   ## The measurement of the thermal conductivity of a good conductor

The method uses an apparatus called Searle's bar, shown in the following diagram. A specimen of the material in the form of a bar, polished on the outside to reduce radiation losses, is heavily lagged and placed in a wooden box. The length of the bar is large compared with its diameter so that a measurable temperature gradient can be produced. A heating coil wrapped round one end provides a heat input at a constant rate and the heat is removed at the other end by water flowing slowly through a copper tube which is soldered round the bar at the other end. The temperature gradient is measured by thermometers placed in holes in the bar; these may be filled with mercury to increase thermal contact.

When steady state has been reached the incoming temperature (q3) and outgoing temperature (q4) of the water is recorded as is its rate of flow (m) in kgs-1. The cooling water must flow from a constant-head apparatus so that the rate of flow does not vary.

The diameter of the bar is measured at a number of different points using a pair of vernier calipers and a mean value found. From this the cross-sectional area (A) can be found. The value of k is found from the following equation:

Searles Bar equation:     Rate of flow of heat energy = DH/Dt = -kA(q1 - q2)/L = mcw(q4 - q3)

where q1 and q2 are the temperatures of the thermometers in the bar, L is their separation and cw is the specific heat capacity of the water.