PC1142 Physics II
Thermal Conductivity
1
Purpose
• Demonstration that the rate of thermal conduction depends on the type of materials
• Determination of the value of the thermal conductivity k for several materials
• Comparison of the experimental values for k with the known values
2
Equipment
• Thermal conductivity apparatus: base and steam chamber with hardware for mounting
sample
• Steam generator
• Ice block with cover
• Laboratory balance
• Vernier caliper
• Thermometer
• Two containers
• Sample materials
3
Theory
Heat can be transferred from one point to another by three common methods: conduction,
convection and radiation. Each method can be analyzed and each yields its own specific mathematical relationship. In this experiment, we will investigate the rate of thermal conduction
through some common materials used in building construction.
The equation giving the amount of heat conducted through a material is:
∆Q =
kA∆T ∆t
h
In this equation, ∆Q is the total amount of heat conducted, A is the cross-sectional area
through which conduction takes place, ∆T is the temperature difference between the sides of
the material, ∆t is the time during which the conduction occurred and h is the thickness of
the material. The remaining term, k, is called the thermal conductivity of a given material.
Page 1 of 4
Thermal Conductivity
Page 2 of 4
The units for k depend upon the units used to measure the other quantities involved. The
importance of k lies in whether one wishes to conduct heat well (good conductor) or poorly
(good insulator). Therefore, the relative size of k is of importance to designers and builders,
and should be of importance to home owners.
Note further that choosing a material with a small value for k does not guarantee a wellinsulated structure. The amount of heat conducted out in winter (and therefore needed to be
replaced) depends also upon three other factors: area, thickness and temperature difference.
The same holds true for heat conducted in during the summer.
The equation for determining the thermal conductivity k is then given by
k=
∆Q h
∆t A∆T
The technique for measuring thermal conductivity is straightforward. A slab of the material
to be tested is clamped between a steam chamber, which maintains a constant temperature
(boiling point of water), and a block of ice, which maintains another constant temperature (ice
point of water). A fixed temperature difference is thereby established between the surfaces of
the material. The amount of heat transferred across the material is measured by collecting
the water from the melting ice. The ice melts at a rate of 1 gram per 333 Joules of heat flow
(the latent heat of melting for ice).
The thermal conductivity, k, is therefore measured using the following equation:
k=
(mass of melted ice)(333 J/g)(thickness of material)
(area of ice)(time during which ice melted)(temperature difference)
where distances are measured in centimeters, masses in grams and time in seconds.
4
Experimental Procedure
Figure 1: Equipment Setup
PC1142 Physics II
Semester I, 2007/08
Thermal Conductivity
Page 3 of 4
1. Measure the thickness of the sample material at FIVE different positions along the
surface. Record your data as h in the Data Table 1.
2. Mount the sample material onto the steam chamber as shown in Figure 1.
Note: Take care that the sample material is flush against the water channel, so water
will not leak, then tighten the thumbscrews. A bit of grease between the channel and
the sample will help create a good seal.
3. Measure the diameter of the ice block at FIVE different positions across the surface.
Record your data as d1 in the Data Table 1.
4. Place the ice on top of the sample as shown in Figure 1. Do not remove the ice but
make sure that the ice can move freely in the mold. Just place the open end of the mold
against the sample and let the ice slide out as the experiment proceeds.
5. Let the ice sit for several minutes so it begins to melt and comes in full contact with
the sample. DO NOT begin taking data before the ice begins to melt because its
temperature has yet stabilized.
6. Determine the mass of small container used for collecting the melted ice and record it
as m0 in the Data Table 2.
7. Collect the melting ice in the container for a measured time (approximately 10 minutes).
Record this value as t1 in the Data Table 2.
8. Determine the mass of the container plus water and record it as m1 in the Data Table 2.
9. Determine the temperature of the ice block and record it as T1 in the Data Table 2.
10. Run steam into the steam chamber. Let the steam run for several minutes until temperatures stabilize so that the heat flow is steady. Place a container under the drain spout
of the steam chamber to collect the water that escapes from the chamber.
11. Empty the container used for collecting the melted ice.
12. Collect the melting ice in the container (with the steam running) for a measured time
(5–10 minutes). Record this value as t2 in the Data Table 2.
13. Determine the mass of the container plus water and record it as m2 in the Data Table 2.
14. Determine the temperature of the steam and record it as T2 in the Data Table 2.
15. Remeasure the diameter of the ice block at FIVE different positions across the surface.
Record your data as d2 in the Data Table 1.
16. Repeat the procedures for another sample material. Record your data in the corresponding Data Table 3 and 4 respectively.
PC1142 Physics II
Semester I, 2007/08
Thermal Conductivity
5
Page 4 of 4
Data Analysis
D1. Enter your data in the Data Table 1 and 3 into the spreadsheet. Calculate the means,
standard deviations and standard errors of the thickness of the sample h and diameters
of the ice block (d1 and d2 ) in the spreadsheet.
D2. Determine the area A over which the heat flow between the ice and the steam chamber
took place. Assume that A is just the area of the ice in contact with the sample material.
Hint: The area A can be determined from the average diameter of the ice during the
experiment, i.e. davg = (d1 + d2 )/2.
D3. Calculate the rate R (mass per unit time) at which the ice melted before and after the
steam was turned on. Note that this rate R is the rate at which the ice melted due to
the temperature difference only.
D4. Estimate the conductivity of the sample k and its corresponding uncertainty. The
conductivity of the sample is given by
k=
Rh
A∆T
Hint: ONLY the uncertainties of the measurements on the thickness of the sample
material and the diameters of the ice block are significant. The uncertainties of the rest
of the measurements are negligible in this experiment.
D5. Obtain the accepted values for the thermal conductivities of the sample material used
from your laboratory demonstrator. Calculate the percentage discrepancy for each experimental value of the thermal conductivity k compared to the known value.
Hint: The percentage discrepancy is defined as
Percentage discrepancy =
PC1142 Physics II
|Experimental value − Known value|
× 100%
Known value
Semester I, 2007/08