Celebrating Einstein

"Solid Cold" (continued)

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C.  Temperature and energy

Most basically, temperature is related to energy flow.  If you have two things at different temperatures, and you put them together so that heat can flow between them, the heat will flow from the higher-temperature object to the other one.  This much was understood from the early days of thermodynamics, when the concept of "temperature" was first developed.

That is not to say that the energy flow will be in one direction only.  As was understood later, energy will actually flow in both directions, but the flow will be mostly from the higher temperature to the lower because there are more possible ways for heat to flow in that direction.

Less basically, but just as importantly, is the relation between the temperature of an object and how much energy it is likely to have at any given moment.  If an object at a uniform temperature is in contact with something much smaller than itself, both objects will very soon reach the same temperature, since only a small amount of energy will be transferred between the two.  Once this has happened, the amount of energy in the small object may fluctuate up or down from moment to moment, but its energy will usually be close to its average amount.

It turns out that the smaller object will most likely have very little energy most of the time, and only rarely have a great deal more energy.  How rarely depends on what the temperature is.

Suppose our small object is one atom in a solid, and the larger object is all the rest of the solid.  Under ordinary conditions, our one atom has a greater chance of having lower energies than higher energies.  The lower the temperature, the likelier a low energy is and the less likely a high one; at higher temperatures, the chance of finding the atom with a high energy is much closer to the chance that it has a low one.

Now consider all the atoms in the solid.  If there is an x% chance that the energy of any one atom will be in the low range, then x% of the atoms will be in that low range; if there's a y% chance that an atom's energy is in some higher range, y% of the atoms will be in that higher range.  From these percentages, we could find the average energy of all the atoms in the solid.  Since the percentages depend on the temperature of the solid, it would even be possible to figure out how much the temperature would change if we add energy to the solid, by adding a certain amount of heat per atom.

And if we do that using the 19th-century theory of atoms, the answer for a lot of solids comes out wrong.     (.....continued)

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Date Modified: 09/01/2005
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