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From early childhood,
we can tell by touch

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whether an object is hot
or whether it is cold.

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If you want to heat an object,
you bring it in contact

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with a hot object,
for instance a flame.

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If you want to cool an object,

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you bring it in contact
with a cold object.

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When objects are heated or
when they're cooled, then--

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and the temperature changes--

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then some of
their properties change,

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and those properties are called
thermometric properties:

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ther-mo-metric properties.

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One very characteristic
thermometric property

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is that most substances when
you heat them, they expand,

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and when you cool them,
they shrink.

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We'll talk more about it later.

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If you take a gas in a closed
volume and you heat it,

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the pressure goes up.

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That's a thermometric property.

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If you take an electric
conductor and you heat it,

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in general the electric
resistance will change.

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If you heat an iron bar,
it will expand.

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And if you place it in contact

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with another iron bar
which is cold,

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then the one that is hot
will shrink

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and the one that is cold will
heat up and will get longer,

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and this process will go on

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up to the point that the hot one
will not get shorter

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and that the cold one
will not get longer anymore.

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And that is when the two
objects, as we say,

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are in thermal equilibrium
with each other,

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and that is when the temperature
of the two objects are the same.

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And so you can define
a temperature scale

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by looking at the length
of an object.

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For instance, here is a bar,

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some material, I clamp it
in here, has length L,

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and I increase the temperature
by an amount delta T,

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and it gets longer
by a certain amount delta L.

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I could put the whole thing
in melting ice...

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melting ice...

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and I could say, "Aha."

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The length then is L1.

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Then I could put the whole thing
in boiling water

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and I do that at one atmosphere
pressure, and then I say, "Aha."

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I call that the length L2.

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And those are my reference
points for my temperature scale.

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Celsius did just that.

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The idea that
he used melting ice,

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which is now called
zero degrees centigrade,

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and he used boiling point
of water,

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which was his 100 degrees
centigrade.

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He was a Swedish astronomer; 

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in 1742 he introduced
this temperature scale.

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So you could make yourself
a plot now

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of the temperature versus
the length of that bar,

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and you could say, okay,
100 degrees centigrade...

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if the length of the bar... L2,

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zero degrees centigrade if
the length of the bar is L1.

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And now you can draw
a straight line--

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you can always draw a straight
line through two points,

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you have one point here,
you have one point there--

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and you can define temperature
now by saying,

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if my bar has this length,
L of T,

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then this will be
the temperature.

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So you can introduce a linear
scale in this fashion,

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and the thing, in principle,
could act like a thermometer.

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I'll show you a demonstration
of this shortly.

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Centi in Greek
means "one hundredth,"

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and therefore we also call
this scale often "centigrade."

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One degree centigrade
is often called...

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one degree Celsius is often
called one centigrade,

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for the reason that it divides

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the scale from zero to one
hundred in equal portions.

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So we call them degrees
centigrade, degrees Celsius.

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Fahrenheit,
a German scientist,

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invented the mercury
thermometer.

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We'll talk about the mercury
thermometer a little later.

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In 1714 he introduced
a new scale.

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He lived in Holland at the time,
he lived there most of the time,

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and he used as his reference
point body temperature,

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which he called
100 degrees Fahrenheit,

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and he used a mixture of salt
and ice at zero degrees.

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Now, neither one of these two
are very reproducible.

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If you pick one person,

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the temperature today may be
a little higher than tomorrow.

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A person may have fever.

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In fact, the one that he picked

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probably did have
a little bit of fever.

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And so the Fahrenheit scale,
in that sense,

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is not very reproducible,
and it has been redefined now

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in such a way that
zero degrees centigrade

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is 32 degrees Fahrenheit,

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and 100 degrees centigrade
is 212 degrees Fahrenheit.

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And so if you convert--
if you want to convert

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from Fahrenheit to centigrade
or the other way around--

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then the temperature
in Fahrenheit

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is 9/5 times the temperature
in Celsius plus 32.

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If you take room temperature,

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the temperature is
20 degrees centigrade,

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what I was growing up with--

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in Europe, everyone
uses centigrade there--

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then you can see that
in terms of Fahrenheit,

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that becomes 68 degrees
Fahrenheit.

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9/5 times 20 gives you 36,
and then you add 32.

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Minus 40 degrees centigrade

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is the same as
minus 40 degrees Fahrenheit.

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Check that.

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That's where the two scales
cross over.

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So almost the entire world
uses the Celsius scale; 

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it's part of our metric system.

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United States is one
of the very, very few countries

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who still, in a rather stubborn
way, uses degrees Fahrenheit.

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And it is really a pain in
the neck, degrees Fahrenheit--

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at least for me.

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I have very little feeling
for it.

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I just happen to know
that room temperature is 68,

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because that's the way I set
my thermostat at my home,

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but that's about all.

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I can't think in terms
of degrees Fahrenheit.

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There is no limit
to high temperature,

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but there is a limit
to the low temperatures.

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There is an absolute zero.

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This absolute zero
below which you cannot go

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is about minus 273 degrees
Celsius...

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And if you take a system

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that cannot transfer energy
to any other system

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that it is
in thermal contact with,

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then it is at that lowest
possible temperature.

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This is the way we define it.

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It's about minus 460 degrees
Fahrenheit.

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And so we now have
a third scale,

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which was introduced by Lord
Kelvin, was a British scientist.

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He did a lot of research
on heat,

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and he introduced
the absolute scale

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whereby he uses the lowest
possible temperature

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as zero degrees Kelvin.

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But the increments in terms
of increase of one degree,

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he uses the same
as the Celsius scale.

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So an increase of two or three
degrees Kelvin is the same

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as an increase of two or three
degrees centigrade.

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So if we now compare
the three scales--

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Celsius, Fahrenheit and Kelvin--

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then 20 degrees centigrade
would be 68 Fahrenheit,

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and that would
be 273.15 plus 20.

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Let's round it off
and make it 293,

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and if we take zero Kelvin,
then we would have minus 273.15,

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but let's leave that off
for now,

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and it is approximately
minus 460.

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We will almost always work
with degrees Kelvin in physics

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and we'll discuss that
in more detail Friday.

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Most substances expand
when you heat them,

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and if we start with an object
which has length L

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and I heat it up
delta T degrees,

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it gets longer
by an amount delta L.

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And that delta L can be
expressed in a very simple way.

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It is alpha
times L times delta T,

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and alpha is called the linear
expansion coefficient.

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And the units are one
over degrees centigrade,

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or one over degree Kelvin,
which is the same,

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because it's the increments
that matter.

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The various values for alpha
differ a great deal.

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Give you some values for alpha.

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I'll give you copper, I'll give
you brass, I'll give you Pyrex,

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I'll give you Invar
and I'll give you steel,

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and they are in units

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of ten to the minus six
per degree centigrade,

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and we will use
some of them today.

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Brass is about 19.

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Copper is 17.

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Pyrex 3.3; Invar 0.9; 
and steel is roughly 12,

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but there are many
different kinds of steel.

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Invar was a great invention.

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Notice it has a very low
expansion coefficient.

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It was very important in
the 19th century, even today,

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to make instruments
very precise, like clocks.

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Clocks are affected by
the expansion of the gears.

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And so the invention of Invar,

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which is a mixture
of 64% iron and 36% nickel,

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was invented by
a physicist Guillaume in 1898,

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and for this discovery,

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he received
the Nobel Prize in 1920.

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It tells you something how
important it was to get an alloy

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that has a very low
expansion coefficient.

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If we use these numbers,

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let us look at the expansion of,
for instance, a railroad.

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We take a railroad, and we take
a piece, a stretch of rail

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which is, say,
a thousand meters.

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We take steel, iron--

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so this is the expansion
coefficient, roughly--

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and we compare a cold day,
not extremely cold,

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but a cold day
with a hot summer day.

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A cold winter day,
minus 15 degrees centigrade,

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and a hot summer day,
plus 35 degrees centigrade.

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So delta T would be
about 50 degrees centigrade.

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So what is delta L?

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Well, that would be 12
times ten to the minus six

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times ten to the third,
times 50,

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and that is about 0.6 meters,
which is about 60 centimeters.

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So what are you going
to do with that now?

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How is that solved?

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If the rail wants to get longer
and can't get longer,

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it will start to bulge
either in this way, or sideways,

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whichever is the easiest.

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But the way this is solved
is actually quite simple.

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When you look at rails, there
are openings between them.

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They're very distinct.

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They're about five centimeters.

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If you walk along the rail,
you can see the openings.

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And if you make these openings,
say, five centimeters,

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then you would need 12
of them in thousand meters,

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so every 80 meters
you would need a gap.

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And you can hear these gaps when
the train goes over these gaps.

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It's a very typical sound.

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Because imagine when
the wheel goes over it,

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you hear a certain click.

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You can see them
and you can hear them,

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and that's the way they correct

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for this expansion
and contraction.

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Bridges can be
many kilometers long,

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and they have, of course,
the same problem of expansion,

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and the way that that is
dealt with, also very clever,

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is as follows.

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This is a picture that I copied
actually from your book.

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It's called an expansion joint,

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and there are many
of them in bridges,

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and so what it allows
the bridge is to do this--

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to breathe, so to speak,
adjust to the temperature.

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There is a bizarre picture
whereby the claim is made

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that this railroad
became so warped

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because of an extremely hot day.

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I trust it, although
it's hard to believe

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that it could be so bad.

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It must have been
extraordinarily hot.

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As I mentioned, if a rail cannot
expand, then all it can do

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is either bulge in
this way or this way,

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whichever way is easiest for it,

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and apparently here, the easiest
way is to go sideways,

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so you see a remarkable
destruction, actually,

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due to an unexpected
high temperature.

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00:14:31 --> 00:14:37
 

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I have here a brass bar which
is about 36 centimeters long,

247
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and I'm going to heat
that brass bar.

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You'll see it there, too.

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The brass bar is right here,

250
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and we have a way
of showing you the extension,

251
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even though it is
extremely small--

252
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only a fraction
of a millimeter.

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00:15:07 --> 00:15:13
We can show that
to you very easily.

254
00:15:09 --> 00:15:15
The way we do that is we have
some kind of an amplifier.

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00:15:14 --> 00:15:20
If this is the rod,
and I would put here a hand,

256
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and pivot that hand here,

257
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then it's easy to see that
if you push against it here,

258
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that this hand
will go like this.

259
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So very little extension here

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will give you
a large extension there.

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We do it twice,
so we have two levels.

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And that is this arm.

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I have here a set screw,

264
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and I can make... I can move
the bar in this direction.

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I'm not making it longer,
but I can move it,

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and you will see
what effect it has.

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If I move the bar one way,
it goes up.

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Move the bar back, it goes down.

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You can think of this
as a thermometer.

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It will be 70 degrees,
as it is now,

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and if I heat it up,
then it will get longer

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and you will see this end go up.

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We could try that.

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00:16:08 --> 00:16:14
(blowtorch hissing )

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There it goes.

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Doesn't take very much.

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So we have brass.

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And L is 36 centimeters.

280
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Delta L would be
about one millimeter

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for a temperature increase
of only 150 degrees centigrade,

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which of course is trivial
for us with that blowtorch.

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It's still hot.

284
00:16:48 --> 00:16:54
I could cool it.

285
00:16:51 --> 00:16:57
I could force it to cool it,

286
00:16:52 --> 00:16:58
and then I could
even go below this point.

287
00:16:55 --> 00:17:01
This was our 70 degrees,
remember?

288
00:16:57 --> 00:17:03
It was the room temperature.

289
00:16:59 --> 00:17:05
I can cool it with some liquid

290
00:17:01 --> 00:17:07
and see whether I can get it
down quickly,

291
00:17:03 --> 00:17:09
and even past this point,
which would indicate

292
00:17:06 --> 00:17:12
that it is shorter than it
was when the lecture started.

293
00:17:10 --> 00:17:16
 

294
00:17:13 --> 00:17:19
(air whooshing )

295
00:17:18 --> 00:17:24
 

296
00:17:23 --> 00:17:29
You see, it's now shorter.

297
00:17:25 --> 00:17:31
Now, what you're looking at

298
00:17:26 --> 00:17:32
is only something
like maybe a millimeter

299
00:17:28 --> 00:17:34
or even a little less.

300
00:17:30 --> 00:17:36
But we amplify it

301
00:17:32 --> 00:17:38
and we show that in
a quite convincing way, then.

302
00:17:37 --> 00:17:43
A very important implication--

303
00:17:40 --> 00:17:46
an application of
the expansion of metals--

304
00:17:44 --> 00:17:50
is what we call bimetals.

305
00:17:47 --> 00:17:53
They're all around you.

306
00:17:51 --> 00:17:57
A bimetal is the following.

307
00:17:54 --> 00:18:00
Say I have a strip here,
length L, of Invar.

308
00:18:04 --> 00:18:10
And I have another strip here
which is attached to it

309
00:18:09 --> 00:18:15
so that they cannot slip
relative to each other,

310
00:18:12 --> 00:18:18
and let this be copper.

311
00:18:16 --> 00:18:22
And suppose I make,
just as a working example,

312
00:18:20 --> 00:18:26
I make the thickness of each
one of them two millimeters.

313
00:18:27 --> 00:18:33
 

314
00:18:30 --> 00:18:36
And I'm going to heat it.

315
00:18:33 --> 00:18:39
I'm going to heat it,
increase in temperature delta T.

316
00:18:37 --> 00:18:43
I'm not interested really in
knowing how long the copper gets

317
00:18:41 --> 00:18:47
and how long the Invar gets,

318
00:18:43 --> 00:18:49
but I'm very interested

319
00:18:44 --> 00:18:50
in knowing the difference
in the length between the two.

320
00:18:48 --> 00:18:54
Because what's going to happen

321
00:18:49 --> 00:18:55
when one gets longer
than the other,

322
00:18:51 --> 00:18:57
something got to give.

323
00:18:53 --> 00:18:59
What do you think will happen?

324
00:18:54 --> 00:19:00
And they're stuck together,

325
00:18:55 --> 00:19:01
they can't slip
relative to each other.

326
00:18:57 --> 00:19:03
What will they do?

327
00:19:01 --> 00:19:07
They will bend.

328
00:19:03 --> 00:19:09
And since the Invar is not
going to expand very much,

329
00:19:06 --> 00:19:12
but the copper will,

330
00:19:07 --> 00:19:13
if you heat it up,
it will go like this.

331
00:19:12 --> 00:19:18
And we'll see that there are
many applications of that.

332
00:19:16 --> 00:19:22
So what I'm interested in is
really the delta L of the copper

333
00:19:20 --> 00:19:26
minus the delta L of the Invar.

334
00:19:24 --> 00:19:30
That's what I'm after.

335
00:19:26 --> 00:19:32
And that is the alpha of copper
minus alpha of Invar

336
00:19:31 --> 00:19:37
times L times delta T.

337
00:19:36 --> 00:19:42
So it is the difference
that matters.

338
00:19:38 --> 00:19:44
So the difference
is 17 minus one,

339
00:19:41 --> 00:19:47
so that is 16 times ten to the
minus six times L times delta T.

340
00:19:50 --> 00:19:56
And if I take a length
of ten centimeters

341
00:19:58 --> 00:20:04
and I increase the temperature
by 100 degrees centigrade,

342
00:20:02 --> 00:20:08
then this difference,
which you can easily calculate,

343
00:20:06 --> 00:20:12
is .16 millimeters--
0.16 millimeter.

344
00:20:13 --> 00:20:19
Very little.

345
00:20:15 --> 00:20:21
And yet, this one
will curve substantially.

346
00:20:22 --> 00:20:28
For those of you who are
mathematically oriented,

347
00:20:26 --> 00:20:32
I would advise you to make
an attempt to calculate that.

348
00:20:29 --> 00:20:35
So you have, you assume
that it is a perfect circle--

349
00:20:33 --> 00:20:39
that's a reasonable
approximation--

350
00:20:35 --> 00:20:41
and so you have an outer circle

351
00:20:37 --> 00:20:43
which is longer by .16
millimeters than the inner one,

352
00:20:42 --> 00:20:48
and you try to solve
and find what that D is.

353
00:20:45 --> 00:20:51
And I went through
that exercise,

354
00:20:47 --> 00:20:53
and you want to do
that, too, perhaps,

355
00:20:49 --> 00:20:55
and I found that
it's four millimeters

356
00:20:51 --> 00:20:57
for these dimensions.

357
00:20:52 --> 00:20:58
Four millimeters--
that's substantial.

358
00:20:56 --> 00:21:02
So this thing is being used
for thermostats.

359
00:20:59 --> 00:21:05
Um... you break and make
a contact in a heating system,

360
00:21:05 --> 00:21:11
which could, for instance,
be as follows.

361
00:21:09 --> 00:21:15
Here would be your bimetal,
very schematically.

362
00:21:13 --> 00:21:19
You plug it in the wall here,
your 110 volts.

363
00:21:17 --> 00:21:23
Here is your heater.

364
00:21:19 --> 00:21:25
 

365
00:21:23 --> 00:21:29
And you let it sit like that,

366
00:21:25 --> 00:21:31
and when it's cold,
this is down.

367
00:21:29 --> 00:21:35
It's not curled,
and the heater works.

368
00:21:32 --> 00:21:38
And when the room temperature
goes up, this starts to curl,

369
00:21:36 --> 00:21:42
it breaks,
and that's a thermostat.

370
00:21:39 --> 00:21:45
That is the basic idea
behind a thermostat.

371
00:21:41 --> 00:21:47
And you have them in your cars,
you have them at home.

372
00:21:43 --> 00:21:49
Your central heating system,
air conditioner

373
00:21:47 --> 00:21:53
and your heaters--
they're all over the place.

374
00:21:51 --> 00:21:57
They're also being used
for safety devices.

375
00:21:54 --> 00:22:00
If you have a gas hot water
heater, in the pilot light,

376
00:21:58 --> 00:22:04
in the flame of the pilot light,
is a bimetal.

377
00:22:03 --> 00:22:09
And when that bimetal is hot,
your gas valve is open.

378
00:22:07 --> 00:22:13
But when that bimetal gets cold,
it shuts off the gas valve,

379
00:22:10 --> 00:22:16
which is a safety device.

380
00:22:12 --> 00:22:18
In fact, in Europe,

381
00:22:13 --> 00:22:19
all gas stoves are protected
that way by law.

382
00:22:17 --> 00:22:23
Strangely enough,
not in the United States,

383
00:22:19 --> 00:22:25
which is very surprising.

384
00:22:21 --> 00:22:27
If I open my gas valves
at home of my stove,

385
00:22:24 --> 00:22:30
the gas will just come out,
just like that.

386
00:22:28 --> 00:22:34
There's no prevention
of that happening.

387
00:22:30 --> 00:22:36
In Europe, that's not possible.

388
00:22:32 --> 00:22:38
There is always a pilot light
somewhere with a bimetal

389
00:22:35 --> 00:22:41
that senses that there is a
flame nearby to ignite the gas.

390
00:22:39 --> 00:22:45
And if that flame is out,
the gas valve will be closed.

391
00:22:42 --> 00:22:48
So bimetals can also be used
very effectively

392
00:22:45 --> 00:22:51
for safety devices.

393
00:22:48 --> 00:22:54
I have here a bimetal.

394
00:22:51 --> 00:22:57
One side I believe,
we believe, is aluminum,

395
00:22:54 --> 00:23:00
and the other side
we believe is iron.

396
00:22:58 --> 00:23:04
And when I heat that, you will
see that it starts to bend.

397
00:23:03 --> 00:23:09
 

398
00:23:07 --> 00:23:13
(blowtorch hissing )

399
00:23:10 --> 00:23:16
Here we go.

400
00:23:11 --> 00:23:17
 

401
00:23:47 --> 00:23:53
I think you get the idea.

402
00:23:49 --> 00:23:55
You could use that
as a thermometer--

403
00:23:51 --> 00:23:57
very crude one,

404
00:23:52 --> 00:23:58
but this is the idea
of the thermometer, of course.

405
00:23:56 --> 00:24:02
 

406
00:24:00 --> 00:24:06
Mark Bessette, who is the person

407
00:24:04 --> 00:24:10
who is preparing always
these demonstrations

408
00:24:06 --> 00:24:12
in a fabulous way,

409
00:24:08 --> 00:24:14
told me he had at home
a coffee maker.

410
00:24:12 --> 00:24:18
And the coffee maker is
designed in such a way

411
00:24:15 --> 00:24:21
that there is a bimetal at the
bottom of the water reservoir.

412
00:24:18 --> 00:24:24
You heat up the water reservoir,

413
00:24:21 --> 00:24:27
and when the water heats
to a certain temperature,

414
00:24:23 --> 00:24:29
the bimetal opens
and the water comes out

415
00:24:25 --> 00:24:31
and it goes through the coffee.

416
00:24:27 --> 00:24:33
I'd like to show that to you--
it's really cute.

417
00:24:29 --> 00:24:35
 

418
00:24:36 --> 00:24:42
Here is that coffee machine.

419
00:24:38 --> 00:24:44
It's not working anymore,
it's a very old one,

420
00:24:40 --> 00:24:46
but I want to show you
at least that bimetal.

421
00:24:45 --> 00:24:51
This is that bimetal strip.

422
00:24:47 --> 00:24:53
Water goes in here, you heat it,

423
00:24:49 --> 00:24:55
and when it's hot enough,
the bimetal lifts up

424
00:24:54 --> 00:25:00
and you can see
there is a hole there.

425
00:24:55 --> 00:25:01
This is the hole.

426
00:24:57 --> 00:25:03
And the water comes out, and
when the bimetal is closed,

427
00:24:59 --> 00:25:05
then it closes off that hole.

428
00:25:02 --> 00:25:08
So it's an amazing, simple idea.

429
00:25:04 --> 00:25:10
The criterion for letting
the water go through the coffee

430
00:25:07 --> 00:25:13
is simply when the water reaches

431
00:25:09 --> 00:25:15
that temperature
close to boiling

432
00:25:11 --> 00:25:17
and you have your bimetal
control it.

433
00:25:15 --> 00:25:21
So bimetals in many ways
control matters.

434
00:25:19 --> 00:25:25
Thermostats, in this case they
act like... like a valve.

435
00:25:24 --> 00:25:30
Bimetals can be used
as thermometers.

436
00:25:30 --> 00:25:36
In fact, the one
that you see right here

437
00:25:35 --> 00:25:41
is driven exclusively
by a bimetal.

438
00:25:40 --> 00:25:46
If you look in the back
of this thermometer--

439
00:25:42 --> 00:25:48
and I will show that
to you shortly

440
00:25:44 --> 00:25:50
because I broke one open
for you--

441
00:25:47 --> 00:25:53
then it looks like this.

442
00:25:50 --> 00:25:56
There's a coil.

443
00:25:53 --> 00:25:59
This end of the coil is
attached to the plastic casing.

444
00:25:58 --> 00:26:04
And here is the red hand.

445
00:26:02 --> 00:26:08
It's a pivot here--
the red hand.

446
00:26:07 --> 00:26:13
But this is fixed,
this cannot move.

447
00:26:10 --> 00:26:16
I heat it up.

448
00:26:11 --> 00:26:17
What will happen
when I heat it up?

449
00:26:13 --> 00:26:19
This is already a bimetal,
it's already curved.

450
00:26:15 --> 00:26:21
But when I heat it up,
it will tighten even more,

451
00:26:17 --> 00:26:23
it will curl up even more.

452
00:26:19 --> 00:26:25
And when this one curls up
even more,

453
00:26:21 --> 00:26:27
it will go into this direction.

454
00:26:23 --> 00:26:29
So this is when
the temperature increases.

455
00:26:26 --> 00:26:32
And when it, of course,
gets colder, it will uncurl,

456
00:26:29 --> 00:26:35
and so here is cold.

457
00:26:32 --> 00:26:38
And that's what the whole
thermometer is based upon.

458
00:26:35 --> 00:26:41
And in the back is this coil.

459
00:26:39 --> 00:26:45
And so I broke one open for you

460
00:26:41 --> 00:26:47
in order to make
you see that coil.

461
00:26:43 --> 00:26:49
 

462
00:26:48 --> 00:26:54
Now, I have that here.

463
00:26:49 --> 00:26:55
 

464
00:26:54 --> 00:27:00
This is the part
that is in the back,

465
00:26:57 --> 00:27:03
and this is that bimetal--
the bimetal coil.

466
00:26:59 --> 00:27:05
This is the bottom part,
this is the top,

467
00:27:02 --> 00:27:08
and this is just the hand
that is attached to it.

468
00:27:05 --> 00:27:11
And then it goes into this case.

469
00:27:09 --> 00:27:15
Let's make sure that the pivot
goes in there-- yeah.

470
00:27:16 --> 00:27:22
If I increase the temperature,
try to see that.

471
00:27:20 --> 00:27:26
You see the coil tightens up.

472
00:27:23 --> 00:27:29
See, the coil gets tighter.

473
00:27:25 --> 00:27:31
And when I make the temperature
go down artificially now

474
00:27:28 --> 00:27:34
by uncurling the coil,
it goes in this direction.

475
00:27:33 --> 00:27:39
Now, what we can do is
we can actually heat it up.

476
00:27:38 --> 00:27:44
We have to set the temperature
at whatever we think it is now.

477
00:27:41 --> 00:27:47
It's about 70 degrees
in the room.

478
00:27:43 --> 00:27:49
Is that what it is?

479
00:27:46 --> 00:27:52
Well, that's close enough.

480
00:27:48 --> 00:27:54
This is Fahrenheit--
oh, what a terrible scale.

481
00:27:50 --> 00:27:56
Yeah, by the way, you also see
some civilized scale there.

482
00:27:52 --> 00:27:58
You see centigrade in addition
to the Fahrenheit.

483
00:27:58 --> 00:28:04
So it's close enough,
it's a little bit over 70,

484
00:28:01 --> 00:28:07
and I can now make sure
that this is stuck to it,

485
00:28:06 --> 00:28:12
to the case.

486
00:28:08 --> 00:28:14
I can heat it.

487
00:28:09 --> 00:28:15
(motor purring )

488
00:28:13 --> 00:28:19
 

489
00:28:20 --> 00:28:26
The bimetal tightens up more.

490
00:28:26 --> 00:28:32
So when I heat it,
the bimetal tightens up more,

491
00:28:29 --> 00:28:35
and when I blow air over it,
I can actually make it cool

492
00:28:31 --> 00:28:37
a little faster
than it will otherwise.

493
00:28:36 --> 00:28:42
(blowing )

494
00:28:45 --> 00:28:51
So as simple as that.

495
00:28:47 --> 00:28:53
Very simple device with...

496
00:28:50 --> 00:28:56
the bimetals have
many, many applications.

497
00:28:54 --> 00:29:00
 

498
00:29:04 --> 00:29:10
Your thermostats
in your dormitories

499
00:29:10 --> 00:29:16
of your heating systems,

500
00:29:12 --> 00:29:18
and also perhaps of the
air-conditioning systems,

501
00:29:15 --> 00:29:21
almost all have a coil
like this in there.

502
00:29:17 --> 00:29:23
It was an extremely
ingenious device.

503
00:29:21 --> 00:29:27
It has a coil, and at the end of
the coil is a little glass tube,

504
00:29:26 --> 00:29:32
only one centimeter large,
and there is mercury inside.

505
00:29:30 --> 00:29:36
So the coil is like this.

506
00:29:32 --> 00:29:38
 

507
00:29:35 --> 00:29:41
Bimetal.

508
00:29:37 --> 00:29:43
And at the end here
is a glass container

509
00:29:42 --> 00:29:48
and there is some mercury,

510
00:29:43 --> 00:29:49
and the mercury is here
on this side,

511
00:29:46 --> 00:29:52
because notice the way
I have tilted it a little.

512
00:29:49 --> 00:29:55
The mercury rolls to the left.

513
00:29:52 --> 00:29:58
And there are here two wires,
electric wires,

514
00:29:55 --> 00:30:01
one here and one here,
which go to the heating system.

515
00:29:59 --> 00:30:05
And so when the mercury is here,
which has a good conductivity,

516
00:30:02 --> 00:30:08
the heater is on.

517
00:30:06 --> 00:30:12
Now, the room gets warmer
and warmer and warmer

518
00:30:08 --> 00:30:14
and the bimetal will tighten up,
will curl even more.

519
00:30:12 --> 00:30:18
And so there comes a time

520
00:30:13 --> 00:30:19
that this glass thing
will go like this

521
00:30:17 --> 00:30:23
and the mercury rolls out.

522
00:30:19 --> 00:30:25
And when the mercury rolls out--
here is the mercury--

523
00:30:24 --> 00:30:30
these contacts here are open,
and the heater will stop.

524
00:30:28 --> 00:30:34
And that's in almost every room.

525
00:30:31 --> 00:30:37
Very ingenious device.

526
00:30:33 --> 00:30:39
 

527
00:30:36 --> 00:30:42
Now I want to move from
linear expansion coefficients

528
00:30:41 --> 00:30:47
to cubic expansion coefficients.

529
00:30:44 --> 00:30:50
I will leave
these numbers there,

530
00:30:45 --> 00:30:51
because I will
need them later on.

531
00:30:50 --> 00:30:56
But now I take a block
of some material

532
00:30:53 --> 00:30:59
and want to discuss the volume
increase-- not just the length,

533
00:30:57 --> 00:31:03
but the volume increase.

534
00:31:01 --> 00:31:07
So here I have a solid material.

535
00:31:07 --> 00:31:13
Let's make it simple,
all sides L.

536
00:31:10 --> 00:31:16
And I increase it by an amount
of temperature delta T.

537
00:31:15 --> 00:31:21
Well, the old volume is L cubed,

538
00:31:20 --> 00:31:26
and then I'm going to increase
the temperature by delta T,

539
00:31:22 --> 00:31:28
so all these sides will get
longer by amount delta L,

540
00:31:26 --> 00:31:32
and so the new volume will be L
plus delta L to the power 3.

541
00:31:33 --> 00:31:39
 

542
00:31:37 --> 00:31:43
This can also be written
as L to the third times one

543
00:31:43 --> 00:31:49
plus delta L
over L to the power 3.

544
00:31:48 --> 00:31:54
Same thing, right?

545
00:31:51 --> 00:31:57
Now, perhaps you remember,
or at least you should remember,

546
00:31:55 --> 00:32:01
that one plus x to the power n,

547
00:32:00 --> 00:32:06
in case that x is much,
much smaller than one,

548
00:32:03 --> 00:32:09
is approximately one plus nx.

549
00:32:06 --> 00:32:12
We've used that before when we
discussed the Doppler shift--

550
00:32:09 --> 00:32:15
light from receding stars.

551
00:32:13 --> 00:32:19
This is called the binomial
series, binomial expansion.

552
00:32:17 --> 00:32:23
It's really the first order
terms of the Taylor expansion.

553
00:32:21 --> 00:32:27
If you, as an example,
if you take x equals 0.05

554
00:32:27 --> 00:32:33
and you calculate the exact
value with your calculator,

555
00:32:32 --> 00:32:38
you would find 1.158.

556
00:32:35 --> 00:32:41
If you do it this way, you will
find 1.15, which is very close.

557
00:32:41 --> 00:32:47
Approximation is better
than one percent.

558
00:32:44 --> 00:32:50
So I will use the same
approximation here,

559
00:32:47 --> 00:32:53
and so we're going to get
L to the third

560
00:32:51 --> 00:32:57
times one plus three
delta L divided by L.

561
00:32:59 --> 00:33:05
So that is L to the third
plus three delta L, L squared.

562
00:33:10 --> 00:33:16
So the difference
in terms of delta V,

563
00:33:15 --> 00:33:21
the old volume was this.

564
00:33:17 --> 00:33:23
And this volume
is V plus delta V,

565
00:33:21 --> 00:33:27
so delta V is the difference
between the two,

566
00:33:27 --> 00:33:33
is three delta L, L squared.

567
00:33:31 --> 00:33:37
But I know that delta L equals
alpha times L times delta T.

568
00:33:38 --> 00:33:44
And so I can substitute that in
here, and so I find that delta V

569
00:33:43 --> 00:33:49
equals three alpha
times L squared times L--

570
00:33:49 --> 00:33:55
that is L cubed-- times delta T.

571
00:33:52 --> 00:33:58
But L cubed was the old volume,

572
00:33:55 --> 00:34:01
and so I now find that delta V
equals three alpha

573
00:34:00 --> 00:34:06
times the old volume
times delta T,

574
00:34:03 --> 00:34:09
and this one is
often called beta.

575
00:34:06 --> 00:34:12
Beta is the cubical
expansion coefficient,

576
00:34:09 --> 00:34:15
as opposed to the linear one.

577
00:34:12 --> 00:34:18
So you will say, well, big deal.

578
00:34:13 --> 00:34:19
I mean, why are you
talking about beta?

579
00:34:15 --> 00:34:21
Because if we have the values
for alpha, all we have to do

580
00:34:18 --> 00:34:24
if we go to a volume,
to make that beta three alpha,

581
00:34:22 --> 00:34:28
and we are in business.

582
00:34:24 --> 00:34:30
Well, when you have liquids,
in general,

583
00:34:27 --> 00:34:33
you don't find in the tables
values for alpha.

584
00:34:30 --> 00:34:36
So when you deal with liquids,
for instance, mercury,

585
00:34:34 --> 00:34:40
which is the one
that I want to use today,

586
00:34:38 --> 00:34:44
then you find that the cubic
expansion coefficient

587
00:34:42 --> 00:34:48
is 18 times ten to the minus
five per degree centigrade.

588
00:34:49 --> 00:34:55
If I compare that with Pyrex,

589
00:34:54 --> 00:35:00
you have to take
three times this value,

590
00:34:56 --> 00:35:02
so that's very roughly
ten to the minus five

591
00:35:02 --> 00:35:08
per degree centigrade.

592
00:35:05 --> 00:35:11
And so now you begin
to smell the idea

593
00:35:08 --> 00:35:14
of a mercury thermometer.

594
00:35:11 --> 00:35:17
 

595
00:35:14 --> 00:35:20
I put some mercury
in Pyrex glass,

596
00:35:18 --> 00:35:24
and the Pyrex glass is not
going to expand very much,

597
00:35:21 --> 00:35:27
but the mercury will.

598
00:35:25 --> 00:35:31
And then the mercury, which is
in an enclosed environment,

599
00:35:29 --> 00:35:35
will have to expand, and it
expands into my thermometer

600
00:35:34 --> 00:35:40
and that's the way that
we read the temperature.

601
00:35:37 --> 00:35:43
 

602
00:35:41 --> 00:35:47
So here is a glass tube
which is very, very narrow.

603
00:35:47 --> 00:35:53
All this is closed here.

604
00:35:49 --> 00:35:55
And let's say the radius here
is only 0.1 millimeter.

605
00:35:56 --> 00:36:02
And here is a reservoir,
mercury, just a working example,

606
00:36:03 --> 00:36:09
and suppose we take
one cubic centimeter--

607
00:36:07 --> 00:36:13
just simple numbers.

608
00:36:08 --> 00:36:14
Just want to show you the basic
idea behind the thermometer.

609
00:36:13 --> 00:36:19
I'm going to increase the
temperature of this mercury,

610
00:36:16 --> 00:36:22
say by ten degrees,

611
00:36:19 --> 00:36:25
so delta T,
ten degrees centigrade.

612
00:36:24 --> 00:36:30
So by how much will
this volume expand?

613
00:36:27 --> 00:36:33
Well, delta V equals beta 18
times ten to the minus fifths

614
00:36:37 --> 00:36:43
times the volume, which is
one cubic centimeter--

615
00:36:39 --> 00:36:45
let me just put the volume
in there;

616
00:36:41 --> 00:36:47
you may want to do it in cubic
meters-- I leave it up to you--

617
00:36:44 --> 00:36:50
times the delta T.

618
00:36:47 --> 00:36:53
And you will find

619
00:36:48 --> 00:36:54
that the expansion in terms
of cubic centimeters

620
00:36:52 --> 00:36:58
is 0.0018 cubic centimeters.

621
00:36:58 --> 00:37:04
See, if you leave V in cubic
centimeters, which you can do,

622
00:37:01 --> 00:37:07
then you get your answer also
in cubic centimeters, of course.

623
00:37:04 --> 00:37:10
You do not always work...
have to work mks.

624
00:37:09 --> 00:37:15
So this is an extraordinarily
small increase

625
00:37:11 --> 00:37:17
in terms of its volume.

626
00:37:13 --> 00:37:19
However, the Pyrex is
not expanding at all.

627
00:37:17 --> 00:37:23
You can just
forget that for now.

628
00:37:19 --> 00:37:25
If you want to calculate
how much it is, it's fine,

629
00:37:21 --> 00:37:27
but it is 18 times less,

630
00:37:24 --> 00:37:30
so the fact that the vessel
gets a little larger

631
00:37:26 --> 00:37:32
of course is important,

632
00:37:27 --> 00:37:33
but I will just ignore
that for now.

633
00:37:30 --> 00:37:36
And so I will just assume

634
00:37:31 --> 00:37:37
that all this mercury
will be driven up here.

635
00:37:35 --> 00:37:41
And so if the mercury,
then, changes its height

636
00:37:39 --> 00:37:45
by an amount delta h,

637
00:37:41 --> 00:37:47
and if this is a tube
with a radius .1 millimeters,

638
00:37:45 --> 00:37:51
then this amount of mercury

639
00:37:48 --> 00:37:54
must be the same as
pi r squared times delta h,

640
00:37:53 --> 00:37:59
which is the volume
of the new column--

641
00:37:56 --> 00:38:02
the increase in the column.

642
00:37:59 --> 00:38:05
And so you take your .1
millimeters and you'll find

643
00:38:04 --> 00:38:10
that delta h for this example
that I chose is 5.7 centimeters.

644
00:38:15 --> 00:38:21
That's huge.

645
00:38:17 --> 00:38:23
That's very easy to see.

646
00:38:18 --> 00:38:24
For ten degrees increase
in temperature,

647
00:38:22 --> 00:38:28
it's 5.7 centimeters.

648
00:38:24 --> 00:38:30
So for one degree centigrade,
you would get six millimeters.

649
00:38:28 --> 00:38:34
It's very easy to see,

650
00:38:29 --> 00:38:35
and so that's the idea
behind a mercury thermometer.

651
00:38:37 --> 00:38:43
I have a mercury
thermometer here,

652
00:38:40 --> 00:38:46
but they're very hard to read.

653
00:38:44 --> 00:38:50
But I have one here.

654
00:38:46 --> 00:38:52
It's a medical one.

655
00:38:49 --> 00:38:55
It says "oral,"

656
00:38:50 --> 00:38:56
not to be confused.

657
00:38:53 --> 00:38:59
And I can stick it in my mouth
and measure my temperature

658
00:38:57 --> 00:39:03
using this scale.

659
00:38:59 --> 00:39:05
It's easier for me to show you

660
00:39:01 --> 00:39:07
the one that
I have in my office,

661
00:39:04 --> 00:39:10
which also works on liquid.

662
00:39:09 --> 00:39:15
(mumbling ):
This one.

663
00:39:10 --> 00:39:16
 

664
00:39:15 --> 00:39:21
So this one, you see
the red liquid?

665
00:39:22 --> 00:39:28
Let me be sure that we have
the right light setting.

666
00:39:27 --> 00:39:33
This should go off.

667
00:39:29 --> 00:39:35
Okay.

668
00:39:30 --> 00:39:36
So you see the red liquid.

669
00:39:32 --> 00:39:38
There it is.

670
00:39:35 --> 00:39:41
And also notice that
it is degrees Fahrenheit,

671
00:39:39 --> 00:39:45
which is unfortunate.

672
00:39:41 --> 00:39:47
But it's helping.

673
00:39:43 --> 00:39:49
When the temperature is here,

674
00:39:44 --> 00:39:50
at least you know that
you're going to get ice.

675
00:39:46 --> 00:39:52
(a few chuckles )

676
00:39:50 --> 00:39:56
Well, that's somewhere near
32... 32 Fahrenheit.

677
00:39:53 --> 00:39:59
That must be here.

678
00:39:55 --> 00:40:01
Snow.

679
00:39:56 --> 00:40:02
And this makes
you feel good-- sun.

680
00:40:00 --> 00:40:06
Yeah.

681
00:40:01 --> 00:40:07
You know, just in case
you don't remember.

682
00:40:03 --> 00:40:09
I could heat it up.

683
00:40:05 --> 00:40:11
(blow-dryer humming )

684
00:40:09 --> 00:40:15
 

685
00:40:31 --> 00:40:37
You always should be careful
when you heat it up

686
00:40:34 --> 00:40:40
that you don't go too far,

687
00:40:35 --> 00:40:41
because the top of the
thermometer is closed.

688
00:40:38 --> 00:40:44
In the case of
a mercury thermometer,

689
00:40:39 --> 00:40:45
there is vacuum in here,
and so if you--

690
00:40:42 --> 00:40:48
when I was a kid,
I loved to do this--

691
00:40:44 --> 00:40:50
to take the medical
thermometer of my parents

692
00:40:46 --> 00:40:52
and heat it up with a hair dryer

693
00:40:48 --> 00:40:54
and then it would
just burst through it,

694
00:40:50 --> 00:40:56
it would just break the glass,

695
00:40:51 --> 00:40:57
because the expansion
is huge, the force,

696
00:40:53 --> 00:40:59
and it would just pop off.

697
00:40:54 --> 00:41:00
And then I'd put it back
and say nothing.

698
00:40:57 --> 00:41:03
And that can happen
with this, too.

699
00:40:59 --> 00:41:05
So it doesn't have an opening.

700
00:41:01 --> 00:41:07
It is not open,
it's a closed thing,

701
00:41:03 --> 00:41:09
so you've got
to be quite careful.

702
00:41:09 --> 00:41:15
There is a technique which
is called "shrink fitting,"

703
00:41:14 --> 00:41:20
and shrink fitting
is the following.

704
00:41:18 --> 00:41:24
 

705
00:41:19 --> 00:41:25
You have a piece of metal--

706
00:41:21 --> 00:41:27
let's take just a solid cylinder
as a working example--

707
00:41:26 --> 00:41:32
and you have a ring.

708
00:41:28 --> 00:41:34
The ring could be itself
a cylinder.

709
00:41:31 --> 00:41:37
Well, this one, this opening
is smaller than this--

710
00:41:38 --> 00:41:44
just a little smaller--
purposely made that way.

711
00:41:41 --> 00:41:47
Just a little smaller.

712
00:41:42 --> 00:41:48
You heat this one.

713
00:41:44 --> 00:41:50
Expands.

714
00:41:46 --> 00:41:52
And you put it over here,
it will fit.

715
00:41:49 --> 00:41:55
And then you let it sit.

716
00:41:50 --> 00:41:56
It cools,
and it tightens itself up.

717
00:41:52 --> 00:41:58
That's called shrink fitting,
a technique which is often used.

718
00:41:57 --> 00:42:03
I have something
to show you here

719
00:41:59 --> 00:42:05
which is the opposite
of shrink fitting.

720
00:42:02 --> 00:42:08
I have a ring-- I'll show you
shortly on the screen there--

721
00:42:08 --> 00:42:14
and that's made of brass,

722
00:42:11 --> 00:42:17
and I have a ball which goes
through there.

723
00:42:17 --> 00:42:23
Just barely, but it
goes through there.

724
00:42:20 --> 00:42:26
And then I will
heat up this ball,

725
00:42:22 --> 00:42:28
and then it won't
go through there,

726
00:42:24 --> 00:42:30
so it's the reverse,
but at least you get the idea.

727
00:42:27 --> 00:42:33
And then if you wait
and it cools,

728
00:42:30 --> 00:42:36
when you bring them
in contact with each other,

729
00:42:32 --> 00:42:38
this one will cool and
this one will get warmer.

730
00:42:35 --> 00:42:41
So you catch two birds
with one stone.

731
00:42:38 --> 00:42:44
This one will shrink,

732
00:42:39 --> 00:42:45
and at the same time, this one
will become a little larger,

733
00:42:42 --> 00:42:48
and so then clearly
it will fall through,

734
00:42:46 --> 00:42:52
and that's the idea.

735
00:42:48 --> 00:42:54
And let's try that.

736
00:42:51 --> 00:42:57
Get the best lighting that we
can under the circumstances,

737
00:42:56 --> 00:43:02
and we'll change to...
is that it?

738
00:43:02 --> 00:43:08
Yeah, this is the ring.

739
00:43:05 --> 00:43:11
And here is that brass ball.

740
00:43:08 --> 00:43:14
It goes through there
quite easily.

741
00:43:13 --> 00:43:19
I'll put it horizontal now.

742
00:43:16 --> 00:43:22
 

743
00:43:20 --> 00:43:26
And then I will start
heating up this ball.

744
00:43:22 --> 00:43:28
(flame whooshing )

745
00:43:27 --> 00:43:33
Here's the ball.

746
00:43:32 --> 00:43:38
It can't be too close
to the ring,

747
00:43:33 --> 00:43:39
because then the ring
will also be heated,

748
00:43:37 --> 00:43:43
and then of course if the two
have the same temperature,

749
00:43:41 --> 00:43:47
then the ball
will still go through.

750
00:43:44 --> 00:43:50
(flame whooshing )

751
00:43:45 --> 00:43:51
 

752
00:44:11 --> 00:44:17
Let's see.

753
00:44:14 --> 00:44:20
Now it doesn't want
to go through.

754
00:44:16 --> 00:44:22
So we'll leave it like that,
and we'll see what happens.

755
00:44:20 --> 00:44:26
So the ring will now expand
a little because it gets hotter,

756
00:44:25 --> 00:44:31
and the ball will shrink
a little because it gets colder

757
00:44:28 --> 00:44:34
and it shouldn't take too long

758
00:44:30 --> 00:44:36
for the ball to be able
to get through.

759
00:44:33 --> 00:44:39
If I heat them both
with the torch,

760
00:44:37 --> 00:44:43
then of course
they will always be able

761
00:44:39 --> 00:44:45
to go through each other.

762
00:44:45 --> 00:44:51
And there it goes.

763
00:44:49 --> 00:44:55
So if I heat them both...

764
00:44:50 --> 00:44:56
(flame whooshing )

765
00:44:54 --> 00:45:00
 

766
00:45:00 --> 00:45:06
...so they both expand,
since it's both brass,

767
00:45:04 --> 00:45:10
there is no differential
expansion like with bimetals,

768
00:45:10 --> 00:45:16
then no matter what you do,

769
00:45:14 --> 00:45:20
it will always be able
to go through.

770
00:45:18 --> 00:45:24
 

771
00:45:23 --> 00:45:29
It's only when I...

772
00:45:24 --> 00:45:30
 

773
00:45:27 --> 00:45:33
...heat the ball
and not the ring

774
00:45:29 --> 00:45:35
that you get the effect
that it won't get through.

775
00:45:32 --> 00:45:38
It may actually get through now,
still get through.

776
00:45:34 --> 00:45:40
Yeah.

777
00:45:35 --> 00:45:41
 

778
00:45:39 --> 00:45:45
What I've left out of my
discussion with you is water.

779
00:45:44 --> 00:45:50
Why have I not mentioned to you

780
00:45:46 --> 00:45:52
what is the expansion
coefficient,

781
00:45:49 --> 00:45:55
the cubical expansion
coefficient of water?

782
00:45:51 --> 00:45:57
Water is so important
in our lives.

783
00:45:53 --> 00:45:59
Well, there is a reason
why I left it out,

784
00:45:55 --> 00:46:01
because there is something
very special with water.

785
00:45:59 --> 00:46:05
If you take 20-degree centigrade
water and you cool it,

786
00:46:03 --> 00:46:09
it shrinks.

787
00:46:04 --> 00:46:10
Normal behavior.

788
00:46:06 --> 00:46:12
Beta has a positive value.

789
00:46:07 --> 00:46:13
But when you reach
four degrees centigrade

790
00:46:10 --> 00:46:16
and you go all the way
down to zero,

791
00:46:13 --> 00:46:19
then it doesn't shrink--
it expands.

792
00:46:16 --> 00:46:22
So in that range,

793
00:46:17 --> 00:46:23
from zero degrees centigrade
to four degrees centigrade,

794
00:46:20 --> 00:46:26
water has a negative value
for beta.

795
00:46:23 --> 00:46:29
When you heat it, it shrinks,

796
00:46:26 --> 00:46:32
and when you cool it,
it expands.

797
00:46:28 --> 00:46:34
And that makes water
extremely unusual.

798
00:46:32 --> 00:46:38
But it's great for fish,

799
00:46:34 --> 00:46:40
because it means that water
of four degrees centigrade

800
00:46:37 --> 00:46:43
has the highest
possible density.

801
00:46:40 --> 00:46:46
It's higher density
than at 20 degrees,

802
00:46:43 --> 00:46:49
and a higher density
than at zero degrees.

803
00:46:46 --> 00:46:52
And so when in the winter
the ponds freeze,

804
00:46:50 --> 00:46:56
the highest density water
goes to the bottom,

805
00:46:52 --> 00:46:58
and that's why the way... that's
the way that fish can survive.

806
00:46:55 --> 00:47:01
Rather than becoming deep-freeze
fish right there, they can swim.

807
00:46:59 --> 00:47:05
So most of the pond
in the winter,

808
00:47:02 --> 00:47:08
the bottom layers
are four degrees centigrade,

809
00:47:05 --> 00:47:11
which is safely
from the freezing point.

810
00:47:09 --> 00:47:15
Now, when you melt a solid
and it becomes liquid,

811
00:47:13 --> 00:47:19
in almost all cases
the liquid expands.

812
00:47:17 --> 00:47:23
Sort of natural.

813
00:47:18 --> 00:47:24
And so the solids sink
in the liquids.

814
00:47:21 --> 00:47:27
If you take crystals,
they sink in their own liquid.

815
00:47:26 --> 00:47:32
But not water.

816
00:47:27 --> 00:47:33
Water and ice
are very anomalous.

817
00:47:30 --> 00:47:36
If you take water at zero
degrees and you freeze it

818
00:47:35 --> 00:47:41
and it becomes ice crystals,
it expands.

819
00:47:39 --> 00:47:45
And the expansion is enormous,

820
00:47:41 --> 00:47:47
because the density of ice
is eight percent lower

821
00:47:45 --> 00:47:51
than the density of water.

822
00:47:47 --> 00:47:53
The density of ice is 0.92 grams
per cubic centimeter,

823
00:47:50 --> 00:47:56
and water per definition is one.

824
00:47:52 --> 00:47:58
This is why pipes can burst
in the winter when they freeze.

825
00:47:58 --> 00:48:04
The pipes freeze,

826
00:47:59 --> 00:48:05
people have water pipes
near the outside walls.

827
00:48:02 --> 00:48:08
They cool, they freeze,
the pipes burst,

828
00:48:04 --> 00:48:10
because the ice expands.

829
00:48:06 --> 00:48:12
They're not aware of that,

830
00:48:07 --> 00:48:13
and in the spring when the water
melts, when the ice melts,

831
00:48:11 --> 00:48:17
all of a sudden-- they have
a flood because the pipe burst.

832
00:48:15 --> 00:48:21
This is why theTitanic sank.

833
00:48:17 --> 00:48:23
Because ice floats on water.

834
00:48:20 --> 00:48:26
Ice has a lower density.

835
00:48:22 --> 00:48:28
Without ice floating,
no icebergs.

836
00:48:26 --> 00:48:32
This is why you can skate
on ponds,

837
00:48:29 --> 00:48:35
because ice has a lower density
than water,

838
00:48:32 --> 00:48:38
so ice floats on water.

839
00:48:35 --> 00:48:41
The best way that
I can demonstrate to you

840
00:48:37 --> 00:48:43
that ice floats
is to treat myself

841
00:48:40 --> 00:48:46
and give myself
a glass of something.

842
00:48:43 --> 00:48:49
Today it will be apple cider.

843
00:48:47 --> 00:48:53
And I have here some ice cubes.

844
00:48:50 --> 00:48:56
And I put some ice cubes
in here, and they float.

845
00:48:53 --> 00:48:59
And if you don't believe it,
come and take a look.

846
00:48:57 --> 00:49:03
Okay, enjoy your weekend.

847
00:48:59 --> 00:49:05
Oh, no, we still have
a lecture on Friday.

848
00:49:01 --> 00:49:07
See you then.

849
00:49:03 --> 00:49:09
 

850
00:49:06 --> 00:49:12