Lee’s Disk – for the Measurement of the Thermal Conductivity of a Poor Conductor such as a Polymer

The sample used to measure the thermal conductivity using the Lee’s Disk method is in the form of a disk whose thickness, x,  is small relative to its diameter, D. This aspect ratio removes the need to lag the edge of the disk to reduce heat loss, since the cross-sectional area of the disk, , is large compared with the exposed area of the edge, . Using a thin sample also means that the system will reach thermal equilibrium more quickly.

Ignoring heat losses from the edge of the disk, the heat transfer, Q, across the thickness of the sample is given by :

               (1)

Figure 1

Method

The thin polymer sample is placed between two brass plates in conjunction with a heat source as in Figure 2 below.

Figure 2

Because of the very low thermal conductivity of the polymer compared with that of brass (approximately 3 orders of magnitude), the temperature of Brass Plate (1) can be assumed to be very close to that of one surface of the polymer sample. Similarly, the temperature of Brass Plate (2) can be assumed to approach that of the other surface of the sample. In this way the temperature difference across the sample, , can be measured.

At equilibrium, heat entering the Brass Plate (2) equals the rate of heat loss due to cooling. The heat loss can be determined by measuring the cooling rate at the equilibrium temperature T₁ (with the Brass Plate (2) covered with a pad of insulation as in Figure 3 below). If the disk cools at a rate of then the rate of heat loss is given by :

                      (2)

Where m is the mass of the brass plate and C_p is the heat capacity of brass.

Procedure

In a transparent box, to minimise convection currents, the Lee’s Disk apparatus is assembled as in Figure 2 and the heat source is switched on and the whole is left to equilibrate – depending on the material of the sample, make sure that Brass Plate (1) is thermostatically controlled at about 100°C ± 0.1°C.

At equilibrium – when the temperatures of the two plates, T₁ and T₂, each change by less than 0.5°C in one minute – record the two temperatures T₁ and T₂.

Carefully remove the Brass Plate (1) and the sample (using heat resistant gloves) and place the heat source directly onto  Brass Plate (2)

Heat the plate to about 110°C then remove the heat source and replace it with a pad of insulation as in Figure 3.

Record the temperature, T, of Brass Plate (2) every 30 seconds until it is about 5-10°C below that of the equilibrium temperature T₁.

Plot the cooling curve for the brass plate and determine the slope at the temperature T₁ as in Figure 4 below.

Weigh Brass Plate (2) and record its mass, m, and, using Equation (2) above, calculate Q  –  (the heat capacity, C_p, of brass can be taken as 0.38 kJ kg^-1 K^-1).

Measure the thickness and diameter of the polymer sample and calculate the cross-sectional area, A, of the sample disk.

Substitute these values along with into Equation (1) and calculate k.