Measurement of thermal conductivity of a poor conductor by Lee's Disk method.

Object

Measure the thermal conductivity of glass.

SAFETY WARNING

This experiment uses steam heating. Be careful to avoid touching the hot surfaces of the steam generator, plastic tubing and the Lee's disk apparatus. Make sure that the steam outlet tube from the apparatus goes to a sink.

Apparatus

Lee's Disk apparatus, thermometers T1 and T2, steam generator, disk shaped poor conductor (glass), gloves, ruler, Vernier callipers.

Figure 1

Introduction

Assuming that the heat losses to the from sides of the sample are negligible, the steady state rate of heat transfer (H) by conduction is given by: Equation 1

where the k is the thermal conductivity of the sample, A is the cross sectional area and is the temperature difference across the sample thickness x (see figure 1).

As the sample is an insulator, lagging at the sides will not significantly reduce the energy losses. Therefore to keep these losses small the sample is a thin disk with a large cross sectional area compared to the area exposed at the edge . Keeping A large and x small produces a large rate of energy transfer across the sample. Keeping x small also means that the apparatus reaches a steady state (when temperatures T1 and T2 are constant) more quickly.

Figure 2

The thin sample is sandwiched between the brass disk and brass base of the steam chest (see figure 2). The temperature of the brass base (measured by thermometer T2) is very close to the temperature of the top surface of the glass disk because the thermal conductivity of brass is about one hundred times that of glass. Similarly the temperature of the brass disk (measured by T1) is very close to the temperature of the lower glass surface. In this way the temperature difference across such a thin sample can be accurately measured.

Figure 3

When the apparatus is in a steady state (temperatures T1 and T2 constant), the rate of heat conduction into the brass disk must be equal to the rate of heat loss due to cooling (by air convection) from the bottom of the brass disk. The rate of heat loss can be determined by measuring how fast the brass disk cools at the previous (steady state) temperature T1 (with the top of the brass disk covered with insulation, see figure 3). If the disk cools down at a rate then the rate of heat loss is given by: Equation 2

where m is the mass of the brass disk and c is the specific heat capacity of brass.

Experimental Procedure

1. Assemble the Lee's Disk apparatus (see figure 2).
2. Pass steam through the steam chamber
3. When a steady state is reached (temperatures T1 and T2 change by less than 0.5 Celsius in 1 minute) make a note of T1 and T2.
4. Heat the brass disk directly with the steam chamber. Hold the steam chamber using gloves and carefully remove the glass disk (using gloves).

Figure 4

1. When the temperature of the brass disk is steady (T1 about 96 Celsius and changes by less than 0.5 Celsius in 1 minute) remove the steam chamber and place an insulator on top of the brass disk. Make a note of the temperature of the disk every 30 seconds until the temperature is 5 Celsius below the previous (steady state) value of T1.
2. Plot the cooling curve and determine the slope at temperature T1 (see figure 4). Hence determine H using equation 2 and using m = 1.49 kg and c = 370 J Kg-1 C-1.
3. Measure the diameter (d) and thickness (x) of the glass disk using a ruler and Vernier callipers respectively. Hence calculate the cross sectional area .
4. Use your values of H, A, T2 - T1 and x in equation 1 to calculate k.
5. Calculate the absolute error (Dk) in k. The maximum relative error in k can be estimated using the following equation (errors in m and c can be neglected): Equation 3