Pique the Geek 20111030: Heat and Temperature

(9 pm. – promoted by ek hornbeck)

This might sound like a foolish title, but actually the concepts of heat and temperature are quite different.  Obviously things that feel “hotter” must have more heat in them, right?  Actually, that is not always, and is often NOT, the case.  The two concepts are quite different, but are related.

In a bit we shall go into specific definitions of what heat and temperature actually are, but it is more interesting to look at the historical thoughts about them.  Back before quantitative physics, the higher the temperature that an object had, the more heat that it was thought to have.  That is correct for a specific object, as the temperature increases, the amount of heat in it also increases.

But it is easy to show that for dissimilar objects, the amount of heat is quite unrelated to the temperature.  I shall show you that ice might contain more heat than red hot steel!  Ready to look more deeply?  Then let us go to it!

Heat is the amount of thermal energy in a body.  That is a fairly straightforward concept, but actually was not understood until relatively recently, when the concepts of work and energy were elucidated. Not that long ago the concept of energy was not well understood at all, so heat did not have a very good definition.

Temperature is related to heat, but not as in such a simple manner as one might expect.  While it is true that a given body contains more heat as the temperature increases, to a point, two different substances, in the same amount, will in general have differing amounts of heat in them.

First, let us look at the commonly used temperature scales.  The one in general use in the US is the Fahrenheit scale, where the freezing point of water is designated as 32 degrees and the boiling point at 212 degrees.  Thus there are 180 degrees betwixt the freezing point and the boiling point.

The temperature scale used by most of the rest of the world is the Celsius (also called the centigrade) scale, with the freezing and boilings points of water at zero and 100 degrees, making a Celsius degree “bigger” than a Fahrenheit one by almost a factor of two.

Both scales are arbitrary, using water as the basic material on which to define the scales.  We know that it gets colder than the freezing point of water, so both scales have negative temperatures.  This causes quite a bit of mathematical complication when trying to apply them to physics, so other scales are used instead.  The one used for most US engineering work is the Rankine scale, starting at absolute zero as the zero point.  The degrees are the same “size” as Fahrenheit scale, so the freezing point of water is 491.67 degrees R and the boiling point is 180 degrees higher, at 671.64 degrees R.  (The deviation of the 0.03 degree has to do with better measurements since the scale was originally devised).

By far the most commonly used absolute scale is the Kelvin scale.  In it, absolute zero is again zero, but the degrees are the same size as the Celsius ones, making the freezing point of water 273.15 kelvins and the boiling point 373.13 kelvins.  Note that, in modern usage, the term “degrees Kelvin as been replaced by kelvins.

One might ask why it is important to use absolute scales, and how absolute zero was determined.  It was through the work of Lord Kelvin and others with gases that brought about the idea of a coldest possible temperature.  It turns out that the 18th and 19th centuries were critical times for the development of science from speculation, and work with gases was a central part of this advancement.

It had long been known that gases expand when heated and contract when cooled.  Kelvin and others discovered that most gases contract by about 1/273 of their volume for each degree C that they are cooled.  By extrapolation, it was discovered that the volume of a gas approaches zero at minus 273 degrees C, and since a negative volume for matter is fundamentally impossible, the great minds of the day reasoned that no temperature could be less that this absolute zero.

We now know that negative absolute temperatures are possible, but only in highly contrived systems and only in microregions of them.  Taken as an aggregate, the temperature of any body can not be less than absolute zero.  It has taken many years to make very accurate measurements, but we now have good data to define absolute zero as exactly 273.15 degrees below zero C.

The implication of this are enormous.  This means that there is a fundamental limit to temperature at the low end.  Some current data indicate that there is a fundamental limit on the high end as well.  This is thought to be 1.417×10³² K, speculated to have occurred 5.391×10⁻⁴⁴ seconds after the Big Bang.

Temperature, as previously stated, has to do with how fast atoms or molecules are moving, but there is a bit more to it that that.  There are different ways to move other than simple translational motion, i.e., motion in a straight line.  To explore that, let us visualize some simple systems.

For the first example, let us take the element helium, with molecules composed of single atoms.  These kinds of gases are called monatomic.  Since single atoms behave essentially as geometric points, translational motion is the only kind of movement that they can have.  Imagine wee tiny billiard balls moving about inside a container.  They continue to move in a straight line until they hit either the surface of the container or another helium atom, and then they change direction, still in a straight line, until striking something else.

The next case is that of diatomic gases, like hydrogen.  In these, two atoms are chemically bonded together and they about in the container.  To return to the billiard ball analogy, these are like two wee billiard balls connected together by a massless spring.  The balls are then free to get closer and further from each other, but always have an average distance apart called the bond length.  Now think about how these molecules can move:  they can travel in straight lines, like single billiard balls, but they can also rotate about an imaginary axis in the center of the spring.  It like when we were in school and put a ruler on a pencil and spun it.

They also have another way to move, and that is for the spring to stretch and contract.  These motions are called vibrational motions, and that opens a third possible motion for diatomic gases.  In addition, diatomic molecules can exhibit all three kinds of motion simultaneously.  This makes the maths sort of difficult, but you get the idea.  There is essentially no limit to extend this, to three, four, or even more atoms in a molecule until it gets too heavy and becomes a liquid or a solid.  Let us take one more example for clarity, and then go to something completely different.

Carbon dioxide, CO₂, has three atoms.  There is a central carbon and bonded to it with a stiff spring are two oxygen atoms, one on either side.  This give us many more vibrational possibilities.  Once again, there is the translational motion and the rotational motion, but instead of only one vibration, there are many.  Think again of wee billiard balls connected with springs.

You can imagine the two end balls being stretched away from the center one, and this is called symmetric stretching.  But you can also imagine one end ball heading towards the middle one whilst the other one is moving away from it.  This is called asymmetric stretching, and is know to happen.  But, as they say on sorry TeeVee adverts, there is more!

It is also possible now to take one of the wee balls at one end of the string and push it up or down, whislt keeping the distance betwixt it and the central ball constant, and no other motion with the ball at the other end.  You can also pull or push both end balls up or down at the same time, or even push one up while you pull the other one down.  These motions are called bending, and are also known to exist.  So now we have all these kinds of motion possible in only a three atom molecule!

Imagine now how complex the picture is in a condensed phase (liquid or solid), when instead of only a few atoms we have many atoms or molecules in close contact!  The mutual influence is over 1000 times greater than in the gas phase at atmospheric pressure, and the maths get very complicated.  The bottom line is that temperature has to do with the motion of atoms or molecules, but these motions can become extremely complicated.

To give you a bit of flavor about temperatures of things (in kelvins), here is a short list.

We know that absolute zero is zero kelvins.  We have never attained that temperature experimentally.

The lowest experimentally achieved temperature of which I am aware is 450 pK (picokelvins), only 450 billionth of a kelvin above absolute zero.  That is pretty cold!

A standard (and rapidly vanishing) incandescent light bulb has a filament that is around 2500 K.  At this point, we can start to ignore the small difference betwixt kelvins and degrees C, since they are only around 300 degrees C apart.

The visible surface of the sun is around 5800 K.

The center of a strong lighting bolt is around 28,000 K.

The heart of the sun is around 16 million K.

A hydrogen bomb peaks at about 350 million K.

The highest experimental temperature (from CERN) is around 10 trillion K (but in a very small space, so do not worry!)

I already have stated the highest temperature that has been proposed to be possible.

I think that I shall stop here.  I think that you have sort of gotten an idea about what temperature is, or at least the basis of it.  Next week we shall talk about how temperature relates to heat, and it is fascinating.  I have a few examples that will blow off your socks about how much energy several common substances, and the folks who are not technical will likely be surprised when you see the numbers.

Well, you have done it again!  You have wasted many more einsteins of perfectly good photons reading this hot piece!  And even though Rick Perry admits to himself that he is out of the race when he reads me say it, I always learn much more than I could possibly hope to teach by writing this series.  Thus, please keep those comments, questions, corrections, and other feedback coming!  I shall return tomorrow after Keith’s show for Review Time to answer comments that I might miss by going to the bed tonight.  Bill Nye indeed!

Warmest regards,

Doc, aka Dr. David W. Smith

Crossposted at

The Stars Hollow Gazette,

Daily Kos, and

firefly-dreaming