# Thermal Conductivity Meter: Lee’s Disc Method

## 1. Introduction to Lee’s Disc Method

Little is known of the origins of Lee and Charlton’s method of thermal conductivity determination, the earliest mention of their work was found to be in the Philosophical Magazine’s 41st Volume, 1896(1). This method, commonly known as Lee’s Disc method, is a simple and effective way to calculate the thermal conductivity of materials with low thermal conductivities. With the use of easy-to-find parts, anyone can assemble and operate a Lee’s disc apparatus with the goal of thermal conductivity calculation. Ultimately Lee’s Disc method will provide a better understanding of how to calculate thermal conductivity.

## 2.0 Background Information and Relevant equations

### 2.1 Background Information

In order to obtain accurate readings, the brass discs should be wrapped in a thermal insulator such as cotton, felt or plastic. Loss of heat by conduction and convection with the environment (air) can skew the results obtain thus using an insulating material where appropriate is important in order to obtain proper results using Lee’s Disc method.

### 2.2 Relevant equations and constants

Heat Flow Rate (Q) = k ⋅ A ⋅ (T1-T2) / d

• k = Thermal Conductivity in Watts/meter-Kelvin
• A = Area (m2)
• T1 and T2 = Temperatures in Kelvin
• d = Distance which the heat travels in meters
• Q = Heat Flow Rate in Watts

Cross-sectional Area = πD2 / 4 OR πr2

Rate of heat loss (Q) = m ⋅ c ⋅ (dT/dt)

• m = mass of a given sample in Kilograms
• c = specific heat of a given material in Joules/Kilogram-Kelvin
• (dT/dt) = Rate of cooling in °Kelvin/Second
• Q = rate of heat loss in Watts

Specific heat capacity of Brass: 377 Joules/Kilogram-Kelvin

Steady-State = Heat entering the system is the same as the heat exiting the system OR no change in temperature (by more than 0.5°C) for 10 minutes.

## 3.0 Materials, Experimental Set up and Procedure

### 3.1 Materials

Materials Required Price Location of Purchase
Brass disc (2’’ by 0.5’’ = 50mm by 13mm) x 2 20$x 2 = 40$ Speedymetals.com
Lab Stands 11$Amazon Vernier Caliper 10$ Amazon
Steam Generator 100-110$or maker your own Amazon Steam Chamber Make your own OR any Can made of a metal with high thermal conductivity* Ring Clamp (minimum 2’’ = 50 mm) 10$ Fisher Scientific
Cord (32’’-4’ = 820 – 1200mm) 100’ for 6$Amazon Balance 20$ Amazon
Thermometers x2 10$x2 = 20$ Amazon
Two Channel Thermocouples (optional) 30$Amazon Bolts x4 (bolt diameter smaller than ½ the width of the brass disc) Various prices as low as 0.6$ per Bolt Digi-Key
Insulating material (cotton, felt, plastic) 9$Amazon Thermal Grease 4$ Amazon

## Reference

• (1) Charles H. Lees, J. D. Chorlton; LIV. On a Simple apparatus for determining the thermal conductivity of cements and other substances used in the Arts; Philosophical Magazine; Vol 41; Issue 253, 1896.

## 6.0 Save a few dollars

For the more technological savvy, certain components of this experiment may be made at home. These components include the steam chamber, steam generator and two channel thermometer.

### 6.1 Steam chamber

In order to make a steam chamber all that is required is some metal cylinder with thin walls. The metal used should have a relatively high thermal conductivity (safe bets: Aluminum, Copper). The height of said cylinder should be shorter than the area available above the upper brass disc and should cover the cross-sectional area of the upper brass disc. Two holes must be made in either side of the cylinder (one of the steam inlet and one for the steam outlet).

### 6.2 Steam Generator

In order to make a steam generator all that is required is a hot plate, metal container full of water and an air tight lid with a hole large enough for tubing. It is important to note that the airtight seal will produce a closed system and pressure could build with faulty tubing. The tubing will be connected to the steam inlet hole in the steam chamber.

### 6.3 Two Channel Thermometer

Below is an appropriate design of a two channel thermometer capable of auto-recording the temperature.

The metal plates temperature signal from thermocouples could be read by ADC chips like ADS1248 or MCP3424, and then the digital value would be sent to a CPU like ARM cortex 0. Do remember the thermocouples need cold joint compensation, this could be completed by a thermistor or IC temperature sensor like DS18B20 at thermocouples’ cold joint. The CPU can record the temperatures along with time and then, display, store, or send the recorded data to a computer.