Measurement of the thermal conductivity of a poor
conductor
With a poor conductor the rate of flow of heat will be small and so a thin
specimen with a large cross-sectional area has to be used. The apparatus is known as Lee's
disc, and is shown in Figure 1.
The specimen rests on a brass base plate and a steam chest is placed
on top. Steam is passed through the chest and the temperature of the base plate and the base
of the steam chest is measured.
The
thermometers are set in good thermal conductors and therefore the temperatures that they
measure are effectively those of the faces of the specimen. Vaseline may be placed in the holes
to ensure even better contact.
When a steady state has been reached the temperatures
q1 and
q2 are recorded. The rate of loss of heat from the baseplate
being by radiation and convection, the baseplate is polished so that radiation losses are small
and Newton's law of cooling can be applied. We can assume that the heat lost from the sides of
the specimen itself is negligible.
The
rate of loss of heat from the base plate can be found as follows. The specimen is removed and
the base plate heated directly by the steam chest to nearly 100
oC. The steam chest
is then removed, the specimen replaced and a cooling curve plotted for the base plate and
specimen (Figure 2). The rate of cooling R at the temperature
q2 can be found by taking the gradient of the curve at that
point, and if the mass m and specific heat capacity C of the material of the base plate are
known, its rate of loss of heat can be found.
The thickness L and cross-sectional area A
of the specimen can be found using vernier calipers.
Hence k can be
calculated.
