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Hey Crazies.
Black holes seem like the ultimate absorbers.
If something crosses the event horizon, it’s trapped.
It’ll never interact with anything in our universe again.
Given that, you’d expect a black hole to be absolute zero, but it isn’t.
The spacetime around them emits Hawking radiation,
and that radiation is surprisingly thermal.
What’s Hawking radiation?
Ok, fine, but just the quick version.
Contrary to popular belief, this is not what a black hole looks like.
They’re not holes in a flat plane.
They’re actually spheres.
They’re balls.
Black balls in space!
They completely enclose a certain amount of space.
A space from which nothing can escape, ever.
The outer edge of that space is called an event horizon.
That’s just a boundary we can’t see beyond.
But plenty of stuff escapes from just outside that boundary.
Usually, that stuff is emitted by in-falling matter.
These accretion disks, as they’re called, can emit light across the EM spectrum,
from radio waves all the way up to x-rays.
They can even emit matter in the form of astrophysical jets.
But even if a black hole doesn’t have one of those disks around it, it’ll still emit light.
The space itself emits that light.
No infalling matter necessary.
It’s called Hawking radiation
because it was predicted by Stephen Hawking back in 1974.
I have a whole video on how that works if you want to check it out later.
What matters today is the pattern we see in it.
Brightness or intensity patterns in light can give us a feel for it.
If we see something like this, we know the light is just reflected off a surface.
This pattern is light emitted due solely to temperature.
This one has quantum origins.
So what kind is Hawking radiation?
The temperature kind.
Wait, black holes have a temperature?
Apparently, yes.
[Title Screen: The 4 Laws of Thermodynamics]
These days, thermodynamics is the study of energy exchanges on the atomic and molecular level,
but it didn’t start that way.
To the timeline!
Thermodynamics began as the study of pressure, volume, and temperature.
In 1662, Robert Boyle published a law relating pressure and volume.
In 1780, Jacques Charles discovered a relationship between volume and temperature.
He didn’t publish it though.
Joseph Louis Gay-Lussac confirmed the result and published it in 1802,
crediting Jacques for the discovery.
At least there’s some honor among science thieves.
Anyway, at the same time, Joseph also published a law relating pressure and temperature,
which was ultimately named after him.
They wouldn’t be combined into a single law until 1834 by Émile Cl…
By Émile Clapa.
Clap-Ay-Raw.
[Laughing]
You can do it.
Ah! The French names are going to be the death of me!
…by Émile Clapeyron.
But, these laws only applied to gases, not liquids or solids,
so we already knew we were missing something.
Let’s rewind a bit.
Back in 1702, Guillaume Amontons suggested a value for the minimum possible temperature.
An absolute zero.
His suggestion was -400 degrees fahrenheit or -240 degrees celsius,
which is honestly impressively close.
This idea would later become known as the third law of thermodynamics.
In 1749, Émilie du Châtelet derived the conservation of energy for the first time ever.
Conservation of energy shall not be violated!
It was commentary she wrote in the margin as she was translating Newton’s book into French.
Unfortunately, she doesn’t get a lot of notoriety because she was a woman in science.
Conservation of energy wouldn’t be officially recognized until almost 100 years later
when Hermann von Helmholtz publishes it as the first law of thermodynamics.
In 1824, Sadi Carnot laid the groundwork for the second law of thermodynamics
which Rudolf Clausius formalized in 1850 with his concept of entropy.
Aren’t there four laws of thermodynamics?
Yes, but the zeroth law wasn’t added until 1936.
The zeroth law?
Hey look. I didn’t name it, ok?
It essentially defines how thermometers work, so everyone wanted it to be the first on the list,
but it was way too late to renumber the other three.
Hence, zeroth.
Just go with it.
What’s important about these laws is they don’t just apply to gases.
They apply to all substances: gases, liquids, and solids.
Physicists like it when rules apply to as many things as possible.
And the craziest thing about this is that these laws of thermodynamics also apply to black holes.
[Title Screen: Black Hole Thermodynamics]
If we’re going to measure the temperature of anything,
we’re going to need some kind of thermometer.
You know, that thing we were just talking about with the zeroth law of thermodynamics.
Everyday thermometers like that use something called heat conduction.
You put in the thermometer and energy moves directly from whatever is hotter
to whatever is cooler until thermal equilibrium is reached.
At that point, you get a reading from an expanding fluid or from a digital heat sensor.
That is, unless you have one of these.
They actually detect the infrared light from things like your forehead.
It doesn’t have to be your forehead though.
It could really be anything in the range of the sensor.
Boom!
Boom.
[Laughter] Boom!
I love this thing.
Anyway, the light isn’t limited to infrared.
That just happens to be what most everyday objects are emitting.
Light bulbs are so hot, they emit visible light.
Empty space is so cold, it emits microwave light.
It depends on temperature, which is why it can used as a thermometer.
And it’s the only thermometer available for things in outer space.
It’s how we know the surface temperature of the Sun is 5800 kelvin
and it’s how we know black holes are crazy cold.
Sure, the infalling matter can get hot, but the black holes themselves are really cold.
At most, we’re talking 20 nanokelvin.
That’s 20 billionths of a kelvin.
For comparison, the background temperature of empty space is 2.73 kelvin.
That’s whole kelvins, not nanokelvins.
The background temperature of the universe is 100 million times hotter
than the hottest black hole, which is why none of them are shrinking yet.
The extreme freeze of the vacuum is too hot.
But, if black holes have a temperature,
then it stands to reason they should obey the four laws of thermodynamics.
And they do!
It’s just that they do it in a way that’s a little counterintuitive.
Let’s say you preheat an oven and then you put a pan inside it.
The oven air is hot. It’s much hotter than the pan.
Our instincts tell us that the pan will heat up.
The air gives it heat.
No no no! No no! Don’t touch it!
There you go. Safety first.
Just like the pan, black holes can exchange energy with their surroundings.
They can absorb energy by eating and they can release it through Hawking radiation.
In both cases, energy is conserved.
Conservation of energy shall not be violated!
That means black holes obey the first law of thermodynamics.
It’s their temperature that’s counterintuitive.
We’d expect this eating growing black hole to get hotter because it’s absorbing energy.
But it doesn’t. It gets cooler.
Black holes cool down by eating and they heat up by emitting Hawking radiation.
What? What?! WHAT?!
I know. I know. It sounds like crazy talk,
but it’s what our model for Hawking radiation tells us.
Remember that thermal radiation curve from earlier?
Well, when we plot out Hawking radiation for black holes of various sizes, they look like this.
The bigger black holes emit lower frequency light and less light overall.
The only logical conclusion is that bigger black holes are colder than smaller black holes.
This doesn’t break the zeroth law though.
They do still find thermal equilibrium with their surroundings.
It just doesn’t happen until they completely evaporate.
This temperature pattern also helps them obey the third law.
That’s the one that says nothing can reach absolute zero.
It’s the minimum temperature.
Black holes can get very cold, but they’ll never reach absolute zero,
which makes sense.
For a black hole to be absolute zero, it would have to be infinitely big.
Wait.
No no. No! The universe is not a black hole!
Ok, so what about the second law?
It’s obeyed too, but that’s a giant can of worms I don’t want to open right now.
Don’t worry. I’m going to do a whole video on it.
The point is that all four laws of thermodynamics are obeyed by black holes.
We know they have a temperature because the light they emit matches a thermal curve.
Most of the light is extreme radio waves though because they’re very very cold.
The smallest stellar-mass black holes are only about 20 nanokelvin.
That’s 100 million times colder than the background temperature of the universe.
The supermassive black hole at the center of our Milky Way galaxy is only 15 femtokelvin.
That’s over a million times colder than the smallest stellar-mass black holes.
Black holes are the coldest things in the universe.
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And until next time, remember: It’s ok to be a little crazy.
The featured comment comes from Chingam Fong who brought up an interesting point
about the rate at which space expands compared to the passage of time.
Yes, the Boltzmann universe has problems.
It’s a little outdated.
I was just hoping to use it as a launching point for more modern cyclic models.
Anyway, thanks for watching!