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Lab 14: Thermal Conductivity
1994-2009, James J. DeHaven, Ph.D and 1997-1998, Sandra Ceraulo Ph.D.
Suppose you have a sheet of some sort of structural material, and you want to find the rate at which
heat is transferred from one surface to another. The process by means of which the heat moves through the
material is called conduction, and the rate at which it is transferred from one place to another is governed by
the so-called heat conduction equation:
[1]
ΔQ
Δt
( _
= κ A T1 T2 )
l
ΔQ/ΔT = rate of heat transferred (SI unit are watts)
T1 = temperature on the hot side of material
T2 = temperature on the cold side of material
l = thickness of insulator
A = cross sectional area over which the transfer takes place
κ = thermal conductivity of material (a constant for each substance)
Figure 1 (next page) shows a schematic drawing for heat conduction across a surface, and you
should consult it to get a good picture of the meaning of each of these variables.
In this lab, you will measure the thermal conductivity, κ , of five different insulators:
1) Glass
2) Wood (plywood)
3) Lexan (plexiglass)
4) Sheet Rock (wall board)
5) Masonite
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Substances for which the thermal conductivity is large conduct heat rapidly and are said to be good
conductors. Most metals fall into this category. Substances with the low values of κ such as down and
asbestos are called insulators and are poor conductors. On the basis of this lab, you should be able to
evaluate the suitability of these materials for construction from the perspective of their insulating properties.
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Method
The experimental setup for determining κ is show in figure 2. A steam generator is used to
provide a high temperature region inside a “steam chamber”. A piece of insulating material is placed on
top of the steam chamber, and a cylindrical block of ice is placed on the insulator. The rate at which the ice
melts tells us how fast heat is flowing across the insulator.
-2-
l
A=
a
f
r
u
S
ea
r
a
ce
T2
T1
ΔQ
ΔT
κ = thermal conductivity
coefficient
Figure 1: Schematic diagram of heat conduction across a slab of material.
-3Ice Block
Tared 200ml
Beaker for
Melted water
Wooden
Block
Insulator
Clamped off
Steam Hose
am er
e
t
S mb
a
Ch
Support
Stand
250ml Beaker for
condensed steam
Steam
Generator
Figure 2: Experiment Apparatus for determining the coefficient of thermal conductivity.
To find κ we must measure all the other quantities in equation [1]. Our principal efforts will be
aimed at finding the rate of heat transfer, ΔQ / Δt , for the heat that penetrates the insulator separating the
steam chamber from the ice. We find this by using the heat of fusion of water and by measuring the mass
of ice melted during a time Δt . The rate at which heat is absorbed by the block is easily calculated by:
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[2]
ΔQ
Δt
=
Δ Hfusion m water
Δt
-4However, even if no steam is applied, some of the ice will melt anyway due to the fact that room
temperature is warm enough to melt ice. We have to take this into account, and so, at the beginning of the
experiment we find
[3]
Δ Q ambient
Δ t ambient
=
Δ Hfusion m water, ambient
Δ t ambient
where mwater, ambient is the mass of ice melted without applying any steam. This ice melts in a measured
amount of time Δtambient , which we can measure.
We can then find the rate of heat transferred from the steam to the ice separately, by subtracting the
rate of heat transferred from the room (ambient conditions) from the combined rate subtracting the rate of
heat transfer,
which is what we measure when the steam is operating. To put this algebraically:
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[4]
( )
ΔQ
Δt
=
steam only
( )
ΔQ
Δt
_
steam + ambient
( )
ΔQ
Δt
where (ΔQ / Δt )steam+ ambient is what you measure when you measure the mass of ice melted after the
steam has been running at a stable temperature for a time Δt
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(ΔQ / Δt )ambient is what you measure with the steam turned off, prior to commencing the experiment with
€ the steam on.
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(ΔQ / Δt )steam only is what you use to calculate the thermal conductivity of the insulator.
In addition to this you will have to measure the other quantities in the heat conduction equation. You
will have to measure l, the thickness of the sample material. You can do this using either the ruler or calipers
provided.
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You will have to know T1 and T2. The low temperature will be the melting point of ice. The high
temperature will be the condensation point of steam. To obtain an accurate value for the condensation point
you will have to include the variation (if any) due to the deviation of the current atmospheric pressure from
1 atmosphere (760 torr). To do this, you will need to know the current barometric pressure. You can obtain
this from the barometer located in the lab. Near 100 degrees centigrade, each additional torr of atmospheric
pressure adds 0.037 degrees to the boiling point, and for every torr less than 760, the boiling point is
lowered by 0.037 degrees centigrade. In other words:
[5]
Boiling point = 100 ° C + (0.037 ° C/torr) • (Barometric pressure - 760torr)
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-5Finally, it will be necessary to measure the area. Normally you might be inclined to simply measure
the area of the insulator. But, in this experiment, we are only interested in the heat that is conducted to the
ice--consequently, the surface area will simply be equal to the area of the bottom of the cylinder of ice.
Since the block of ice may shrink as you proceed through an experiment, you will need to use an
“average” area. To do this, you will need to measure the diameter of the ice before and after each
experiment.
A = Surface area
of ice
T2
l
T1
A
Inside Steam Chamber
Figure 3 : side and bottom view of ice cylinder. Note that the cross sectional area of the ice, not the
area of the insulator, governs the rate of heat transfer fro the steam chamber to the ice.
Procedure
Set up the apparatus as shown in figure 2 but clamp off the line to the steam chamber and leave the
other vent open. Make sure that the unused steam nozzle in the steam generator is clamped off. Make sure
to use boiling chips in the steam generator. Fill the generator about 3/4 full of water and turn the knob to
the highest setting. Again--do not open the line to the steam chamber until you have completed part 1
below.
Part 1. Determination of Heat Transfer Rate at Room Temp (ΔQ / Δt )ambient
1) Run the cylinder of ice under warm water to free the ice from the mold. With the glass insulator in place,
find (ΔQ / Δt )ambient by measuring the mass of water that melts and the time it takes it to melt (see
equation [3]). Steps 2-6 outline how to do this in greater€detail.
2) Measure and record l, the thickness of the sample material
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-63) Mount the glass sample material onto the steam chamber using the plates and thumb screws
4) Make sure that the material sample (insulator) is flush against the water channel so water will not leak. A
bit of vaseline put between the channel and the sample will create a good seal. Tighten the thumbscrews to
press the glass against the red rubber gasket. DO NOT OVER TIGHTEN!!
Do not remove the ice completely from the mold. Instead, allow it to slide out as the experiment proceeds.
You only need to be sure that the ice is capable of sliding freely out of the mold.
5) Let the ice sit for several minutes until it begins to melt and comes in full contact with the sample
material. The ice may be at a temperature lower than zero degrees. Since the ice may be rough on top at the
beginning of the experiment give it a chance to melt so that the entire top surface area rests against the
glass.
During a phase change, the temperature remains constant. For example, during the melting of the ice,
the temperature remains at zero degrees C.
During the waiting period, you may determine the mass in kg of the 200 ml tall-form beaker used to collect
the melted ice and record it.
6) To determine the rate of melting due to room temperature, do the following:
a) If you have not already done so, determine the mass in kg of the 200 ml tall-form beaker used to
collect the melted ice and record it.
b) Collect the meting ice in the beaker for a measured amount of time (approximately 10 minutes).
Determine the precise time interval by measuring it with a stopwatch. This is Δtambient
c) Determine the combined mass (in kg) of the beaker and melted ice after the time tambient
d) Subtract the mass in 6a from the mass in step 6c to determine
€ the mass of the melted ice at
ambient temperature.
You now have all the information needed to determine the heat absorbed by the ice at ambient (room)
temperature.
Part II. Calculation of Heat Transfer ΔQ / Δt of Steam plus Ambient Temp
7) Make sure the steam generator is connected and that the small piece of tubing is clamped off, and that
the tubing leading from the generator to the steam chamber is NOT clamped. Place a container under the
drainer spout of the steam chamber
€ to collect condensed steam that escapes from the chamber.
8) Run steam into the steam chamber. Let the steam run for a few minutes until the temperature stabilizes.
Then the heat flow will be steady.
9) Measure the diameter of the ice block. Record the value as dbefore
10) Empty the cup used to collect the melted ice. Repeat step 6 but this time with the steam running into the
steam chamber. Record the mass of the melted ice (remember to subtract the mass of the beaker) as before.
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-7Record the exact time Δt during which the ice melted while the steam was running. This quantity
corresponds to Δtsteam+ ambient
11) Measure€the diameter of the ice block, dafter . When calculating A, use the average of dbefore and
dafter€
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12) Repeat this procedure for the other materials provided, a total of 5 in all.
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Part III. Calculations
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This experiment is ideal for a spreadsheet because it contains many simple calculations involving several
measured quantities. Prepare an EXCEL spreadsheet showing your calculations (attach this to your lab
report). Below is a rough outline of the calculations that need to be done.
For each material:
1) Calculate ΔQ / Δt for the ambient temperature (equation 3). Be sure to take into account the mass of
water melted at room temperature in your calculations.
2) Calculate ΔQ / Δt for steam and ambient temperature (equation 2)
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3) Calculate ΔQ / Δt for steam only using equation 4
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Using the measured values for l, dbefore , dafter , T1 and T 2 , in your spreadsheet, calculate κ using
equation 1. Remember to use the average diameter of the ice to calculate its cross sectional area, A.
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5) Write up your lab using the usual report format.
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Report:
Introduction: Write a brief introduction stating the objectives of the experiment, and a concise summary of
the methods that will be used.
Experimental: Describe the experimental apparatus and precisely what variables will be measured and how
they will be measured.
Results: Summarize the results of the experiment. Show sample calculations. If you are attaching computer
generated tables or graphs, briefly explain them here.
Discussion: Explain the significance of your results and their connection with more general physical
principles. Where it is possible, compare your numbers with accepted values. Explain any sources of error.