Liquids, Solids, and Compressibility
Name: Jared K.
Date: Monday, September 30, 2002
How come, when most solids are more dense than liquids,
liquids are not compressible, but most solids are?
Both liquids and solids are compressible -- only slightly, but
compressible nonetheless. The compressibility of solids is generally smaller
(they resist deformation more, because compressibility is defined with an
explicit negative sign) than for liquids by ~ 3X. However, there is overlap
because other factors are also important.
The compressibility: K = -(dV/dP)/V
varies with temperature, pressure, and other variables, so it
is quite difficult to measure. The compressibility of solids, especially
single crystals, is even more complicated. Assume the atoms in a crystal
have coordinates (x,y,z). The crystal structure is often not isotropic, i.e.
the arrangement of atoms/molecules in the 'x', 'y', and 'z' directions is
not the same. So an increase in pressure in the 'x' direction results in a
DIFFERENT change in volume in the 'y' and 'z' directions. The same is true
for the other coordinates. So the compressibility now has NINE components --
Kij where both 'i' and 'j' can equal 'x', 'y', and 'z' -- i.e. components
Kxx, Kxy, Kyx,..., Kzz. The term Kxy, for example, measures how the
dimensional change in the 'y' direction if I squeeze in the 'x' direction.
For some crystals Kxy may not even equal Kyx!! Such nine component arrays
are called "tensors" and they have a whole "algebra" that governs their
Liquids are compressible. They just do not compress much compared to gases.
Richard E. Barrans Jr., Ph.D.
Director of Academic Programs
PG Research Foundation, Darien, Illinois
Click here to return to the General Topics Archives
Update: June 2012