Download preview - SOL*R

PHYSICS COURSE NAME
LAB 11
THERMOCOUPLES
Lab format: This lab is performed with a lab kit.
Relationship to theory: This lab corresponds to the study of the thermocouple effect, linear regression /
least squares fitting and Newton’s Law of Cooling.
OBJECTIVES
To construct thermocouple junctions
To perform temperature measurements using thermocouples
To apply least squares fitting to data obtained
To observe Newton’s Law of Cooling
EQUIPMENT/SUPPLY LIST








Copper/constantan wire (approx. 6 m) – to be supplied in lab kit
Cable ties – to be supplied in lab kit (or use alternatives such as rubber bands or electrical tape)
Solder – to be supplied in lab kit
Soldering iron
Wire cutter/stripper
Multimeter
Ice water
Boilng water
INTRODUCTION
Thermocouples:
When two dissimilar metals are connected together so that a wire made of one metal is
attached at each end to a wire made of the other metal (see Fig. 3), there is a resulting voltage
difference across the ends that depends linearly on the temperature difference between the two
junctions (and types of metals used). This is called a thermocouple. The thermocouple can be used to
measure temperature differences and if the temperature at one junction is well determined, the
thermocouple can be used to measure the temperature at the second junction.
Newton’s Law of Cooling:
Newton’s Law of Cooling is a differential equation whose solution describes the temperature of
an object as a function of time. It is also expressed as the rate of conductive heat transfer in thermal
physics (see, for example, Urone et al., ch.14). This law states that if the difference T = Tobj - Tsur
Creative Commons Attribution 3.0 Unported License
1
PHYSICS COURSE NAME
LAB 11
between the temperature of an object Tobj and the temperature of its surroundings Tsur is not too great,
the time rate of change of T is proportional to T itself. In equation form, this is statement looks like
𝑑
(∆𝑇)
𝑑𝑡
= −𝐴 ∆𝑇
where A is a constant.
[1]
The solution to this differential equation has the form
∆𝑇(𝑡) = ∆𝑇𝑜 𝑒 −𝐴𝑡
where To is the value of T at t = 0.
[2]
Thus T decreases exponentially toward zero, or we can say that Tobj approaches Tsur asymptotically.
Physically, we can expect rapid cooling initially, but as the object cools down, the rate of cooling
becomes very slow.
From a measurement point of view, because the thermocouple is a device that measures temperature
differences (i.e. T rather than Tobj ), it is well suited for observing Newton’s Law of Cooling.
Further, we could determine the coefficient A in Equation [2] using linear regression – however,
Equation [2] is not linear. Equation [2] can be linearised by taking the logarithm of both sides, such that
it becomes
𝑙𝑛 ∆𝑇(𝑡) = −𝐴𝑡 + 𝑙𝑛∆𝑇𝑜
[2A]
From a data analysis point of view, Equation [2A] is an equation of a straight line with slope –A. We can
graph the data points and use least squares fitting [Bevington and Robinson 2003] on ln T vs. t to
determine A.
WARNINGS

Be careful of boiling hot water: burn hazard
PROCEDURE
Part I:



Constructing a simple thermocouple
Using an appropriate tool, cut one piece of constantan wire, approximately 40 cm long.
Using an appropriate tool, cut two pieces of copper wire, each approximately 40 cm long.
Using an appropriate tool, strip the insulation from the both ends of all three pieces of wire.
Ideally, about 1.5 cm of metal should be exposed at each end. (See Figure 1)
Creative Commons Attribution 3.0 Unported License
2
PHYSICS COURSE NAME
LAB 11
Figure 1 – Stripped wires


Figure 2 – Soldered wire connection
Connect one of the copper wires to the constantan wire by twisting the ends together. (See
Figure 2. This will be referred to as a junction.) Ensure a lasting good connection by soldering
this connection (see Appendix 6 about soldering.)
Make another junction at the other end of the constantan wire by twisting and soldering the
second copper wire to it. You have now constructed a thermocouple. (See Figure 3)
Figure 3 – Thermocouple constructed

Connect the two loose copper wire ends to the voltage inputs of the multimeter. Set the
multimeter to read DC voltages at its most sensitive setting. The meter should read very nearly
zero volts. You are now ready to test the thermocouple. (See Figure 4)
Creative Commons Attribution 3.0 Unported License
3
PHYSICS COURSE NAME
LAB 11
Figure 4 – Thermocouple ready for testing



You can go straight to the most extreme reading your thermocouple will give by immersing one
junction in boiling hot water (~100 oC) and the other junction in ice water (~0 oC) such that
there is ~100 oC difference between the two junctions. Record the thermocouple voltage. This
would normally be a very small voltage, typically a few millivolts, and the typical multimeter
would only register one non-zero digit (i.e. one significant figure).
Question: is this reading enough to tell that your thermocouple is working? (Try taking the
junctions in and out of the water.)
Question: is your equipment giving you precise enough readings to allow you to study the
changes in the thermocouple output as the hot water cools to room temperature?
Part II: Constructing a thermocouple probe
 We can extract greater output from a thermocouple probe by using, not one, but several pairs
of junctions connected in series. We will refer to this as a probe, to distinguish it from a single
junction. Construct a probe by joining ten pairs of junctions in series (Figure 5) and bundling the
ten probe junctions together and the ten reference junctions together (Figure 6).
The bundles shown in Figure 6 are secured using cable ties. They can also be secured using
alternatives such as electrical tape or rubber bands. At each bundle, we need to ensure that
the junctions do not touch and make electrical contact with each other, which would defeat the
purpose of connecting them in series.

Test the probe in the same manner as we tested the single pair thermocouple using ice water
and boiling water. The output should be roughly ten times the value obtained for a single pair.
(If the output is smaller, it is likely some of the junctions are touching each other. If the output
is zero, one or more junctions are disconnected.)
Creative Commons Attribution 3.0 Unported License
4
PHYSICS COURSE NAME
LAB 11
Figure 5 – Ten junctions in series
Figure 6 – Bundled junctions
Part III: Cooling curve of a cup of hot water
 We can use the new probe to observe the cooling of a hot cup of water.
[Note – these are not really temperature measurements as we are not taking steps to calibrate
the thermocouple. How might we perform such a calibration? Discuss.]
Desired is the widest range of temperatures practically achievable. To this end, we start by
pouring hot water into a cup straight from a boiling kettle. An ice-bath will be used again for
reference (Figure 7).
Figure 7 – Thermocouple probe in use. The ceramic mug contains hot water and the glass bowl contains ice water.
 Our observations will consist mainly of a data table with time and thermocouple voltage. Rather
than measuring the voltage at regular time increments, we will measure the time every time the
voltmeter shows a new, lower value.
[Why is this a preferred approach? Discuss.]
Creative Commons Attribution 3.0 Unported License
5
PHYSICS COURSE NAME
LAB 11
 Start a run and continue until the water in the cup approaches room temperature enough that
temperatures changes becomes so slow that the thermocouple output remains unchanged for
several minutes at a time.
 Repeat at least two more runs to ensure consistency.
ANALYSIS AND/OR QUESTIONS

For each run, plot a graph of the probe voltage V vs. time t. Recalling that the voltage is a linear
function of temperature, we expect from Equation [2] that this graph will show a curve
representing logarithmic decay.

For a quantitative analysis, now plot graphs of ln V vs. t for each run. Equation [2A] predicts a
straight line with slope –A.

Using linear least squares fitting, determine the cooling constant A.

Discussion: Were the cooling constants the same or similar for your runs? What could we do to
observe very different cooling rates purposefully? In other words, what simple changes could
be made to our experiment that changes the cooling rates? Support your hypotheses with
theory, and perhaps new data.
REFERENCES
Urone, P., Hinrichs, R., Dirks, K., and Sharma, M., 2014. College Physics. OpenStax-CNX, March 7, 2014.
http://cnx.org/content/col11406/1.8/.
Bevington, P.R., and Robinson, D.K., (2003), Data Reduction and Error Analysis for the Physical Sciences,
3rd Ed., McGraw-Hill, New York.
Original introduction by Jill Lang, KPU.
Activity developed for remote delivery by T. Sato under the Remote Science Labs for Second
Year Physics Project (2012 – 2013) funded by BCcampus.
Creative Commons Attribution 3.0 Unported License
6