shape.

1:19Now, of course, over very large timescales, they too can flow because of geological processes, but we're gonna ignore that, okay? Solids do not flow because they have a fixed shape. But why? Why do solids have a fixed shape? To answer that question, we need to zoom in at the atomic or the molecular level.

1:35If you could zoom into a solid, like for example ice, the molecules experience a force of attraction that makes them stick to each other, but they also have a thermal motion, which makes them move away from each other. I mean, solids, the thermal motion is low enough that the attraction wins, and as a result, molecules and atoms end up sticking to each other, giving them a particular shape.

1:56However, when you consider the liquid phase of that same substance, the temperatures are relatively higher. So thermal motions are relatively higher, high enough to partially overcome the attraction because of which they no longer are able to retain the shape.

2:10That's why liquids tend to take the shape of the container. And what about the gas phase? Well, here the thermal motion is so high that it completely overcomes the attractive forces, because of which the particles are pretty much moving freely. So look, in liquids and gases, the thermal motion of the molecules can overcome the attractive forces, that makes them flow.

2:29All right, so fluids flow, what's the big deal? Well, the big deal is because they flow, when you mix two different fluids, or a fluid and a solid, they can sink or float, and that has a huge consequence, as we'll see. But what decides whether something sinks or floats?

2:45Well, that depends on an important property called density. You can think of density as a ratio of mass and volume. So the standard unit for density would be, well, mass is in kilograms and volume would be meter cube, so density's standard units would be kilograms per meter cube.

3:03But what exactly does it represent? Well, think about density as a measure of how crowded something is or how packed something is. You know, how much mass is packed in a unit volume? How many kilograms are packed in a meter cube? Or you know, a more convenient unit would be how many grams are packed in a centimeter cube?

3:23Whatever it is, it's a measure of how packed something is. So let's take some examples. If you take water, for example, it has a density of 1000 kilograms per meter cube. So you can imagine a meter cube of water contains a thousand kilograms of water. But again, I like to think in terms of grams per cm cube, that's more convenient.

3:40So if you convert this, you end up with one gram per cm cube. The idea is the same. If you now take a centimeter cube of water, it'll have a mass of one gram. In contrast, if you consider iron, it has a density of 7.8 grams per centimeter cube. A centimeter cube of iron has 7.8 grams of iron packed into it, which is much higher density compared to water.

4:02And by the way, if you're wondering whether this is a coincidence that the, you know, density of water is exactly one gram per centimeter cube, such a nice number, it's not a coincidence. We define our gram this way. The mass of one centimeter cube of water by definition is one gram.

4:17But anyways, if you consider water or iron for that matter, the densities are uniform, it's the same everywhere, which means if you take a small amount of water here or a large chunk of water over here, the density will be the same, one gram per centimeter cube.

4:28Similarly, if you take a small chunk of iron from here, or a big chunk of iron from a ship, for example, the density would be the same, 7.8 grams per centimeter cube. But that's not always the case. If you consider the density of the air, for example, close to the surface of the earth, it is roughly about 0.001 grams per cm cube.

4:47You can see the density of the air is much, much smaller than that of water, it's about 1000 times smaller. However, if you consider the density of the air, you know, at say about 10 kilometers, which is usually the cruising altitude of a commercial airline, you would find the density even lower, 0.0004 approximately grams per centimeter cube.

5:09And in fact, the higher you go, the smaller the density. But why? Well, think about it this way, if you consider the layer of air over here, it's carrying the weight of the atmosphere on top of it. That weight is pushing down on the molecules over here, squeezing them together, packing them together, giving them a specific density.

5:29But now if you consider a layer of air that is even lower, then look, it's carrying an additional weight compared to this layer, so it's carrying more weight. In fact, the layer at the bottom carries the entire weight of the atmosphere, and therefore the forces are much higher, and so the molecules are squeezed together much higher, packed together more tightly, giving you a higher density.

5:52And that's why the lower you go, the higher the density. But wait, shouldn't the same the case with water as well? For example, if you consider the ocean, then shouldn't the layer at the bottom of the ocean have a higher density than the layer at the top of the ocean?

6:05Well, that's a great question, but turns out not to be so because of one main difference between liquids and gases. Gases can be easily compressed, and to demonstrate this, here's a syringe which contains only air and I have sealed the top with my finger. Now, let me try and push it, and you can see I can easily compress it.

6:23I have compressed the gas and I've increased the density just by using my finger. But now let's see what happens if you fill the syringe with water. Again, seal the top with my finger, and now if I'm pushing it, look, I can't compress it even a little bit. I'm pushing as hard as I can, it's just not possible.

6:41So this means liquids are extremely hard to compress, and because you can't compress them, you can't squeeze the molecules closer and you can't increase the density. And so that's why even though at the bottom, the pressures are insanely high compared to the top of the oceans.

6:57In fact, the pressures at the bottom are so high that even submarines can get crushed. But because compressing water is extremely difficult, the molecules will not come any closer than they are at the top, and as a result, the density is pretty much the same everywhere.

7:10And so we would model water as an ideal fluid which is incompressible. I mean, technically you can compress water if you put horrendous amounts of forces, but since we're not dealing with such high forces usually, we can model it to be incompressible. So ideal fluids are incompressible, and they also have no viscosity.

7:33What does that mean? Well, some fluids can be very thick, making them very hard to flow. Think about ketchup or honey, for example. Because of their thickness or viscosity, it can produce resistance to motion. But if we're dealing with ideal fluids, we model them by saying that, hey, ideal fluids have no viscosity at all.

7:52All right, now let's try to explore why stuff sinks or floats when we mix fluids or fluid in a solid. So let's see what happens when you mix water and oil. What we notice is that if you allow them to settle, oil floats, or you could say that water sinks, but why?

8:06Well, first of all, we can easily model them as ideal fluids because their density is pretty much the same everywhere. What you would find now is that oil has a density that's less than that of water, so stuff that has less density tends to float. Or you could say that water has a density more than that of oil, and therefore it sinks.

8:22Stuff that has more density tends to sink. Let's take another example. If you put an iron bolt in in water, it sinks, why? Because we already saw iron has a much higher density than water. What about ice? Ice floats on water because it has a less density than water.

8:40Here's another way to think about it. Here, the gravitational field is acting downwards, isn't it? So stuff which has more density tends to move in the direction of the gravitational field, sinking, and stuff that has less density tends to move against the gravitational field.

8:54What's interesting is that without the gravitational field, we wouldn't have flotation or sinking. And it's for the same reason why helium balloons tend to move up, because they have a density that's less than the surrounding air, and therefore they move up against the gravitational field.

9:11Okay, now let's see if we can use this to explain our original question about the earth. When the earth was formed, we believe that it was highly molten, and so we can model them as a, you know, as an ideal fluid. Now in this fluid, the gravitational field acts towards the center.

9:27So stuff that is having a high density, like iron and nickel, they will tend to move along the gravitational field, sinking and eventually settling towards the core. On the other hand, stuff that has lighter, you know, lower density, like the silicates, for example, tend to move against the gravitational field.

9:47They tend to float, and that's why they settle near the surface. And that's why eventually when this molten rock cooled to form the earth, the core ended up having high density heavy metals, and the crust ends up having the silicates. Amazing, isn't it? Finally, we go back to water.

10:04We know that ice floats on water, but that's a little weird if you think about it, because whenever you cool something, the molecule tends to have less thermal motion because of which they tend to come closer together. So the density actually increases when you cool stuff generally, okay.

10:21That kinda makes sense, right? So in reality, density depends on temperature. And the same thing works for water. As you cool down water, its density will keep increasing until we reach four degrees Celsius. Guess what? Turns out that water has a maximum density at four degrees Celsius, and that maximum density is one gram per cm cube.

10:41So we should have actually told, you know, that water density is one gram per cm cube or 1000 kilogram per meter cube, whatever you wanna think of it as, at four degrees Celsius because density does depend on temperature. But wait, what happens if you cool down water below four degrees Celsius?

10:55Well now, molecules will have such low thermal energy that they lock in places, and look, in doing so, they start forming gaps in between, which reduces the overall density, and that's why density tends to decrease below four degrees Celsius. And eventually as water crystallizes into ice, ice ends up having lower density than water and therefore ends up floating.

11:20And this has a huge consequence on the aquatic life in really, really cold places. So if we go back to our Antarctica, for example, we can model water by considering three different layers, okay. Let's say the current temperature is about six degrees Celsius, okay?

11:34Now what if the temperature outside reduces to five degrees Celsius? What's going to happen? Well, the surface of the water which is in in direct contact with the surrounding, that is first going to lose heat, and as a result, reduce its temperature to five degrees Celsius.

11:48Now, because it is colder, it has a higher density, and as a result, it will sink below the other layers. And now this one will, you know, cool down to five degrees Celsius. It gets colder, it gets higher density, it'll sink, and eventually the last layer will come on top.

12:04So this is how we can model how extremely large water bodies cool down. Now, if the temperature gets lower to say four degrees Celsius, again, the same thing repeats, and the whole ocean now is at four degrees Celsius. But at four degrees Celsius, remember we have maximum density.

12:18Now if the surrounding temperature goes below four degrees Celsius, let's say three degrees Celsius, again, the top layer will go down to three degrees Celsius because it's in direct contact, but look, now the density is lower than the layers below, which means it cannot sink.

12:33It will keep floating, and these layers will not have a chance to keep come in contact with the surrounding layer, and therefore, relatively, they'll stay warm, pretty close to 40 degrees Celsius. And now as the temperature keeps dropping, this is the layer whose temperature will keep dropping, keeping the lower layers warm, and eventually this layer will crystallize.

12:53And now it doesn't matter how cold it gets outside, the lower layers are protected. And this is why only the top of the water body tends to get frozen and the bottom will stay relatively warm, and it'll stay in the liquid form. It allows aquatic life to exist.