From early childhood,
we can tell by touch whether an object is hot
or whether it is cold. If you want to heat an object,
you bring it in contact with a hot object,
for instance a flame. If you want to cool an object, you bring it in contact
with a cold object. When objects are heated or
when they're cooled, then-- and the temperature changes-- then some of
their properties change, and those properties are called
thermometric properties: ther-mo-metric properties. One very characteristic
thermometric property is that most substances when
you heat them, they expand, and when you cool them,
they shrink. We'll talk more about it later. If you take a gas in a closed
volume and you heat it, the pressure goes up. That's a thermometric property. If you take an electric
conductor and you heat it, in general the electric
resistance will change. If you heat an iron bar,
it will expand. And if you place it in contact with another iron bar
which is cold, then the one that is hot
will shrink and the one that is cold will
heat up and will get longer, and this process will go on up to the point that the hot one
will not get shorter and that the cold one
will not get longer anymore. And that is when the two
objects, as we say, are in thermal equilibrium
with each other, and that is when the temperature
of the two objects are the same. And so you can define
a temperature scale by looking at the length
of an object. For instance, here is a bar, some material, I clamp it
in here, has length L, and I increase the temperature
by an amount delta T, and it gets longer
by a certain amount delta L. I could put the whole thing
in melting ice... melting ice... and I could say, "Aha." The length then is L1. Then I could put the whole thing
in boiling water and I do that at one atmosphere
pressure, and then I say, "Aha." I call that the length L2. And those are my reference
points for my temperature scale. Celsius did just that. The idea that
he used melting ice, which is now called
zero degrees centigrade, and he used boiling point
of water, which was his 100 degrees
centigrade. He was a Swedish astronomer; in 1742 he introduced
this temperature scale. So you could make yourself
a plot now of the temperature versus
the length of that bar, and you could say, okay,
100 degrees centigrade... if the length of the bar... L2, zero degrees centigrade if
the length of the bar is L1. And now you can draw
a straight line-- you can always draw a straight
line through two points, you have one point here,
you have one point there-- and you can define temperature
now by saying, if my bar has this length,
L of T, then this will be
the temperature. So you can introduce a linear
scale in this fashion, and the thing, in principle,
could act like a thermometer. I'll show you a demonstration
of this shortly. Centi in Greek
means "one hundredth," and therefore we also call
this scale often "centigrade." One degree centigrade
is often called... one degree Celsius is often
called one centigrade, for the reason that it divides the scale from zero to one
hundred in equal portions. So we call them degrees
centigrade, degrees Celsius. Fahrenheit,
a German scientist, invented the mercury
thermometer. We'll talk about the mercury
thermometer a little later. In 1714 he introduced
a new scale. He lived in Holland at the time,
he lived there most of the time, and he used as his reference
point body temperature, which he called
100 degrees Fahrenheit, and he used a mixture of salt
and ice at zero degrees. Now, neither one of these two
are very reproducible. If you pick one person, the temperature today may be
a little higher than tomorrow. A person may have fever. In fact, the one that he picked probably did have
a little bit of fever. And so the Fahrenheit scale,
in that sense, is not very reproducible,
and it has been redefined now in such a way that
zero degrees centigrade is 32 degrees Fahrenheit, and 100 degrees centigrade
is 212 degrees Fahrenheit. And so if you convert--
if you want to convert from Fahrenheit to centigrade
or the other way around-- then the temperature
in Fahrenheit is 9/5 times the temperature
in Celsius plus 32. If you take room temperature, the temperature is
20 degrees centigrade, what I was growing up with-- in Europe, everyone
uses centigrade there-- then you can see that
in terms of Fahrenheit, that becomes 68 degrees
Fahrenheit. 9/5 times 20 gives you 36,
and then you add 32. Minus 40 degrees centigrade is the same as
minus 40 degrees Fahrenheit. Check that. That's where the two scales
cross over. So almost the entire world
uses the Celsius scale; it's part of our metric system. United States is one
of the very, very few countries who still, in a rather stubborn
way, uses degrees Fahrenheit. And it is really a pain in
the neck, degrees Fahrenheit-- at least for me. I have very little feeling
for it. I just happen to know
that room temperature is 68, because that's the way I set
my thermostat at my home, but that's about all. I can't think in terms
of degrees Fahrenheit. There is no limit
to high temperature, but there is a limit
to the low temperatures. There is an absolute zero. This absolute zero
below which you cannot go is about minus 273 degrees
Celsius... And if you take a system that cannot transfer energy
to any other system that it is
in thermal contact with, then it is at that lowest
possible temperature. This is the way we define it. It's about minus 460 degrees
Fahrenheit. And so we now have
a third scale, which was introduced by Lord
Kelvin, was a British scientist. He did a lot of research
on heat, and he introduced
the absolute scale whereby he uses the lowest
possible temperature as zero degrees Kelvin. But the increments in terms
of increase of one degree, he uses the same
as the Celsius scale. So an increase of two or three
degrees Kelvin is the same as an increase of two or three
degrees centigrade. So if we now compare
the three scales-- Celsius, Fahrenheit and Kelvin-- then 20 degrees centigrade
would be 68 Fahrenheit, and that would
be 273.15 plus 20. Let's round it off
and make it 293, and if we take zero Kelvin,
then we would have minus 273.15, but let's leave that off
for now, and it is approximately
minus 460. We will almost always work
with degrees Kelvin in physics and we'll discuss that
in more detail Friday. Most substances expand
when you heat them, and if we start with an object
which has length L and I heat it up
delta T degrees, it gets longer
by an amount delta L. And that delta L can be
expressed in a very simple way. It is alpha
times L times delta T, and alpha is called the linear
expansion coefficient. And the units are one
over degrees centigrade, or one over degree Kelvin,
which is the same, because it's the increments
that matter. The various values for alpha
differ a great deal. Give you some values for alpha. I'll give you copper, I'll give
you brass, I'll give you Pyrex, I'll give you Invar
and I'll give you steel, and they are in units of ten to the minus six
per degree centigrade, and we will use
some of them today. Brass is about 19. Copper is 17. Pyrex 3.3; Invar 0.9;
and steel is roughly 12, but there are many
different kinds of steel. Invar was a great invention. Notice it has a very low
expansion coefficient. It was very important in
the 19th century, even today, to make instruments
very precise, like clocks. Clocks are affected by
the expansion of the gears. And so the invention of Invar, which is a mixture
of 64% iron and 36% nickel, was invented by
a physicist Guillaume in 1898, and for this discovery, he received
the Nobel Prize in 1920. It tells you something how
important it was to get an alloy that has a very low
expansion coefficient. If we use these numbers, let us look at the expansion of,
for instance, a railroad. We take a railroad, and we take
a piece, a stretch of rail which is, say,
a thousand meters. We take steel, iron-- so this is the expansion
coefficient, roughly-- and we compare a cold day,
not extremely cold, but a cold day
with a hot summer day. A cold winter day,
minus 15 degrees centigrade, and a hot summer day,
plus 35 degrees centigrade. So delta T would be
about 50 degrees centigrade. So what is delta L? Well, that would be 12
times ten to the minus six times ten to the third,
times 50, and that is about 0.6 meters,
which is about 60 centimeters. So what are you going
to do with that now? How is that solved? If the rail wants to get longer
and can't get longer, it will start to bulge
either in this way, or sideways, whichever is the easiest. But the way this is solved
is actually quite simple. When you look at rails, there
are openings between them. They're very distinct. They're about five centimeters. If you walk along the rail,
you can see the openings. And if you make these openings,
say, five centimeters, then you would need 12
of them in thousand meters, so every 80 meters
you would need a gap. And you can hear these gaps when
the train goes over these gaps. It's a very typical sound. Because imagine when
the wheel goes over it, you hear a certain click. You can see them
and you can hear them, and that's the way they correct for this expansion
and contraction. Bridges can be
many kilometers long, and they have, of course,
the same problem of expansion, and the way that that is
dealt with, also very clever, is as follows. This is a picture that I copied
actually from your book. It's called an expansion joint, and there are many
of them in bridges, and so what it allows
the bridge is to do this-- to breathe, so to speak,
adjust to the temperature. There is a bizarre picture
whereby the claim is made that this railroad
became so warped because of an extremely hot day. I trust it, although
it's hard to believe that it could be so bad. It must have been
extraordinarily hot. As I mentioned, if a rail cannot
expand, then all it can do is either bulge in
this way or this way, whichever way is easiest for it, and apparently here, the easiest
way is to go sideways, so you see a remarkable
destruction, actually, due to an unexpected
high temperature. I have here a brass bar which
is about 36 centimeters long, and I'm going to heat
that brass bar. You'll see it there, too. The brass bar is right here, and we have a way
of showing you the extension, even though it is
extremely small-- only a fraction
of a millimeter. We can show that
to you very easily. The way we do that is we have
some kind of an amplifier. If this is the rod,
and I would put here a hand, and pivot that hand here, then it's easy to see that
if you push against it here, that this hand
will go like this. So very little extension here will give you
a large extension there. We do it twice,
so we have two levels. And that is this arm. I have here a set screw, and I can make... I can move
the bar in this direction. I'm not making it longer,
but I can move it, and you will see
what effect it has. If I move the bar one way,
it goes up. Move the bar back, it goes down. You can think of this
as a thermometer. It will be 70 degrees,
as it is now, and if I heat it up,
then it will get longer and you will see this end go up. We could try that. (blowtorch hissing) There it goes. Doesn't take very much. So we have brass. And L is 36 centimeters. Delta L would be
about one millimeter for a temperature increase
of only 150 degrees centigrade, which of course is trivial
for us with that blowtorch. It's still hot. I could cool it. I could force it to cool it, and then I could
even go below this point. This was our 70 degrees,
remember? It was the room temperature. I can cool it with some liquid and see whether I can get it
down quickly, and even past this point,
which would indicate that it is shorter than it
was when the lecture started. (air whooshing) You see, it's now shorter. Now, what you're looking at is only something
like maybe a millimeter or even a little less. But we amplify it and we show that in
a quite convincing way, then. A very important implication-- an application of
the expansion of metals-- is what we call bimetals. They're all around you. A bimetal is the following. Say I have a strip here,
length L, of Invar. And I have another strip here
which is attached to it so that they cannot slip
relative to each other, and let this be copper. And suppose I make,
just as a working example, I make the thickness of each
one of them two millimeters. And I'm going to heat it. I'm going to heat it,
increase in temperature delta T. I'm not interested really in
knowing how long the copper gets and how long the Invar gets, but I'm very interested in knowing the difference
in the length between the two. Because what's going to happen when one gets longer
than the other, something got to give. What do you think will happen?
If one... And they're stuck together, they can't slip
relative to each other. What will they do? They will bend. And since the Invar is not
going to expand very much, but the copper will, if you heat it up,
it will go like this. And we'll see that there are
many applications of that. So what I'm interested in is
really the delta L of the copper minus the delta L of the Invar. That's what I'm after. And that is the alpha of copper
minus alpha of Invar times L times delta T. So it is the difference
that matters. So the difference
is 17 minus one, so that is 16 times ten to the
minus six times L times delta T. And if I take a length
of ten centimeters and I increase the temperature
by 100 degrees centigrade, then this difference,
which you can easily calculate, is .16 millimeters--
0.16 millimeter. Very little. And yet, this one
will curve substantially. For those of you who are
mathematically oriented, I would advise you to make
an attempt to calculate that. So you have, you assume
that it is a perfect circle-- that's a reasonable
approximation-- and so you have an outer circle which is longer by .16
millimeters than the inner one, and you try to solve
and find what that D is. And I went through
that exercise, and you want to do
that, too, perhaps, and I found that
it's four millimeters for these dimensions. Four millimeters--
that's substantial. So this thing is being used
for thermostats. Um... you break and make
a contact in a heating system, which could, for instance,
be as follows. Here would be your bimetal,
very schematically. You plug it in the wall here,
your 110 volts. Here is your heater. And you let it sit like that, and when it's cold,
this is down. It's not curled,
and the heater works. And when the room temperature
goes up, this starts to curl, it opens,
and that's a thermostat. That is the basic idea
behind a thermostat. And you have them in your cars,
you have them at home. Your central heating system,
air conditioner and your heaters--
they're all over the place. They're also being used
for safety devices. If you have a gas hot water
heater, in the pilot light, in the flame of the pilot light,
is a bimetal. And when that bimetal is hot,
your gas valve is open. But when that bimetal gets cold,
it shuts off the gas valve, which is a safety device. In fact, in Europe, all gas stoves are protected
that way by law. Strangely enough,
not in the United States, which is very surprising. If I open my gas valves
at home of my stove, the gas will just come out,
just like that. There's no prevention
of that happening. In Europe, that's not possible. There is always a pilot light
somewhere with a bimetal that senses that there is a
flame nearby to ignite the gas. And if that flame is out,
the gas valve will be closed. So bimetals can also be used
very effectively for safety devices. I have here a bimetal. One side I believe,
we believe, is aluminum, and the other side
we believe is iron. And when I heat that, you will
see that it starts to bend. (blowtorch hissing) Here we go. I think you get the idea. You could use that
as a thermometer-- very crude one, but this is the idea
of the thermometer, of course. Mark Bessette, who is the person who is preparing always
these demonstrations in a fabulous way, told me he had at home
a coffee maker. And the coffee maker is
designed in such a way that there is a bimetal at the
bottom of the water reservoir. You heat up the water reservoir, and when the water heats
to a certain temperature, the bimetal opens
and the water comes out and it goes through the coffee. I'd like to show that to you--
it's really cute. Here is that coffee machine. It's not working anymore,
it's a very old one, but I want to show you
at least that bimetal. This is that bimetal strip. Water goes in here, you heat it, and when it's hot enough,
the bimetal lifts up and you can see
there is a hole there. This is the hole. And the water comes out, and
when the bimetal is closed, then it closes off that hole. So it's an amazing, simple idea. The criterion for letting
the water go through the coffee is simply when the water reaches that temperature
close to boiling and you have your bimetal
control it. So bimetals in many ways
control matters. Thermostats, in this case they
act like... like a valve. Bimetals can be used
as thermometers. In fact, the one
that you see right here is driven exclusively
by a bimetal. If you look in the back
of this thermometer-- and I will show that
to you shortly because I broke one open
for you-- then it looks like this. There's a coil. This end of the coil is
attached to the plastic casing. And here is the red hand. It's a pivot here--
the red hand. But this is fixed,
this cannot move. I heat it up. What will happen
when I heat it up? This is already a bimetal,
it's already curved. But when I heat it up,
it will tighten even more, it will curl up even more. And when this one curls up
even more, it will go into this direction. So this is when
the temperature increases. And when it, of course,
gets colder, it will uncurl, and so here is cold. And that's what the whole
thermometer is based upon. And in the back is this coil. And so I broke one open for you in order to make
you see that coil. Now, I have that here. This is the part
that is in the back, and this is that bimetal--
the bimetal coil. This is the bottom part,
this is the top, and this is just the hand
that is attached to it. And then it goes into this case. Let's make sure that the pivot
goes in there-- yeah. If I increase the temperature,
try to see that. You see the coil tightens up. See, the coil gets tighter. And when I make the temperature
go down artificially now by uncurling the coil,
it goes in this direction. Now, what we can do is
we can actually heat it up. We have to set the temperature
at whatever we think it is now. It's about 70 degrees
in the room. Is that what it is? Well, that's close enough. This is Fahrenheit--
oh, what a terrible scale. Yeah, by the way, you also see
some civilized scale there. You see centigrade in addition
to the Fahrenheit. So it's close enough,
it's a little bit over 70, and I can now make sure
that this is stuck to it, to the case. I can heat it. (motor purring) The bimetal tightens up more. So when I heat it,
the bimetal tightens up more, and when I blow air over it,
I can actually make it cool a little faster
than it will otherwise. (blowing) So as simple as that. Very simple device with... the bimetals have
many, many applications. Your thermostats
in your dormitories of your heating systems, and also perhaps of the
air-conditioning systems, almost all have a coil
like this in there. It was an extremely
ingenious device. It has a coil, and at the end of
the coil is a little glass tube, only one centimeter large,
and there is mercury inside. So the coil is like this. Bimetal. And at the end here
is a glass container and there is some mercury, and the mercury is here
on this side, because notice the way
I have tilted it a little. The mercury rolls to the left. And there are here two wires,
electric wires, one here and one here,
which go to the heating system. And so when the mercury is here,
which has a good conductivity, the heater is on. Now, the room gets warmer
and warmer and warmer and the bimetal will tighten up,
will curl even more. And so there comes a time that this glass thing
will go like this and the mercury rolls out. And when the mercury rolls out--
here is the mercury-- these contacts here are open,
and the heater will stop. And that's in almost every room. Very ingenious device. Now I want to move from
linear expansion coefficients to cubic expansion coefficients. I will leave
these numbers there, because I will
need them later on. But now I take a block
of some material and want to discuss the volume
increase-- not just the length, but the volume increase. So here I have a solid material. Let's make it simple,
all sides L. And I increase it by an amount
of temperature delta T. Well, the old volume is L cubed, and then I'm going to increase
the temperature by delta T, so all these sides will get
longer by amount delta L, and so the new volume will be L
plus delta L to the power 3. This can also be written
as L to the third times one plus delta L
over L to the power 3. Same thing, right? Now, perhaps you remember,
or at least you should remember, that one plus x to the power n, in case that x is much,
much smaller than one, is approximately one plus nx. We've used that before when we
discussed the Doppler shift-- light from receding stars. This is called the binomial
series, binomial expansion. It's really the first order
terms of the Taylor expansion. If you, as an example,
if you take x equals 0.05 and you calculate the exact
value with your calculator, you would find 1.158. If you do it this way, you will
find 1.15, which is very close. Approximation is better
than one percent. So I will use the same
approximation here, and so we're going to get
L to the third times one plus three
delta L divided by L. So that is L to the third
plus three delta L, L squared. So the difference
in terms of delta V, the old volume was this. And this volume
is V plus delta V, so delta V is the difference
between the two, is three delta L, L squared. But I know that delta L equals
alpha times L times delta T. And so I can substitute that in
here, and so I find that delta V equals three alpha
times L squared times L-- that is L cubed-- times delta T. But L cubed was the old volume, and so I now find that delta V
equals three alpha times the old volume
times delta T, and this one is
often called beta. Beta is the cubical
expansion coefficient, as opposed to the linear one. So you will say, well, big deal. I mean, why are you
talking about beta? Because if we have the values
for alpha, all we have to do if we go to a volume,
to make that beta three alpha, and we are in business. Well, when you have liquids,
in general, you don't find in the tables
values for alpha. So when you deal with liquids,
for instance, mercury, which is the one
that I want to use today, then you find that the cubic
expansion coefficient is 18 times ten to the minus
five per degree centigrade. If I compare that with Pyrex, you have to take
three times this value, so that's very roughly
ten to the minus five per degree centigrade. And so now you begin
to smell the idea of a mercury thermometer. I put some mercury
in Pyrex glass, and the Pyrex glass is not
going to expand very much, but the mercury will. And then the mercury, which is
in an enclosed environment, will have to expand, and it
expands into my thermometer and that's the way that
we read the temperature. So here is a glass tube
which is very, very narrow. All this is closed here. And let's say the radius here
is only 0.1 millimeter. And here is a reservoir,
mercury, just a working example, and suppose we take
one cubic centimeter-- just simple numbers. Just want to show you the basic
idea behind the thermometer. I'm going to increase the
temperature of this mercury, say by ten degrees, so delta T,
ten degrees centigrade. So by how much will
this volume expand? Well, delta V equals beta 18
times ten to the minus fifths times the volume, which is
one cubic centimeter-- let me just put the volume
in there; you may want to do it in cubic
meters-- I leave it up to you-- times the delta T. And you will find that the expansion in terms
of cubic centimeters is 0.0018 cubic centimeters. See, if you leave V in cubic
centimeters, which you can do, then you get your answer also
in cubic centimeters, of course. You do not always work...
have to work mks. So this is an extraordinarily
small increase in terms of its volume. However, the Pyrex is
not expanding at all. You can just
forget that for now. If you want to calculate
how much it is, it's fine, but it is 18 times less, so the fact that the vessel
gets a little larger of course is important, but I will just ignore
that for now. And so I will just assume that all this mercury
will be driven up here. And so if the mercury,
then, changes its height by an amount delta h, and if this is a tube
with a radius .1 millimeters, then this amount of mercury must be the same as
pi r squared times delta h, which is the volume
of the new column-- the increase in the column. And so you take your .1
millimeters and you'll find that delta h for this example
that I chose is 5.7 centimeters. That's huge. That's very easy to see. For ten degrees increase
in temperature, you get 5.7 centimeters. So for one degree centigrade,
you would get six millimeters. It's very easy to see, and so that's the idea
behind a mercury thermometer. I have a mercury
thermometer here, but they're very hard to read. But I have one here. It's a medical one. It says "oral," not to be confused. And I can stick it in my mouth
and measure my temperature using this scale. It's easier for me to show you the one that
I have in my office, which also works on liquid. (mumbling):
This one. So this one, you see
the red liquid? Let me be sure that we have
the right light setting. This should go off. Okay. So you see the red liquid. There it is. And also notice that
it is degrees Fahrenheit, which is unfortunate. But it's helping. When the temperature is here, at least you know that
you're going to get ice. (a few chuckles) Well, that's somewhere near
32... 32 Fahrenheit. That must be here. Snow. And this makes
you feel good-- sun. Yeah. You know, just in case
you don't remember. I could heat it up. (blow-dryer humming) You always should be careful
when you heat it up that you don't go too far, because the top of the
thermometer is closed. In the case of
a mercury thermometer, there is vacuum in here,
and so if you-- when I was a kid,
I loved to do this-- to take the medical
thermometer of my parents and heat it up with a hair dryer and then it would
just burst through it, it would just break the glass, because the expansion
is huge, the force, and it would just pop off. And then I'd put it back
and say nothing. And that can happen
with this, too. So it doesn't have an opening. It is not open,
it's a closed thing, so you've got
to be quite careful. There is a technique which
is called "shrink fitting," and shrink fitting
is the following. You have a piece of metal-- let's take just a solid cylinder
as a working example-- and you have a ring. The ring could be itself
a cylinder. Well, this one, this opening
is smaller than this-- just a little smaller--
purposely made that way. Just a little smaller. You heat this one. Expands. And you put it over here,
it will fit. And then you let it sit. It cools,
and it tightens itself up. That's called shrink fitting,
a technique which is often used. I have something
to show you here which is the opposite
of shrink fitting. I have a ring-- I'll show you
shortly on the screen there-- and that's made of brass, and I have a ball which goes
through there. Just barely, but it
goes through there. And then I will
heat up this ball, and then it won't
go through there, so it's the reverse,
but at least you get the idea. And then if you wait
and it cools, when you bring them
in contact with each other, this one will cool and
this one will get warmer. So you catch two birds
with one stone. This one will shrink, and at the same time, this one
will become a little larger, and so then clearly
it will fall through, and that's the idea. And let's try that. Get the best lighting that we
can under the circumstances, and we'll change to...
is that it? Yeah, this is the ring. And here is that brass ball. It goes through there
quite easily. I'll put it horizontal now. And then I will start
heating up this ball. (flame whooshing) Here's the ball. It can't be too close
to the ring, because then the ring
will also be heated, and then of course if the two
have the same temperature, then the ball
will still go through. (flame whooshing) Let's see. Now it doesn't want
to go through. So we'll leave it like that,
and we'll see what happens. So the ring will now expand
a little because it gets hotter, and the ball will shrink
a little because it gets colder and it shouldn't take too long for the ball to be able
to get through. If I heat them both
with the torch, then of course
they will always be able to go through each other. And there it goes. So if I heat them both... (flame whooshing) ...so they both expand,
since it's both brass, there is no differential
expansion like with bimetals, then no matter what you do, it will always be able
to go through. It's only when I... ...heat the ball
and not the ring that you get the effect
that it won't get through. It may actually get through now,
still get through. Yeah. What I've left out of my
discussion with you is water. Why have I not mentioned to you what is the expansion
coefficient, the cubical expansion
coefficient of water? Water is so important
in our lives. Well, there is a reason
why I left it out, because there is something
very special with water. If you take 20-degree centigrade
water and you cool it, it shrinks. Normal behavior. Beta has a positive value. But when you reach
four degrees centigrade and you go all the way
down to zero, then it doesn't shrink--
it expands. So in that range, from zero degrees centigrade
to four degrees centigrade, water has a negative value
for beta. When you heat it, it shrinks, and when you cool it,
it expands. And that makes water
extremely unusual. But it's great for fish, because it means that water
of four degrees centigrade has the highest
possible density. It's higher density
than at 20 degrees, and a higher density
than at zero degrees. And so when in the winter
the ponds freeze, the highest density water
goes to the bottom, and that's why the way... that's
the way that fish can survive. Rather than becoming deep-freeze
fish right there, they can swim. So most of the pond
in the winter, the bottom layers
are four degrees centigrade, which is safely
from the freezing point. Now, when you melt a solid
and it becomes liquid, in almost all cases
the liquid expands. Sort of natural. And so the solids sink
in the liquids. If you take crystals,
they sink in their own liquid. But not water. Water and ice
are very anomalous. If you take water at zero
degrees and you freeze it and it becomes ice crystals,
it expands. And the expansion is enormous, because the density of ice
is eight percent lower than the density of water. The density of ice is 0.92 grams
per cubic centimeter, and water per definition is one. This is why pipes can burst
in the winter when they freeze. The pipes freeze, they... people have water pipes
near the outside walls. They cool, they freeze,
the pipes burst, because the ice expands. They're not aware of that, and in the spring,
when the ice melts, all of a sudden-- they have
a flood because the pipe burst. This is why theTitanic sank. Because ice floats on water. Ice has a lower density. Without ice floating,
no icebergs. This is why you can skate
on ponds, because ice has a lower density
than water, so ice floats on water. The best way that
I can demonstrate to you that ice floats
is to treat myself and give myself
a glass of something. Today it will be apple cider. And I have here some ice cubes. And I put some ice cubes
in here, and they float. And if you don't believe it,
come and take a look. Okay, enjoy your weekend.
