- I wanted to see if I could find
the value of absolute zero for myself, experimentally.
I'm sure you know what absolute zero is,
but just to recap you can take something
and you could heat it up as much as you like.
You can keep going, getting hotter
and hotter and hotter and hotter indefinitely.
That's not true in the opposite direction.
If you keep cooling something down
eventually you'll reach a limit.
You can't go any colder than that.
That's because temperature is a function of thermal energy
and thermal energy is just like how much of the atoms
and molecules inside something jiggling around.
So the more the atoms and molecules are jiggling around
the hotter the thing is, and the less they're jingling
around the cold of the thing is.
And so if you keep cooling something down
you eventually get to the point
where those atoms and molecules aren't jiggling anymore.
The point I'm trying to make is
there's no such thing as negative jiggle,
it's called absolute zero because of the Kelvin scale.
And by definition on the Kelvin scale,
zero is the coldest possible thing.
So in some sense,
I don't need to find the value of absolute zero
because it's zero on the Kelvin scale.
The question really is what's the value of absolute zero
on the centigrade scale or the Fahrenheit scale
not the Fahrenheit scale that's stupid,
on the centigrade scale, what's the value of absolute zero
or to switch it around you could say,
what is the value of the freezing point of water
at atmospheric pressure on the Kelvin scale?
In other words,
we're trying to link these two scales
to find out what absolute zero really means
in terms of what we already understand.
A degree on the Kelvin scale
and a degree on the Celsius scale of the same size.
It's just the zeros on those two scales are
in different places, by the way, apologies
if I keep switching between Celsius and centigrade
they mean the same thing.
Centigrade is just an older word
that people don't use anymore
but I keep using it because I'm an asshole
interesting word origin by the way, centigrade.
So centi means 100 and there are 100 gradations
between the freezing point of water
and the boiling point of water,
which is why the freezing point is zero.
And the boiling point is a hundred.
So how are we gonna find absolute zero experimentally?
You may have heard of this equation PV equals nRT.
It's the ideal gas law where P is pressure V is volume,
n is how much gas there is R is a constant
and T is temperature.
Let's decide in our experiment
that the amount of gas is gonna stay the same.
We're not gonna let any in or let any out.
So N is constant as well, and let's design our experiment.
So the pressure stays the same.
So P is constant.
Let's rearrange this equation by dividing both sides by P
we've now got V equals nRT divided by P
and because nR and P are all constant
by design of our experiment.
We can say that V equals some constant multiplied by T.
In other words, V and T are proportional to each other.
If you double one of them, you double the other.
If you half one of them, you half the other.
And by the way, in this simplified form
this is Charles's law.
These equations work when you plug in values of temperature
from the Kelvin scale, they don't work
if you plug in temperatures from the Celsius scale
or the Fahrenheit scale,
that's because these equations rely on temperatures
from an absolute scale of temperature
of which the Kelvin scale is an example.
An absolute scale is one where the zero value
on that scale means something.
It means none of something
it's an actual zero, in some sense.
So in the Kelvin scale
it means zero thermal energy or zero jiggle.
Whereas the zero on the Celsius scale
it doesn't mean zero of anything.
You can proceed in either direction from zero.
Another example of relative scale is our date system.
So the zero year on our date system was first defined
by Dionysius Exiguus who believed
it was the date of Jesus' birth.
And you can proceed in either direction from that zero.
If we wanted an absolute date scale
then I guess we should go all the way back
to the birth of the universe.
Two problems with that first, we don't know how far back
the birth of the universe was to that kind of accuracy.
And even if we did, it would make writing out the year
in full, incredibly tedious.
So how can we use this equation
to find the value of absolute zero?
Well, let's assume we've got a volume of gas
and it's at room temperature, 21 degrees centigrade.
Look, there it is.
But you know, for what I just said moments ago
that we've made a mistake.
We can't plug Celsius into this equation.
It needs to be Kellvin.
So we need to convert 21 degrees Celsius
into the Kelvin equivalent.
How do we do that?
Well, 21 degrees Celsius means 21 degrees
above the freezing point of water.
So to convert to Kelvin,
we just need to know the temperature of the freezing point
of water in Kelvin, and then add 21 to that.
So we could look up the temperature of the freezing point
of water in Kelvin, but that would defeat the purpose.
That's the thing we're trying to work out, right?
That's the thing that we're pretending we don't already know
that we want to find experimentally for ourselves.
So let's call that value X and put that into the equation.
So there we go, that value in brackets
that's room temperature in Kelvin
and we've got that unknown value in there.
So all we have to do is take some measurements,
but there's the volume, there's the temperature
and then rearrange the equation to solve for X.
So let's do that.
Divide both sides by a subtract 21 from both sides.
And there's X, there's our value
of the freezing point of water in Kelvin.
So what would happen,
if we did the experiments and plugged some values in?
Well, remember our constant a here is
actually hiding a load of stuff.
A is actually nR divided by P.
So we need to plug those values in as well
as the things we measured experimentally.
So n is the amount of gas we can measure that it's in moles,
the pressure is atmospheric pressure.
We can measure that and plug that in,
R is the ideal gas constant.
And we could plug that in as well.
We just look it up except that's cheating
because the idea of gas constant
and absolute zero are linked.
Like if you know one you get the other for free.
So if we're pretending not to know what absolute zero is
then we need to pretend not to know
what the ideal gas constant R is as well.
In fact, we could reframe this whole video and say
it's about finding R experimentally for ourselves
but let's stick with finding absolute zero and just know
that we could derive R from that if we wanted to.
So how do we proceed?
Well, we need to do the experiment twice
at two different temperatures.
And then we'll end up with two different equations
that we can combine in such a way
as to cancel out those unknown constants.
And then we can solve for X.
Here's the derivation on screen
for how you get X from two sets of measurements.
Pause the video, if you're interested in the details,
by the way you can see from the final equation
that it doesn't matter what units we use for volume
because they're always in ratio with each other.
So we're gonna use milliliters for convenience.
What about the experiment itself?
How do we design this thing?
So we can have a volume of gas, change the temperature,
see how the volume changes record it all.
My first thinking was to use a syringe.
So, you know, seal off the end,
you know how much gas is in there
because it's written on the side of the syringe.
You change the temperature, see how the volume changes.
The issue is that the piston
of a syringe has quite a bit of friction.
So it's not 60 at the moment.
If I push it up and then let go,
it doesn't relax all the way back to 60.
It stays slightly higher than that.
Meaning the pressure inside here is
higher than atmospheric pressure.
We've failed to keep pressure constant,
which if you remember,
that's one of the things we need to do.
So here's my solution.
You take a volume of gas with measurements up the side
like this, and you seal it except for a tube filled
with some liquid like water for example
so that when the volume of gas goes down
because we've lowered the temperature let's say
it's gonna pull liquid in through the tube.
So the other end of the tube will be in a reservoir
of the liquid, which is free to the elements ensuring
that we've got atmospheric pressure everywhere
even inside here.
So instead of having this piston seal
we've got this friction-free liquid seal.
Ideally we want to take measurements at two extremes
of temperature to reduce the impact of measurement errors.
So I had the idea of putting the whole assembly
in a freezer to get it really cold,
but then if the liquid inside is water,
the water's gonna freeze.
So I had the idea,
let's use vodka as the liquid instead of water.
Here I'm sucking air out through a hole,
and that will pull vodka
into the tube and into the container.
I need some vodka in the container to begin with
because the gas will expand when I heat it.
And so I need room for that.
And then I seal off that hole.
So we've got to air tight container.
I originally had the temperature probe embedded
in the volume of gas as well.
The problem with putting the whole assembly
in the freezer is that the electronics inside
just shut off below a certain temperature.
So I've ditched that idea instead of the freezer
we're gonna put the whole thing in a ice salt bath
which gets us below freezing.
And instead of having the thermal probe inside the chamber
we'll have it in the bath water so to speak,
all we have to do is give
the whole setup time to equilibrate.
So the temperature inside the chamber is the same
as the temperature inside the ice salt bath.
So here we go.
So we've got a temperature of minus 0.2
we've got a volume of vodka.
It's hard to see, but it's just shy of 105 milliliters,
subtract that from the total volume of the container
and compensate for the volume of the rubber tube.
You get a volume of gas of 135 milliliters.
In the hot bath the temperature is 51.1.
The volume of vodka is 60 milliliters
which translates to a gas volume of 180 milliliters.
So if you plug all those values into the equation
we get that the freezing point of water
on the Kelvin scale is 154 degrees.
Or in other words,
absolute zero on the centigrade scale is minus 154 degrees.
So at this point we might as well just Google it
and find out what it really is.
Oh, it's not great is it?
I think there's potentially a number of issues
with my experimental setup, but one obvious one is
that maybe we're changing the amount of gas in the chamber.
That seems like it could be possible
because the chamber is sealed but alcohol is quite volatile.
So it's gonna evaporate.
There's gonna be alcohol vapor in that chamber
and when the chamber cools down,
some of the alcohol vapor is gonna turn back
into liquid alcohol.
It's going to be removed from the gas.
The amount of gas in the chamber will go down
and that's consistent with the way
we're getting the number wrong.
The number we get is too small
because the volume is going down too much.
So I decided to revisit the syringe option
but lubricating the syringe to remove the issue of friction
and with a little bit of olive oil,
it seems to have improved the situation drastically.
So we're gonna do the experiment twice.
We're gonna do it with a salt ice bath
and we're gonna do with hot water from the kettle.
And these are the values we've got minus 1.2 degrees
54 milliliters, 75.6 degrees and 68 milliliters.
When we plug all those values into the equation
we get the absolute zero on the Celsius scale is
minus 297 degrees Celsius.
And that is not terrible.
There are a number of ways you can improve this experiment.
Like obviously improving the equipment.
There is still friction in the syringe.
You could figure out a way to avoid that.
You could take several data points
and then you end up with a line of best fit on a graph.
And that's gonna be more accurate too
but that's the general principle at least.
And it seems to be working quite well.
And actually by definition,
absolute zero is this extrapolated value.
You don't find absolute zero by getting colder
and colder and colder and colder,
like going on a quest for it in that direction.
It's extrapolated by definition
because actually the ideal gas laws start to break down
eventually, gases turn into liquids,
liquids turned into solids.
Like if you decrease the temperature to zero
according to the ideal gas or the volume should be zero.
But of course at some point
you've got all these atoms pack together.
It can't go any smaller than that.
And then from a quantum mechanical point of view
you're talking about like the ground state energy
and things like that.
So yeah, what we've done here
really is the definition of absolute zero.
We've just done it quite badly.
Thanks to Jim Lloyd for sending me the idea for this video.
I do appreciate you sending me ideas
from time to time, keep them coming.
You know, I think the lesson for this video is
that if you're trying to work out something for yourself,
it's really helpful.
If someone else has already done a much better job.
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