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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.

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