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A. A puzzle, and a surprising solution
Take equal masses of lead and aluminum. Heat them
until their temperatures are both 10 degrees higher. Will it take
the same amount of heat for each?
Back in the 18th century, the chemist Joseph
Black discovered that different materials required different amounts of
heat to raise their temperatures by equal amounts. The amount by
which the temperature of a material changes as it absorbs or gives off
heat can even be used to help identify the material. Among solid
materials near room temperature, aluminum and lead differ almost as much
as any two chemical elements in this respect: to raise the temperature
of aluminum 10 degrees takes more than five times the amount of heat that
the same mass of lead requires for the same increase.
Why would different materials react so differently to
heat? The idea that heat is just the energy of the random motion
of atoms offers a clue. The atoms of any solid object move constantly,
each atom continually bouncing off its neighbors. At any given temperature,
the atoms will have a certain average energy. If we heat the solid
to a higher temperature, we increase the agitation of its atoms to a higher
average energy.
Whatever the combined energy is of all this agitation,
the average energy of each atom is just this combined energy divided by
the number of atoms. If the solid is a material like lead, each atom
will be massive, so it will take relatively few atoms to make one gram;
with fewer atoms, each atom will have a large share of energy. Materials
made of less massive atoms will require more atoms to make an equal mass
of solid, so each atom will have less energy.
So far, nothing about this seems especially complicated,
but eventually a puzzling fact became known. Given the ideas about
atoms that were common in the 19th century, one could deduce
that the average energy per atom should be directly proportional to the
solid's temperature-double the absolute temperature, and each atom should
have twice the average energy. Put another way, raising the temperature
of a solid by one degree would require the same amount of energy per atom,
no matter what the solid's original temperature was. This conclusion
agreed with observations of real solids made by Pierre-Louis Dulong and
Alexis-Thérèse Petit, which they published in 1819.
But, in time, a puzzling fact emerged as other observations
failed to agree with this theory. Dulong and Petit had experimented
with solids at ordinary temperatures. At extremely low temperatures
we find something quite different. The lower the starting temperature,
the less heat you need to raise the temperature of a solid by one degree. If
you start with extremely low temperatures close to absolute zero, you can
raise the temperature of solids by several degrees with barely any heat
input at all.
Even at ordinary temperatures, the theory was wrong
about some materials. If the theory were only slightly off, it might
be basically sound; some small unaccounted-for disturbance might be affecting
some types of atoms, or any atoms in some situations. But since the
atomic theory was way off for several materials, many physicists suspected
there might be something fundamentally wrong with the very assumption that
atoms even existed.
But by the early 20th century, Albert Einstein
had realized that one thermodynamic phenomenon pointed directly to the
existence of atom-like units of matter, and could even allow a precise
determination of molecular masses. Einstein had found that, if liquids
were made of molecules, small particles suspended in the liquid would share
in the liquid molecules' random motion. Einstein also proved an exact
relation between how far the suspended particles would move on the average,
how long they have been moving, and the size of the unit of molecular mass. Within
a few years, Jean Perrin and his students verified this relation in experiments
and determined the molecular-mass unit.
While these experiments appeared to confirm that heat
energy is the random motion of atoms, they didn't directly address the
theory's apparent discrepancy with the behavior of solid objects. Einstein
found a resolution to this problem while thinking through the implications
of a recent discovery by Max Planck. Einstein found that atoms might
be real after all, but if so, they behaved very differently from what had
previously been suspected.
In the next section, we'll briefly describe what Einstein
found, along with some of the questions this finding raised. To answer those questions,
we'll look first at how temperature is related to energy, and then, with
the help of some graphs illustrating Einstein's findings use that relationship
to answer the questions. Finally, we'll see how these findings exemplify
certain features of scientific progress. (.....continued)
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