Thermodynamics and the Atomic and Molecular Structure of Matter 91
a surface tension, which arises from the attractive aspect of the molecular
forces. The strength of this surface tension is considerable. it enables
certain water bugs to walk upon the surface of the water. Although they
are heavy enough to sink they are not heavy enough to break the surface
tension and they therefore actually walk upon the surface of the water.
Two other forces related to each other and associated with liquids are
the forces due to water pressure and buoyancy. The water pressure at any
given point is related to the weight of the water between the point in
question and the surface, and hence depends solely on the distance to the
surface. The distance to the bottom is irrelevant. The pressure pushes
equally in all directions. It is the difference in the water pressure at the
top and bottom of an object, which accounts for its buoyancy in water.
Let us consider some material, which has the form of a cube each of
whose sides is one meter long. We place our cube under water such that
the top of the cube is one meter from the surface and the bottom of the
cube is two meters from the surface. There are now three distinct forces
in the vertical direction acting on the cube. Two of these forces are due
to water pressure at the upper and lower surface. The one at the upper
surface is pushing down and is less than the one at the lower surface
pushing up. The difference of these two forces is precisely equal to the
weight of the water displaced by the cube. The third force acting on the
cube is the gravitation pull of the Earth and is of course equal to its
weight. If the weight of our material is greater than that of the displaced
water is will sink and if it is less then it will float. We therefore expect
those substances whose density is less than water to float and those
whose density is greater to sink.
Archimedes was the first to explain these ideas over 2000 years
ago. He made this discovery when he stepped into his full bathtub
and observed the water he displaced flow over the sides of the tub.
Reportedly, he jumped out of the tub and ran home naked crying
“Eureka!” for he realized he could solve the problem of whether the
king’s crown was pure gold or a fraudulent mixture of gold and some
base metal. By comparing the amount of water displaced by the king’s
crown and an equal amount of pure gold, he could determine if the crown
was also pure gold. This episode with Archimedes is one of those rare
moments in Greek science when empiricism played a role. It was not
quite a planned experiment but an accidental observation. It is, however,
one of the times that Greek science was absolutely correct unlike most of
the physics of Aristotle that had to be undone.