SCHOOL OF PHYSICS

UNIVERSITI SAINS MALAYSIA

ZCT191/192 PHYSICS PRACTICAL I/II

1TS2 THERMOELECTRIC EFFECT AND
THERMAL CONDUCTIVITY
Lab Manual

OBJECTIVES

1. To investigate the relationship between electromotive force (EMF) and the thermocouple’s
temperatures within 0–100 °C;
2. To use a thermocouple as a thermometer and investigate the characteristic of a two-junction
thermocouple within 0–400 °C; and
3. To estimate the thermal conductivity of solid materials by measuring the thermal energy in
conduction.
ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

THEORY

Thermocouples
Thermocouples are temperature sensors made from two different metals. A voltage is generated
when these metals are brought together to form a junction, creating a temperature gradient
between them. This phenomenon was discovered in 1822 by Thomas Seebeck (German
physicist), where he took two different metals at different temperatures and made a series
circuit by joining them together. He found that this circuit generated an electromotive force
(EMF), and the larger the temperature differences between the metals, the higher the generated
voltage. His discovery is known as the Seebeck effect, and it is the basis of all thermocouples.

The voltage produced in the Seebeck effect is proportional to the temperature difference
between the two junctions at low temperatures. The proportionality constant 𝛼 is known as the
Seebeck coefficient, it can be found by finding the gradient when plotting the voltage against the
temperature (thus has the units of V K −1 ).

The Law of Intermediate Materials

The law of intermediate materials was originally known as the law of intermediate metals. This
law states that the sum of all the EMF in a thermocouple circuit using two or more different
metals is zero if the circuit is at the same temperature. This law is interpreted to mean that the
addition of different metals to a circuit will not affect the voltage the circuit creates, provided
they are at the same temperature as the junctions in the circuit. This means that a third metal
(e.g. a copper wire) may be added to the circuit to allow measurements to be taken. This allows
thermocouples to be used with digital multimeters, or be soldered to join the metals.

Figure 1: A setup of a Cu/Fe thermocouple.

Thermo EMF vs. Temperature

The thermo EMF in a thermocouple increases if the temperature of the hot junction is increased,
while the cold junction (usually kept at 0 °C) is kept constant. Consider a copper-iron (Cu/Fe)
thermocouple with the hot junction (P) placed in a hot water bath, while the cold junction (Q)
kept in ice (Figure 1). A deflection in the galvanometer (G) measures the thermo EMF, while
the thermometer measures the temperature 𝑇 of the water bath.

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

Figure 2: Graph of thermo EMF vs. temperature.

A graph of thermo EMF vs. the temperature in the hot junction is shown in Figure 2. From
the graph, it can be seen that as the temperature of the hot junction increases (keeping the cold
junction at a constant temperature of 0 °C), the thermo EMF increases to a maximum,
corresponding to a temperature known as the neutral temperature ( 𝑇n ). For a given
thermocouple, 𝑇n is fixed and independent of the temperature of the cold junction.

When the temperature is further increased beyond the neutral point, the thermo EMF
decreases to zero, corresponding to a temperature known as the inversion temperature (𝑇i ). Any
further heating will result in the thermo EMF being reversed (having negative values), since the
number densities and rates of diffusion of electrons in the two metals being reversed. 𝑇n , 𝑇i and
the temperature at the cold junction (𝑇c ) are related via the equation
𝑇n − 𝑇c = 𝑇i − 𝑇n , (1)
which gives 2𝑇n = 𝑇i + 𝑇c . Unlike the neutral temperature, the inversion temperature depends
on the temperature of the cold junction, in addition to the nature of the materials forming the
thermocouple.

As seen from Figure 2, the graph of the thermo EMF vs. temperature of the hot junction
is parabolic in nature, in contrast with the Seebeck relation at low temperatures, which is linear.
Thus a more accurate relationship between the thermo EMF (𝐸) and the temperature of the hot
junction (𝑇) is
1
𝐸 = 𝛼𝑇 + 𝛽𝑇 2 , (2)
2
where 𝛼 is just the Seebeck coefficient as seen before. Together, 𝛼 and 𝛽 are collectively known
as the thermoelectric constants.

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

Thermal Conductivity
Heat can be transferred from one place to another in three ways: conduction, convection and
radiation. Each method has its own experimental procedures to determine the thermal
conductivity of a material. In this experiment, the thermal conductivities for solid materials
commonly found in buildings are determined using PASCO’s thermal conductivity apparatus.

Thermal conductivity is a characteristic of a material. Heat (𝑄) flows through a material if

a temperature difference (temperature gradient, Δ𝑇) exist in that material, given by
𝛥𝑡
𝛥𝑄 = 𝑘𝐴𝛥𝑇 , (3)
ℎ
where Δ𝑄 is the heat energy conducted, 𝐴 the area through the conduction takes place, Δ𝑡 the
time when the conduction occurs, ℎ the thickness of the material, and 𝑘 the thermal conductivity
of the material. Rewriting Equation 3 in terms of 𝑘, we get
ℎ𝛥𝑄
𝑘= . (4)
𝐴𝛥𝑇𝛥𝑡
The value of 𝑘 determines whether the material is a good conductor or insulator.

The characteristics of thermal conductivity explained above assumes a semi-static

condition, i.e. the temperature gradient should be uniform or unchanged. If the temperature
starts to change, the values of the parameters will also change, and this makes the process of
determining the conductivity of a material very difficult. In this experiment, temperature
equilibrium is necessary to eliminate uncertainties, but it is hard to achieve.

However, the technique used to determine the thermal conductivity in this experiment is
simple. A material shaped as a plate is placed between a vapour container fixed at temperature
100 °C, and a block of ice at 0 °C. Thus, the steady temperature at 100 °C can be used as a
temperature in equilibrium state.

The amount of heat drained is measured by through the amount of water melted from the
ice. The rate at which the ice melts is 1 g per 80 cal (calories) of heat absorbed. This is the latent
heat of fusion for ice. Therefore, the value of 𝑘 (in units of cal cm−1 s −1 °C−1 ) can be determined
using the equation above, rewritten as
mass of melted ice × 80 cal g −1 × material thickness
𝑘= , (5)
ice area × 𝛥𝑇𝛥𝑡
where distances are measured in cm, mass in g, and time in s. The standard values of 𝑘 for some
materials are listed in Table 1 below.

Table 1: Thermal conductivity for some materials.

Material 𝟏𝟎−𝟒 𝐜𝐚𝐥 𝐜𝐦−𝟏 𝐬 −𝟏 °𝐂 −𝟏 𝐖 𝐦−𝟏 𝐊 −𝟏
Masonite 1.13 0.047
Pine wood 2.06 − 3.30 0.11 − 0.14
Lexan 4.60 0.19
Rock slab 10.30 0.43
Glass 17.20 − 20.60 0.72 − 0.86

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

EQUIPMENT

Parts A and B
1. Thermocouples: Cu/Cn, Cu/Fe and Cn/Fe
2. Potentiometer / voltmeter
3. Heater
4. Thermometer (0–100 °C)

Part C
1. Weighing machine
2. Petroleum gel (Vaseline)
3. Vernier calliper
4. Material sheets (Masonite, wood, Lexan, rock slab and glass)
5. Water container
6. Steam chamber (PASCO TD-8556)

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

PROCEDURE

Part A: The Characteristics of A Thermocouple at Low Temperature

Figure 3: EMF measurement of a Cu/Cn thermocouple.

Measurement
1. Connect the circuit as shown in Figure 3, using the Cu/Cn thermocouple.
2. Set the temperature of the cold junction in the beaker as 0 °C. The temperatures can be
varied between 0–100 °C by either adding ice into the beakers or switching on the heater.
3. Setting the same temperature (𝑇 = 0 °C) at the hot junction, obtain the thermocouple's
electromotive force (EMF, 𝐸) and record it in Table 2.
4. Repeat Steps 2-3 by increasing the temperature from 0 °C to 100 °C in steps of 10 °C. For
every measurement, observe and record whether the thermocouple's hot junction is
connected to the positive or negative terminal of the digital multimeter.*
5. Repeat Steps 2-4 (measurement of EMF) for all the remaining thermocouples (Cu/Fe and
Cn/Fe) provided.

*The EMF of the thermocouple is considered as positive if the potential of hot junction is positive compared to the
potential of cold junction. On the other hand, EMF of the thermocouple is considered as a negative if the potential of
hot junction is negative compared to the potential of cold junction.

Analysis
1. Plot the EMF vs. temperature for the three thermocouples on the same graph paper. The
sign of the EMF for each thermocouple must be shown clearly.
2. Calculate the Seebeck coefficients 𝛼Cu/Cn , 𝛼Cu/Fe and 𝛼Cn/Fe from the graphs and their
respective uncertainties.
3. Compare and find the percentage discrepancy between your experimental values and the
standard values as follows: 𝛼Cu/Cn = 40.87 µV °C−1 , 𝛼Cu/Fe = −13.89 µV °C−1 , and
𝛼Cn/Fe = −54.76 µV °C−1.
4. Verify the law of intermediate materials with the experimental data.

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

Table 2: EMF of Cu/Cn, Cu/Fe and Cn/Fe thermocouples as a function of temperature.

Cu/Cn Cu/Fe Cn/Fe
Voltage: + / – Voltage: + / – Voltage: + / –
Temperature EMF Temperature EMF Temperature EMF
(°C) (μV) (°C) (μV) (°C) (μV)

Part B: The Characteristics of A Thermocouple Between 0–400 °C

Figure 4: EMF measurement for the Cu/Fe thermocouple at temperatures up to 400 °C. The Cu/Cn
thermocouple is used as a thermometer.
Measurement
1. Connect the circuit as shown in Figure 4 (cold junction remains at 0 °C). When the heater
is switched on, the temperature will decrease at a rate of 5 °C per minute. Therefore, the
temperature (Cu/Cn thermocouple) and EMF (Cu/Fe thermocouple) must be recorded
quickly.
2. Read the EMF of the Cu/Cn thermocouple, then change the two-way switch immediately.
3. Read the EMF of the Cu/Fe thermocouple, then change the two-way switch immediately.
4. Read the EMF of the Cu/Cn thermocouple once again.
5. Obtain the average value of the EMF for Cu/Cn (Steps 2 and 4), then find the equivalent
temperature for that particular EMF from Table A1 in the APPENDIX.**
6. Record your readings in Table 3.
7. Repeat Steps 2-5 using different Cu/Cn temperatures, such that the change in EMF in the
Cu/Cn thermocouple is ~1 mV until you reach a reading of 𝑬𝐂𝐮/𝐂𝐧 ~21 mV (~400⸰C).

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

**Here we assume that in such a short time interval, the temperature increases linearly. The temperature of the Cu/Fe
thermocouple (𝑇2 ) is taken to be in between the initial and the final readings, so that we can approximate the average
Cu/Cn thermocouple temperature to be
𝑇1 + 𝑇3
𝑇avg = ≈ 𝑇2 .
2

Analysis
1. Plot the graph of Cu/Fe thermocouple EMF (𝐸) vs. temperature (𝑇).
2. From this graph, determine the neutral temperature (𝑇n ) and inversion temperature (𝑇i )
for the Cu/Fe thermocouple.
3. Compare and find the percentage discrepancies between the experimental values and the
standard values of 𝑇n = 285 °C and 𝑇i = 570°C.
4. From Cu/Fe thermocouple EMF (𝐸) vs. temperature (𝑇) graph, determine 𝑑𝐸/𝑑𝑇 for each
point, and record them down in Table 4. Make an assumption that 𝑑𝐸/𝑑𝑇 ≈ Δ𝐸/Δ𝑇,
where Δ𝐸 is a small change in 𝐸 over a certain range of Δ𝑇 (such as +25 °C and -25 °C
from each point).
5. Plot the graph of 𝑑𝐸/𝑑𝑇 vs. 𝑇, and find the values of 𝛼, 𝛽 and 𝑇n from it.
6. From your graph of 𝐸 vs. 𝑇, calculate 𝐸/𝑡 for some values of 𝑇 (in steps of ~25 °C) and
tabulate the values in Table 5.
7. Plot the graph of 𝐸/𝑇 vs. 𝑇, and identify the values of 𝛼, 𝛽 and 𝑇n from the graph.
1
8. Verify if 𝑇i = 2𝑇n , and if the equation 𝐸 = 𝛼𝑇 + 2 𝛽𝑇 2 is suitable to explain thermoelectric
effects of the Cu/Fe thermocouple in the temperature range of 0–400 °C.

Table 3: EMF (𝐸) of the Cu/Fe thermocouple as a function of temperature (𝑇).

EMF of Cu/Cn, Corresponding EMF of Cu/Fe,
𝑬𝐂𝐮/𝐂𝐧 (μV) Temperature 𝑬 (μV)
(𝑻, °C)

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

Table 4: 𝑑𝐸/𝑑𝑇 as a function of 𝑇.

𝚫𝑬
Temperature, (μV) 𝒅𝑬 𝚫𝑬
T 𝚫𝑻 𝑬 (𝑻 + 𝟐𝟓) 𝑬 (𝑻 − 𝟐𝟓) 𝚫𝑬 ≈
𝒅𝑻 𝚫𝑻
(°𝐂) (°C) (𝛍𝐕 °𝐂 −𝟏 )
25 50
50 50
75 50
100 50
125 50
150 50
175 50
200 50
225 50
250 50
275 50
300 50
325 50
350 50
375 50
400 50

Table 5: Values of 𝐸/𝑇 for their corresponding temperatures 𝑇.

Temperature, EMF,
𝑬/𝑻 (𝛍𝐕 °𝐂 −𝟏 )
𝑻 (°𝐂) 𝑬 (μV)

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

Part C: Thermal Conductivity Measurements for Solid Materials

Figure 5: Experimental setup for Part C.

Measurement
1. Fill the plastic cup with water and place it inside the freezer (with the cover open).
2. Once the water is frozen, wash the cup slightly to loosen the ice inside the cup (do not take
the ice out of the cup yet).
3. Measure and record the thickness ℎ of the Masonite (wood fibre board) in Table 6.
4. Place the Masonite onto the steam chamber as shown in Figure 5. Apply gel to the area
between the sample and the surface of the container before tightening the thumbscrews
to prevent leakage of water later.
5. Measure and record the diameter of the ice block as 𝑑1 .
6. Without removing from the cup, put the ice block onto the Masonite as shown in Figure
5. Make sure the ice is in direct contact with the sample.
7. Leave the ice on the Masonite for 1–2 minutes until the ice starts to melt and water begins
to drip out. Do not start collecting data before the ice melt!
8. Follow the instructions below when collecting data from the ice and water:
a) Determine the mass of the container used to collect the water that drips from the
melting ice.
b) Determine the time taken to collect a specified amount of water, 𝑡a . (~10 minutes).
c) Weigh the container together with the water collected and record the reading.
d) Subtract the mass of the empty container from the value to determine the mass of
the collected water (𝑚ws ).
9. Switch on the steam chamber. Let the steam out for a few minutes until its temperature is
stable (place a container at the spot where the water drips).
10. Empty the container used to collect water from the melted ice.
11. Repeat Step 7 to obtain readings when steam from the steam chamber is used.
12. Measure and record the weight of the water dripping from melting ice as 𝑚w , and the time
taken, 𝑡 (5-10 minutes).
13. Measure the diameter of the ice block again and record it as 𝑑2 .
14. Repeat the experiment by replacing Masonite with wood, Lexan, rock and glass.

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

Analysis
1. Take the average of 𝑑1 and 𝑑2 to obtain 𝑑avg , the mean diameter for the ice block during
the experiment.
2. Use 𝑑avg to determine the value of 𝐴, the area where the heat moves between the ice and
vapour container. (the area where the surface of the block is in contact with the surface
of the sample).
3. Calculate 𝑅a = 𝑚wa /𝑡a and 𝑅 = 𝑚w /𝑡, which are the rates of ice melting before and after
the steam is used, respectively.
4. Calculate 𝑅0 = 𝑅 − 𝑅a, which is the rate of the ice melting in the experiment.
5. Calculate 𝑘, the conductivity of the sample (in cal cm−1 s−1 °C−1):
𝑅0 ℎ × 80 cal g −1
𝑘= .
𝐴Δ𝑇
Take Δ𝑇 to be the boiling point of water at 1 atmospheric pressure.

Table 6: Data for Part C.

Material 𝒉 𝒅𝟏 𝒅𝟐 𝒕𝐚 𝒎𝐰𝐚 𝒕 𝒎𝐰 𝒅𝐚𝐯𝐠 𝑨 𝑹𝐚 𝑹 𝑹𝟎
Masonite
Wood
Lexan
Rock
Grass

REFERENCES

1. Lewis, K. (2017). Thermocouple Laws. Retrieved 4 Aug 2021 from sciencing.com.

2. Northwestern University (n. d.). Brief History of Thermoelectrics. Retrieved 4 Aug 2021
from thermoelectrics.matsci.northestern.edu.
3. Quest Tutorials (n. d.). Thermoelectric Effect of Current. Retrieved 4 Aug 2021 from
questtutorials.com.
4. Study.com (n. d.). What is Neutral Temperature? Retrieved 4 Aug 2021 from study.com.
5. PASCO (1987). Instruction Manual for the Thermal Conductivity Apparatus (TD-8561).

ACKNOWLEDGEMENT

This lab manual was originally created by T. S. T., K. W. K., L. B. S., L. S. H. and Emeritus Prof. Dr.
Lim Koon Ong in 1996, translated by A. Prof. Quah Ching Kheng and I. M. in 2009. This manual
was revamped and standardised by Dr. John Soo Yue Han in 2021.

Last Updated: 04 April 2022 (JSYH)

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

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ZCT191/192 Physics Practical I/II 1TS2 Thermoelectric Effect and Thermal Conductivity

APPENDIX

Table A1 : Thermoelectric voltage (mV) for Cu/Cn thermocouple hot junction at temperature 0–400 °C,
reference junction at 0 °C.
Temperature
0 1 2 3 4 5 6 7 8 9
(°C)
0 0.000 0.039 0.078 0.117 0.156 0.195 0.234 0.273 0.312 0.352
10 0.391 0.431 0.470 0.510 0.549 0.589 0.629 0.669 0.709 0.749
20 0.790 0.830 0.870 0.911 0.951 0.992 1.033 1.074 1.114 1.155
30 1.196 1.238 1.279 1.320 1.362 1.403 1.445 1.486 1.528 1.570
40 1.612 1.654 1.696 1.738 1.780 1.823 1.865 1.908 1.950 1.993
50 2.036 2.079 2.122 2.165 2.208 2.251 2.294 2.338 2.381 2.425
60 2.468 2.512 2.556 2.600 2.643 2.687 2.732 2.776 2.820 2.864
70 2.909 2.953 2.998 3.043 3.087 3.132 3.177 3.222 3.267 3.312
80 3.358 3.403 3.448 3.494 3.539 3.585 3.631 3.677 3.722 3.768
90 3.814 3.860 3.907 3.953 3.999 4.046 4.092 4.138 4.185 4.232
100 4.279 4.325 4.372 4.419 4.466 4.513 4.561 4.608 4.655 4.702
110 4.750 4.798 4.845 4.893 4.941 4.988 5.036 5.084 5.132 5.180
120 5.228 5.277 5.325 5.373 5.422 5.470 5.519 5.567 5.616 5.665
130 5.714 5.763 5.812 5.861 5.910 5.959 6.008 6.057 6.107 6.156
140 6.206 6.255 6.305 6.355 6.404 6.454 6.504 6.554 6.604 6.654
150 6.704 6.754 6.805 6.855 6.905 6.956 7.006 7.057 7.107 7.158
160 7.209 7.260 7.310 7.361 7.412 7.463 7.515 7.566 7.617 7.668
170 7.720 7.771 7.823 7.874 7.926 7.977 8.029 8.081 8.133 8.185
180 8.237 8.289 8.341 8.393 8.445 8.497 8.550 8.602 8.654 8.707
190 8.759 8.812 8.865 8.917 8.970 9.023 9.076 9.129 9.182 9.235
200 9.288 9.341 9.395 9.448 9.501 9.555 9.608 9.662 9.715 9.769
210 9.822 9.876 9.930 9.984 10.038 10.092 10.146 10.200 10.254 10.308
220 10.362 10.417 10.471 10.525 10.580 10.634 10.689 10.743 10.798 10.853
230 10.907 10.962 11.017 11.072 11.127 11.182 11.237 11.292 11.347 11.403
240 11.458 11.513 11.569 11.624 11.680 11.735 11.791 11.846 11.902 11.958
250 12.013 12.069 12.125 12.181 12.237 12.292 12.349 12.405 12.461 12.518
260 12.574 12.630 12.687 12.743 12.799 12.856 12.912 12.969 13.026 13.082
270 13.139 13.196 13.253 13.310 13.366 13.423 13.480 13.537 13.595 13.652
280 13.709 13.766 13.823 13.881 13.938 13.995 14.053 14.110 14.168 14.226
290 14.283 14.341 14.399 14.456 14.514 14.572 14.630 14.688 14.746 14.804
300 14.862 14.920 14.978 15.036 15.095 15.153 15.211 15.270 15.328 15.386
310 15.445 15.503 15.562 15.621 15.679 15.738 15.797 15.856 15.914 15.973
320 16.032 16.091 16.150 16.209 16.268 16.327 16.387 16.446 16.505 16.564
330 16.624 16.683 16.742 16.802 16.861 16.921 16.980 17.040 17.100 17.159
340 17.219 17.279 17.339 17.399 17.458 17.518 17.578 17.638 17.698 17.759
350 17.819 17.879 17.939 17.999 18.060 18.120 18.180 18.241 18.301 18.362
360 18.422 18.483 18.543 18.604 18.665 18.725 18.786 18.847 18.908 18.969
370 19.030 19.091 19.152 19.213 19.274 19.335 19.396 19.457 19.518 19.579
380 19.641 19.702 19.763 19.825 20.886 20.947 20.009 20.070 20.132 20.193
390 20.255 20.317 20.378 20.440 20.502 20.563 20.625 20.687 20.748 20.810
400 20.872

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