Density (conceptual)

0:00- [Teacher] Here's an old joke, what weighs more, a ton of bricks or a ton of feathers? When I first heard this, I was like, "Of course bricks weigh more than the feathers. Come on. That's obvious." But wait, we asked what weighs more, a ton of bricks or a ton of feathers?

0:16Since they're both one ton, they must weigh exactly the same. (laughs) But this feels weird. My brain is telling me bricks must weigh more than the feather. Why is that? Well, because when I hear this question, I completely ignore the one ton part, and I consider them having equal volumes.

0:34I consider equal volumes of bricks and feather. And if you do consider equal volumes of bricks and feather, then of course bricks will weigh more than the feather. But the question asked one ton of bricks and feather, let's see, what would that look like? If you took a ton of bricks, it'll occupy a space which is almost the same as a household refrigerator, but if you take a ton of feathers, you would need as much... (laughs) It'll occupy a space of a small house, okay?

1:02Only then they will have the same mass. So clearly this is very weird and we usually don't think like that. So we completely ignore the ton part, and we assume instinctively that they have the same volume, equal volume, and therefore we conclude that bricks will weigh more than the feathers.

1:20Or we conclude that hey, metals are heavier than plastic, for example, with instinctively thinking that they have the same or equal volume. And this is interesting because what we are instinctively thinking about is something called the density. What exactly is density you ask?

1:34Well, density is a measure of how much mass is packed in a given volume. Now this will make more sense if we take some concrete example. Through that let's first think about the units. In the metric system for mass, we can use units of kilograms or grams. For volume, we can use cubic centimeters or cubic meters.

1:54Let's use cubic centimeters over here. So let's now consider exactly one centimeter cube of bricks and one centimeter cube of feathers. How big is the centimeter cube you ask? Well just consider a box, a cube of length and width and height, all one centimeter, that will have a volume of one centimeter cube.

2:12And this is a very small volume. It's same size as a small die. So a centimeter cube is pretty small. It's actually the same as a milliliter. A centimeter cube is the same as a milliliter as well. But anyways, if you consider one centimeter cube of bricks, you know how much will be its mass?

2:28It'll have a mass of 1.6 grams. And if you take one centimeter cube of feather, it'll have a mass of 0.0025 grams, very little mass. So now over here, look, 1.6 grams of bricks is packed per cm cubed. So we say the density of the bricks is 1.6 grams per cm cubed.

2:48Similarly, over here, look, 0.0025 grams of feather is packed per cm cubed. So it's densities 0.0025 grams per cm cubed. That's what density is all about. And look, density of the bricks is much higher than density of the feathers. And that's what we've been instinctively thinking about.

3:06When we think that bricks are heavier than feathers, we're not thinking about their mass, we are thinking about their density. Pretty cool, right? Okay, let's test our understanding before moving forward. What if I had 10 centimeter cube of the same bricks, same density, what would be its mass?

3:22Can you pause and think about it? All right, since each cm cube has a mass of 1.6 grams, if I have 10 cm cubes, 10 times as much, then the mass will also be 10 times as much. So it'll be 10 times 1.6, which is 16 grams. Does that make sense? And if I had, for example, 100 cm cube of the bricks, then its mass would be 100 times more, 160 grams.

3:47This also helps us understand that density is an intrinsic property, meaning density does not depend upon the amount of stuff. It doesn't matter how many bricks I have or how big the bricks are, the density will be the same. Mass, on the other hand, is an extrinsic property.

4:01It does depend upon the amount of stuff. Look, more stuff, more mass. Volume also depends upon the amount of stuff, more stuff, more volume. But density, which is a mass per volume, that does not depend upon how much stuff you have. That is an intrinsic property of the material itself.

4:16So now let's look at the density values of some common things. You can see gases have very low density. Metals tend to have very high density. Osmium, for example, is one of the densest metals that we know. But compare that with aluminum, it's also a metal, but it has a very low density, and that's why it is used in construction material because you can build lightweight stuff.

4:39That's pretty cool. Right? And before we talk about more interesting things about density, let's again check our understanding. Here's a pop quiz. If I take the same volume of copper and gold, which one do you think will weigh more? Why don't you pause and think about it?

4:53All right, I know that gold has a higher density compared to copper, I can see that over here. Meaning more mass is packed in a given volume compared to copper, which means for equal volumes, gold must be heavier than copper. Okay, another question, a slightly harder one.

5:10I have three materials, aluminum, copper, and gold. But this time I have the same mass. Which of the three will have the biggest size? Why don't you pause and try. All right, let's see. Let's say the mass is 100 grams. Okay? Now of the three aluminum has the lowest density, meaning it has the least amount of mass packed in a given volume.

5:29So it'll take a lot of aluminum to get this up to 100 grams. And therefore, if they need to have the same mass, aluminum needs to be the biggest, next would be copper, and the last would be gold. Makes sense, right? Okay, another interesting thing to note is water has a density of exactly 1.0 grams per cm cube.

5:47Is that some kind of a neat coincidence? No. That's how we define what a gram is. We define a gram as the mass of one cm cube of water. That's our definition of a gram. And that's why water ends up having a density of 1.0 grams per cm cube. And this is pretty useful in predicting whether the stuff will sink or float.

6:05Stuff that has the density less than that of water will float and stuff that has density more than that of water will sink. This is why, for example, if you take a big piece of wood, let's say oak wood, since it has a density less than that of water, it will float.

6:19Even if you take a very tiny piece of an iron nail because it has a density more than that of water, it's going to sink. But finally, guess what's the densest thing in the universe? Well, it happens to be something called the neutron stars. Their density is this big. That's right.

6:38If you take a cm cube of a neutron star, which is like again, of one die worth of neutron star, its mass would be about 900 billion kilograms. Can you imagine that? That is about the mass of a Mount Everest. A tiny die worth of neutron star will have that much mass, wow.

6:59So if you now come down and summarize, density is the amount of mass that is packed in a given volume, mass per volume. It can be measuring grams per cm cube or other units like kilograms per meter cube and so on. But what's important is that it's an intrinsic property of a material.

7:16It does not depend upon how much stuff you have.