Thermal Expansion and the Gas Law
Michael Fowler 4/8/06
Coefficients of Expansion
Almost all materials expand on heating—the most famous exception being water, which
contracts as it is warmed from 0 degrees Celsius to 4 degrees.
This is actually a good thing,
because as freezing weather sets in, the coldest water, which is about to freeze, is less dense than
slightly warmer water, so rises to the top of a lake and the ice begins to form there.
all other liquids, solidification on cooling begins at the bottom of the container. So, since water
behaves in this weird way, ice skating is possible!
Also, as a matter of fact, life in lakes is
possible—the ice layer that forms insulates the rest of the lake water from very cold air, so fish
can make it through the winter.
The coefficient of linear expansion
of a given material, for example a bar of copper, at a given
temperature is defined as the fractional increase in length that takes place on heating through one
might vary with temperature (it does for water, as we just mentioned) but in fact
for most materials it stays close to constant over wide temperature ranges.
17 10 .
liquids and gases
, the natural measure of expansion is the coefficient of volume
Of course, on heating a bar of copper, clearly the
as well as the
expands by an equal fraction in all directions (this could be experimentally verified, or you could
just imagine a cube of copper, in which case all directions look the same).
The volume of a cube of copper of side
Suppose we heat it through one degree.
Putting together the definitions of