Fluids and density | AP Physics | Khan Academy

- [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?

And 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.

But, 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.

So, 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?

Well, 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.

Now, 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.

If 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.

However, 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.

That'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.

All 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?

Well, 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.

But 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?

Whatever 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.

So 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.

And 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.

But 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.

Similarly, 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.

You 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.

And 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.

But 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.

And 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?

Well, 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.

I 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.

So 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.

In 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.

And 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.

What 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.

All 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?

Well, 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.

Stuff 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.

Here'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.

What'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.

Okay, 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.

So 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.

They 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.

We 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.

That 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.

So 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?

Well 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.

And 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?

Now 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.

Now, 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.

So 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.

Now 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.

It 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.

And 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.