,When an object is heated, the constants which characterize it typically change. The elastic constants of a solid material generally become less stiff, and the magnetic and electric polarizabilities generally become smaller. Some materials, called pyroelectrics, develop a polarization when heated.
Curie Law for Paramagnets
The most easily quantified and measured case of temperature dependence is magnetic polarizability. It is traditionally expressed in terms of the magnetic susceptibility,
,
and we will limit ourselves to the isotropic case. Experimentally, many paramagnets have susceptibilities which obey the rule
where 
is measured in Kelvin degrees. This rule is obeyed over a wide range of temperatures, and is know as the Curie Law.
For some materials at low temperatures and high fields the behavior is more accurately described by the Curie-Weiss Law:
Where 
is called the Curie Temperature and represents the temperature below which the material spontaneously magnetizes.
A similar formula applies to some dielectric materials for the temperature dependence of 
in the relation
THERMAL EXPANSION
When an object is heated, it typically expands. The expansion is typically small, but can be significant. Cement sidewalks have joints every meter or so to allow the cement pavement to expand without cracking. Once again we limit ourselves to isotropic samples. There are two common descriptions of thermal expansion.
The description most useful for our work uses the fractional change in volume 
of the sample (the dilatation) for a volume under pressure 
:
where 
is the thermal expansion coefficient.
We can also represent the effect of thermal expansion in terms of the length of a sample. Using the fractional change in length for a uniaxial stressed sample (the strain):
where 
is the linear thermal expansion coefficient.
Finally we note that, for isotropic materials, temperature changes cause no shear distortions.
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