- 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
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