along a line. Their expansion is measured as a
fraction of their initial length.
In Equation 1, you see the equation for linear expansion. The change in length equals
the initial length, times a constant Į (Greek letter alpha), times the change in
temperature. The constant Į is called the coefficient of linear expansion and depends
on the material. A table of coefficients of linear expansion for some materials is shown
above. These coefficients are valid for temperatures around 25°C.
Differing coefficients of linear expansion can be taken advantage of to build useful
mechanisms. A bimetallic strip, shown to the right, consists of two metals with different
coefficients of linear expansion. As the strip increases in temperature, the two materials
expand at different rates, causing the strip to bend. Since the amount of bending is a
function of the temperature, such a strip can be used in a thermometer to indicate
temperature. It can also be used as a thermostat to control appliances, such as coffee
pots and toasters. In these appliances, the bending of the strip interrupts a circuit and
turns off the power when the appliance has reached a specified temperature.
Significant changes in temperature cause fairly minor changes in length. For instance,
in Example 1, we calculate the expansion of a 0.50 meter copper rod when its
temperature is increased 80 C°. The increase in length is just 6.6×10í^4 meters, less
than a millimeter.
Some materials, like carbon fiber, have negative coefficients of expansion, which
means they shrink when their temperature increases. By blending materials with both
positive and negative coefficients, engineers design systems that change shape very
little with changes in temperature. The Boeing Company pioneered the use of negative
coefficient materials in airplanes and satellites.
Thermal expansion: linear
Measured along one dimension
Constant Į depends on materialRods of same material
Expansion proportional to initial length