All language subtitles for What-Everyone-Gets-Wrong-About-Energy-en

- This is a video about
one of the most important,

yet least understood
concepts in all of physics.

It governs everything
from molecular collisions

to humongous storms.

From the beginning of the universe

through its entire evolution,
to its inevitable end.

It may, in fact, determine
the direction of time

and even be the reason that life exists.

To see the confusion around this topic,

you need to ask only one simple question.

What does the Earth get from the sun?

- What does the earth get from sun?

- Well, it's light rays?

- What do we get from the sun?
- Heat.

- Warmth.

- Warmth, light.

- Vitamin D, we get vitamin D from-

- We do get vitamin D
from the ultraviolet rays.

- Well, a lot of energy.

- What does the earth
get from this, energy?

- Yeah, energy.

- Energy.

- Nailed it.

Every day, the earth gets
a certain amount of energy

from the sun.

And then how much energy
does the earth radiate back

into space relative to that amount

that it gets from the sun?

- Probably not as much, I, you know,

I don't believe it's just
radiating right back.

- I'd say less.

- Less.

- Less.
- I say less.

- I guess about 70%?

- It is a fraction.

- I'd say 20%.

- Because...
- Because we use some of it.

- We use some of the energy.
- Mm-hmm.

- We consume a lot, right?

- But the thing about energy
is it never really goes away.

You can't really use it up.

- It would have to
break even, wouldn't it?

Same amount, yeah.

- You know, cause and effect.

It'd be equal in some ways, right?

- For most of the earth's history,

it should be exactly the
same amount of energy

in from the sun as earth
radiates into space.

- Wow.

- Because if we didn't do that,

then the earth would get a lot
hotter, that'd be a problem.

- That'd be a big problem.

- So, if that is the case...

- Yeah.

- Then what are we really
getting from the sun?

- That's a good question.

- Hmm.

- It gives us a nice tan.

- It gives us a nice tan, I love it.

We're getting something
special from the sun.

- I don't know, what do
we get without the energy?

- But nobody talks about it.

To answer that, we have
to go back to a discovery

made two centuries ago.

In the winter of 1813,
France was being invaded

by the armies of Austria,
Prussia, and Russia.

The son of one of Napoleon's generals

was Sadi Carnot, a 17-year-old student.

On December 29th, he
writes a letter to Napoleon

to request to join in the fight.

Napoleon preoccupied in
battle, never replies.

but Carnot gets his
wish a few months later

when Paris is attacked.

The students defend a chateau
just east of the city,

but there're no match
for the advancing armies,

and Paris falls after
only a day of fighting.

Forced to retreat, Carnot is devastated.

Seven years later, he
goes to visit his father

who's fled to Prussia
after Napoleon's downfall.

His father was not only a
general, but also a physicist.

He wrote an essay on how energy

is most efficiently transferred
in mechanical systems.

When his son comes to
visit, they talk at length

about the big breakthrough
of the time, steam engines.

Steam engines were already
being used to power ships,

mine ore, and excavate ports.

And it was clear that
the future industrial

and military might of nations

depended on having the best steam engines.

But French designs were falling behind

those of other countries like Britain.

So, Sadi Carnot took it upon
himself to figure out why.

At the time, even the best steam engines

only converted around 3% of thermal energy

into useful mechanical work.

If he could improve on
that, he could give France

a huge advantage and restore
its place in the world.

So he spends the next three
years studying heat engines,

and one of his key insights

involves how an ideal
heat engine would work,

one with no friction and no
losses to the environment.

It looks something like this.

Take two really big metal
bars, one hot and one cold.

The engine consists of a
chamber filled with air,

where heat can only flow in
or out through the bottom.

Inside the chamber is a piston,

which is connected to a flywheel.

The air starts at a
temperature just below that

of the hot bar.

So first, the hot bar
is brought into contact

with the chamber.

The air inside expands
with heat flowing into it

to maintain its temperature.

This pushes the piston
up, turning the flywheel.

Next, the hot bar is removed,

but the air in the chamber
continues to expand,

except now without heat entering,
the temperature decreases.

In the ideal case,

until it is the temperature
of the cold bar.

The cold bar is brought into
contact with the chamber

and the flywheel pushes the piston down.

And as the air is compressed,

heat is transferred into the cold bar.

The cold bar is removed.

The flywheel compresses the gas further

increasing its temperature
until it is just below that

of the hot bar.

Then the hot bar is connected
again and the cycle repeats.

Through this process, heat
from the hot bar is converted

into the energy of the flywheel.

And what's interesting to note
about Carnot's ideal engine

is that it is completely reversible.

If you ran the engine in reverse,

first the air expands
lowering the temperature,

then the chamber is brought
into contact with the cold bar,

the air expands more, drawing
in heat from the cold bar.

Next, the air is compressed,
increasing its temperature.

The chamber is placed
on top of the hot bar

and the energy of the flywheel
is used to return the heat

back into the hot bar.

However many cycles were run
in the forward direction,

you could run the same number
in reverse, and at the end,

everything would return
to its original state

with no additional input
of energy required.

So by running an ideal engine,
nothing really changes.

You can always undo what you did.

So what is the efficiency of this engine?

Since it's fully reversible,

you might expect the
efficiency to be 100%,

but that is not the case.

Each cycle, the energy
of the flywheel increases

by the amount of heat flowing

into the chamber from the hot bar,

minus the heat flowing out of
the chamber at the cold bar.

So to calculate the efficiency,
we divide this energy

by the heat input from the hot bar.

Now the heat in on the hot
side is equal to the work done

by the gas on the piston,

and this will always be
greater than the work done

by the piston on the gas on the cold side,

which equals the heat out.

And this is because on the hot side,

the hot gas exerts a greater pressure

on the piston than that
same gas when cold.

To increase the efficiency of the engine,

you could increase the
temperature of the hot side,

or decrease the temperature
of the cold side, or both.

Lord Kelvin learns of
Carnot's ideal heat engine

and realizes it could form the basis

for an absolute temperature scale.

Imagine that the gas is allowed
to expand an extreme amount,

so much that it cools to the point

where all the gas particles
effectively stop moving.

Then they would exert no
pressure on the piston,

and it would take no work to compress it

on the cold side, so
no heat would be lost.

This is the idea of absolute zero,

and it would make for a
100% efficient engine.

Using this absolute temperature
scale, the Kelvin scale,

we can replace the
amount of heat in and out

with the temperature of the
hot and cold side respectively,

because they are directly proportional.

So we can express efficiency like this,

which we can rewrite like this.

What we have learned
is that the efficiency

of an ideal heat engine
doesn't depend on the materials

or the design of the engine,

but fundamentally on the temperatures

of the hot and cold sides.

To reach 100% efficiency,
you'd need infinite temperature

on the hot side or absolute
zero on the cold side,

both of which are impossible in practice.

So even with no friction or
losses to the environment,

it's impossible to make a
heat engine 100% efficient.

And that's because to return the piston

to its original position,

you need to dump heat into the cold bar.

So not all the energy
stays in the flywheel.

Now, in Carnot's time,
high pressure steam engines

could only reach temperatures
up to 160 degrees Celsius.

So their theoretical
maximum efficiency was 32%,

but their real efficiency
was more like 3%.

That's because real engines
experience friction,

dissipate heat to the environment,

and they don't transfer heat
at constant temperatures.

So for just as much heat going in,

less energy ends up in the flywheel.

The rest is spread out over
the walls of the cylinder,

the axle of the flywheel,

and is radiated out into the environment.

When energy spreads out like this,

it is impossible to get it back.

So this process is irreversible.

The total amount of energy didn't change,

but it became less usable.

Energy is most usable
when it is concentrated

and less usable when it's spread out.

Decades later, German
physicist, Rudolf Clausius,

studies Carnot's engine,
and he comes up with a way

to measure how spread out the energy is.

He calls this quantity, entropy.

When all the energy is
concentrated in the hot bar,

that is low entropy,

but as the energy spreads
to the surroundings,

the walls of the chamber and the axle

will entropy increases.

This means the same amount
of energy is present,

but in this more dispersed form,

it is less available to do work.

In 1865, Clausius summarizes
the first two laws

of thermodynamics like this.

First, the energy of the
universe is constant.

And second, the entropy of the
universe tends to a maximum.

In other words, energy
spreads out over time.

The second law is core to so
many phenomena in the world.

It's why hot things cool
down and cool things heat up,

why gas expands to fill a container,

why you can't have a
perpetual motion machine,

because the amount of usable
energy in a closed system

is always decreasing.

The most common way to describe
entropy is as disorder,

which makes sense because
it is associated with things

becoming more mixed,
random, and less ordered.

But I think the best way
to think about entropy

is as the tendency of
energy to spread out.

So why does energy spread out over time?

I mean, most of the laws of physics

work exactly the same way
forwards or backwards in time.

So how does this clear
time dependence arise?

Well, let's consider two small metal bars,

one hot and one cold.

For this simple model,

we'll consider only eight atoms per bar.

Each atom vibrates according to the number

of energy packets it has.

The more packets, the more it vibrates.

So let's start with
seven packets of energy

in the left bar and three in the right.

The number of energy packets in each bar

is what we'll call a state.

First, let's consider just the left bar.

It has seven energy packets,

which are free to move around the lattice.

This happens nonstop.

The energy packets hop
randomly from atom to atom

giving different configurations of energy,

but the total energy stays
the same the whole time.

Now, let's bring the cold bar back in

with only three packets
and touch them together.

The energy packets can now hop around

between both bars creating
different configurations.

Each unique configuration
is equally likely.

So what happens if we take a
snapshot at one instant in time

and see where all the energy packets are?

So stop, look at this.

Now there are nine energy
packets in the left bar,

and only one in the right bar.

So heat has flowed from cold to hot.

Shouldn't that be impossible
because it decreases entropy?

Well, this is where Ludwig Boltzmann

made an important insight.

Heat flowing from cold
to hot is not impossible,

it's just improbable.

There are 91,520 configurations

with nine energy packets in the left bar,

but 627,264 with five
energy packets in each bar.

That is the energy is more than six times

as likely to be evenly
spread between the bars.

But if you add up all the possibilities,

you find there's still a
10.5% chance that the left bar

ends up with more energy
packets than it started.

So, why don't we observe
this happening around us?

Well, watch what happens as we
increase the number of atoms

to 80 per bar and the
energy packets to 100,

with 70 in the left bar
and 30 in the right.

There is now only a 0.05%
chance that the left solid

ends up hotter than it started.

And this trend continues as
we keep scaling up the system.

In everyday solids, there
are around 100 trillion,

trillion atoms and even
more energy packets.

So heat flowing from cold
to hot is just so unlikely

that it never happens.

Think of it like this Rubik's cube.

Right now, it is completely solved,

but I'm gonna close my eyes
and make some turns at random.

If I keep doing this, it
will get further and further

from being solved.

But how can I be confident
that I'm really messing

this cube up?

Well, because there's only
one way for it to be solved,

a few ways for it to be almost solved,

and quintillions of ways

for it to be almost entirely random.

Without thought and effort,

every turn moves the Rubik's cube

from a highly unlikely state
that of it being solved

to a more likely state, a total mess.

So if the natural tendency
of energy is to spread out

and for things to get messier,

then how is it possible to have something

like air conditioning where
the cold interior of a house

gets cooler and the hot
exterior gets hotter?

Energy is going from cold to hot,

decreasing the entropy of the house.

Well, this decrease in
entropy is only possible

by increasing the entropy a
greater amount somewhere else.

In this case, at a power plant,

the concentrated chemical energy
and coal is being released,

heating up the power
plant in its environment,

spreading to the turbine
the electric generators,

heating the wires all
the way to the house,

and producing waste heat
in the fans and compressor.

Whatever decrease in entropy
is achieved at the house

is more than paid for by an
increase in entropy required

to make that happen.

But if total entropy is
constantly increasing

and anything we do only
accelerates that increase,

then how is there any
structure left on earth?

How are there hot parts
separate from cold parts?

How does life exist?

Well, if the earth were a closed system,

the energy would spread out completely,

meaning, all life would cease,

everything would decay and mix,

and eventually, reach
the same temperature.

But luckily, earth is not a closed system,

because we have the sun.

What the sun really gives
us is a steady stream

of low entropy that is
concentrated bundled up energy.

The energy that we get
from the sun is more useful

than the energy we give back.

It's more compact, it's
more clumped together.

Plants capture this
energy and use it to grow

and create sugars.

Then animals eat plants
and use that energy

to maintain their bodies and move around.

Bigger animals get their energy

by eating smaller animals and so on.

And each step of the way,

the energy becomes more spread out.

- Okay, interesting.

- Yeah.

- Oh wow, I did not know that.

- There you go.

Ultimately, all the energy
that reaches earth from the sun

is converted into thermal energy,

and then it's radiated back into space.

But in fact, it's the same amount.

I know this is a-
- You do know this is...

- I'm a PhD physicist.

- Oh, okay, but anyway, so...
- I trust you.

The increase in entropy can be seen

in the relative number
of photons arriving at

and leaving the earth.

For each photon received from the sun,

20 photons are emitted,

and everything that happens on earth,

plants growing, trees
falling, herds stampeding,

hurricanes and tornadoes, people eating,

sleeping, and breathing.

All of it happens in the
process of converting fewer,

higher energy photons

into 20 times as many
lower energy photons.

Without a source of concentrated energy

and a way to discard
the spread out energy,

life on earth would not be possible.

It has even been
suggested that life itself

may be a consequence of the
second law of thermodynamics.

If the universe tends
toward maximum entropy,

then life offers a way to
accelerate that natural tendency,

because life is spectacularly good

at converting low entropy
into high entropy.

For example, the surface
layer of seawater produces

between 30 to 680% more
entropy when cyanobacteria

and other organic matter is
present than when it's not.

Jeremy England takes
this one step further.

He's proposed that if
there is a constant stream

of clumped up energy, this
could favor structures

that dissipate that energy.

And over time, this results

in better and better energy dissipators,

eventually resulting in life.

Or in his own words,

"You start with a random clump of atoms,

and if you shine light
on it for long enough,

it should not be so surprising
that you get a plant."

So life on earth survives on
the low entropy from the sun,

but then where did the
sun get its low entropy?

The answer is the universe.

If we know that the total
entropy of the universe

is increasing with time, then
it was lower entropy yesterday

and even lower entropy
the day before that,

and so on, all the way
back to the Big Bang.

So right after the Big Bang,

that is when the entropy was lowest.

This is known as the past hypothesis.

It doesn't explain why
the entropy was low,

just that it must have been
that way for the universe

to unfold as it has.

But the early universe was hot, dense,

and almost completely uniform.

I mean, everything was
mixed and the temperature

was basically the same everywhere,

varying by at most 0.001%.

So how is this low entropy?

Well, the thing we've left out is gravity.

Gravity tends to clump matter together.

So taking gravity into account,

having matter all spread out like this,

would be an extremely unlikely state,

and that is why it's low entropy.

Over time, as the universe
expanded and cooled,

matter started to clump
together in more dense regions.

And in doing so, enormous
amounts of potential energy

were turned into kinetic energy.

And this energy could also be used

like how water flowing
downhill can power a turbine.

But as bits of matter
started hitting each other,

some of their kinetic energy
was converted into heat.

So the amount of useful energy decreased.

Thereby, increasing entropy.

Over time, the useful energy was used.

In doing so, stars, planets,
galaxies, and life were formed,

increasing entropy all along.

The universe started with around 10

to the 88 Boltzmann
constants worth of entropy.

Nowadays, all the stars
in the observable universe

have about 9.5 times 10 to the 80.

The interstellar and
intergalactic medium combined

have almost 10 times more,

but still only a fraction
of the early universe.

A lot more is contained in neutrinos

and in photons of the
cosmic microwave background.

In 1972, Jacob Bekenstein proposed

another source of entropy, black holes.

He suggested that the
entropy of a black hole

should be proportional
to its surface area.

So as a black hole grows,
its entropy increases.

Famous physicists thought
the idea was nonsense

and for good reason.

According to classical thermodynamics,

if black holes have entropy,

then they should also have a temperature.

But if they have temperatures,
they should emit radiation

and not be black after all.

The person who set out
to prove Bekenstein wrong

was Stephen Hawking.

But to his surprise, his
results showed that black holes

do emit radiation, now
known as Hawking radiation,

and they do have a temperature.

The black hole at the
center of the Milky Way

has a temperature of about a
hundred trillionth of a Kelvin,

emitting radiation that
is far too weak to detect.

So still pretty black.

But Hawking confirmed that
black holes have entropy

and Bekenstein was right.

Hawking was able to refine
Bekenstein's proposal

and determine just how
much entropy they have.

The super massive black hole
at the center of the Milky Way

has about 10 to the 91
Boltzmann constants of entropy.

That is 1,000 times as much

as the early observable universe,

and 10 times more than all
the other particles combined.

And that is just one black hole.

All black holes together
account for 3 times 10

to the 104 Boltzmann
constants worth of entropy.

So almost all the entropy of the universe

is tied up in black holes.

That means, the early universe

only had about 0.000000000000003%
of the entropy it has now.

So the entropy was low,
and everything that happens

in the universe like
planetary systems forming,

galaxies merging, asteroids crashing,

stars dying, to life itself flourishing,

all of that can happen because the entropy

of the universe was low
and it has been increasing,

and it all happens only in one direction.

We never see an asteroid uncrash

or a planetary system unmix

into the cloud of dust
and gas that made it up.

There is a clear difference
between going to the past

and the future, and that
difference comes from entropy.

The fact that we are going from unlikely

to more likely states is why
there is an arrow of time.

This is expected to
continue until eventually,

the energy gets spread out so completely

that nothing interesting
will ever happen again.

This is the heat death of the universe.

In the distant future,

more than 10 to the 100 years from now,

after the last black hole has evaporated,

the universe will be in
its most probable state.

Now, even on large scales,
you would not be able to tell

the difference between time
moving forwards or backwards,

and the arrow of time
itself would disappear.

So it sounds like entropy
is this awful thing

that leads us inevitably

towards the dullest outcome imaginable.

But just because maximum
entropy has low complexity

does not mean that low entropy
has maximum complexity.

It's actually more like this tea and milk.

I mean, holding it like this
is not very interesting.

But as I pour the milk
in, the two start to mix

and these beautiful patterns emerge.

They arise in an instant
and before you know it,

they're gone back to being featureless.

Both low and high entropy
are low in complexity.

It's in the middle
where complex structures

appear and thrive.

And since that's where we find ourselves,

let's make use of the low
entropy we've got while we can.

With the right tools, we can
understand just about anything,

from a cup of tea cooling down

to the evolution of the entire universe.

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