Experiment 14: Thermal conductivity
(Loosely translated from the text by Jukka Vaari)
Introduction
The amount of heat transported through a plate is determined by the material properties and the thermal
gradient. The equation for this is
where dQ/dt is the amount of heat per unit time, λ is the thermal conductivity of the plate, A is the area, l is
the plate thickness and dT is the temperature difference. The units of thermal conductivity are W/m/K.
Measurement of a materials thermal conductivity may be accomplished by measuring the amount of heat
which passes through a material with a known temperature gradient. In this experiment, the thermal
gradient is determined by exposing opposite sides of a plate to ice (0°C) and to steam (100°C). The amount
of heat is known from the quantity of ice which melts in a measured amount of time through the heat of
fusion.
A common method for investigating thermal conductivity consists of
stacking different materials together, as shown in Figure 1. The thermal
conductivity through each layer is
dQ
dt
λi
A(Ti
Ti −1 )
li
,i
1...N
where li and λi are the thickness and the thermal conductivity of each
plate, and Ti is the temperature at each junction. The important thing to
note is that, although the temperature each junction is unknown, the
heat conducted through all layers is the same. This allows us to write an
equation for the heat conductivity through the entire structure as
dQ
dt
λtot
A( Ttot )
l tot
L1, λ1
L2, λ2
L3, λ3
:
LN, λN
T0
T1
T2
T3
tot
=
N
i=1
If the LOW WATER light comes on during a measurement, stop the timer and remove the piece of ice from
the steam box so that it does not melt uselessly. Turn off the steam generator and wait until the amount of
steam has slowed. carefully remove the top and refill the steam generator to 3/4 full then turn it back on and
wait until the steam is again coming continuously from the steam box. Replace the ice on the plate, and
resume timing.
For your report:
TN
where ΔTtot is the temperature difference across the entire stack , ltot is
the total thickness of the stack, and λtot is the effective thermal
conductivity of the stack. This may be calculated by using the known thickness of each layer to solve for an
unknown thermal conductivity using the relationship
l tot
6.
Place the plate to be investigated on the steam box using the clamping screws. Set the steam
generator current and voltage to maximum.
7.
Wait until the steam is coming from the drain on the steam box at a steady rate. The steam column
should spray 10-20 cm.
8.
Measure the diameter of the ice.
9.
Place the piece of ice in its container on the plate on the steam box. The hole at the bottom of the
ice container should point down to run-off channel.
10.
Wait until the ice is melting steadily so that the water is flowing continuously. Before you begin
the first measurement, wait until the surface roughness of the ice has melted away.
11.
When you are ready to begin the measurement, empty the container below the steam box run-off
channel and start the stopwatch.
12.
Collect the water from the melting ice at the run-off channel. Collect approximately 50 ml of water
and stop timing. Depending on the plate, this can take 2-15 minutes.
13.
As soon as the measurement is complete, put the ice container aside until you are ready to make
the next measurement. Turn off the voltage and current to the steam generator.
14.
Weigh the amount of water in the container. This is more accurate than using the gauge marks on
the beakers.
To change the disk:
15.
Turn off power to the steam generator and wait until there is no longer any water coming from the
steam box drain. Again fill the steam generator so that it is 3/4 full. Install the next plate and turn the steam
generator back on to full power.
li
i
The system of plates is analogous to a series of resistors, each with a thermal resistance of Ri=li/λi.
Experiment
The experimental apparatus is shown in the Finnish laboratory directions. Ask the assistant for
clarifications before getting started.
1.
Ask the assistant for ice, micrometers, and a stopwatch. You will also need Vernier calipers and a
ruler.
2.
Loosen the ice from the container WITHOUT BREAKING IT. Try using water.
3.
Make sure that the steam generator is at least 3/4 full.
4.
Connect the hose between the steam generator and the steam box. Put a container beneath the
drain hole in the steam box., and a second container beneath the runoff channel. Use paper towels to
minimize the amount of water splashed from the drain-hole.
5.
Measure the thickness of the individual glass plates and of the plate assemblies.
Calculate the thermal conductivity of the glass plates. In this assignment, special glass is used so that it can
withstand the thermal gradient experienced during the test. In this respect, the thermal conductivity is
clearly superior to ordinary glass.
Calculate the error associated with the measured value of the thermal conductivity. Also, using the thermal
conductivity of the individual plates, determine the thermal conductivity of the air gap in the multi-layer
plate. Can this result be generalized and applied to the air-gap of 4 cm typical of household windows? (hint:
the thermal conductivity of a series of plates can be determined in the same manner as the electrical
conductivity of a series of resistors).
Question (optional)
Using the thermal conductivity of the plates and of the air gap, calculate the thermal conductivity of a
window assuming 5 mm glass thickness and the same 4 cm air gap. How much heat is lost if the
temperature difference is 40°C. Assume the window area is 1 m2.