Thermocouple Exercise

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Mechanical Engineering 3870

Measurements and Data Analysis

Temperature Measurement, Seebeck Effect, and Thermocouples

EDUCATIONAL OBJECTIVESThe educational objectives of this lab are for students to:

1. Understand the Seebeck effect2. Learn how thermocouples work in theory and practice3. Fabricate their own thermocouples4. Learn practical measurement of temperatures with thermocouples

5. Understand why modern electronics are needed for temperature measurement

EXPERIMENTAL OBJECTIVEThe experimental objective of this lab is to build a working thermocouple circuit with an output voltage in the

0.1 – 1.0 Volt range for temperatures between 10°C and 70°C that would be practical for application to the

situation described below.

MOTIVATIONYou work for a company that designs high precision computer controlled milling machines. Another group has

designed a prototype milling machine frame using a new material that they suspect will make the machining process more accurate due to better mitigation of unwanted vibrations. The new material is very susceptible toexpansion due to heating, though, which can negatively impact the quality of the machining. You have been put

in charge of measuring and recording the temperature of the frame at 20 different points in the machine, tobetter gauge how heat is transferred away from the tool. You will need to record this information over time to

determine the steady state heat distribution resulting after a long period of continuous machining. A co-workersuggests that you look into mounting thermocouples on the frame to accomplish your task. You find that the shophas thermocouple wire and a welder available for use.

1.1 List 3 different ways to measure the temperature of an object. Include notes on the advantages and

disadvantages of each method as it relates to your situation.

INTRODUCTION

Understanding the Seebeck CoefficientThe thermocouple is an instrument used to measure temperature. Its operating principle is the Seebeck effect,named after its discoverer in 1821. The Seebeck effect refers to the difference in voltage (also known as electric

potential or just potential) that arises between two points in a conductor or semiconductor when there is a

temperature gradient present between those points. Although complete understanding of the phenomenonrequires knowledge of kinetic theory, solid state physics, and irreversible thermodynamics, an intuitive and

phenomenological understanding is possible.Metals contain electrons that are free to move within them. In a crude way, you can think of the electrons ascomprising a gas trapped within the metal. Now, suppose you take a metal rod of material A as shown in Fig. 1,

and heat one end of the rod relative to the other, up to a constant temperature.



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Figure 1: Hypothetical metal rod with temperature gradient

The average energy of the electrons at the hot end is greater than their average energy at the cold end.Consequently, some migrate from the hot end to the cold end until a steady state is reached where there is a

temperature difference (t – c) across the rod. Since there is now an imbalance in the number of electrons

between the two ends of the rod, there is an imbalance of charge. A voltage or potential difference (t – )

is therefore established between the ends of the rod. The potential difference will be such that it opposes anyfurther migration of electrons from the hot to the cold side. Since the potential difference is related to the

temperature difference across the rod, a coefficient called the Seebeck coefficient, , is defined such that

Δ

Δ

, (1)

where has units of Volts per Kelvin or (V/K) whenΔ is measured in Volts andΔ is measured in K. By

convention, the voltage difference is measured between the cold side and the hot side, i.e. 4 − or c − t. Note that the foregoing discussion implies that if > 4, i.e. t > c, it follows that c < t, such that is positive. In reality, because the migrating electrons suffer collisions with the atoms of the material, can be positive or negative, depending on the material (see Table I in Chip Specification sheet located on Carmen).

In practice, to measure the voltage across this rod, you would have to connect a voltmeter with wires to the twoends of the rod. However, the moment you do this, as shown in Figure 2, you have changed the situation.

Figure 2: Rod with attached leads

The metal lead wires now see a temperature difference across them (say between and and possibly between

4 and

), which introduces additional potential differences that augment the potentials you are trying to

measure. Let us examine this further. From the definition of the Seebeck coefficient, we can write the following:

− − (2)4 − 4 − − 4 − 4

where is the Seebeck coefficient of the rod material, and is the Seebeck coefficient of the wire material



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Adding all three equations results in:

− Δ + − − 4 + 4 − , (3)

where and are the temperatures at the voltmeter terminals. If , then

− Δ − − 4 (4)

This can also be written as:

Δ − Δ, (5)

whereΔ is positive (from Figure 2). Thus,

− ΔΔ, (6)

In the limit asΔ

→ 0,

− limΔ→ ΔΔ . (7)

While the alphas are the Seebeck coefficients, − is called the Seebeck coefficient of the thermocouple or the thermoelectric power. The thermocouple’s basis for measuring temperature is found using (6). If the

Seebeck coefficients are presumed known, then measurement of the potential difference − Δ yields a

relation between the two temperatures t and c. If c is known, then t can be determined from (6).Table 1 lists the Seebeck coefficients for several materials as a function of temperature.

Understanding how a thermocouple measures temperature

Returning to Figure 2, let us replace the metal rod and the lead wires with two wires of different material

connected to form a beaded (a.k.a. welded) junction as shown in Figure 3.

Figure 3: Wires of two different materials with junction

Writing the voltage drops for each wire,

− − (8) − − ,

where and are the temperatures (presumed known) at the terminals, and is the desired unknown.

When the two equations above are added, the unknown is eliminated from the resulting equation. In any case,the configuration in Figure 3 is impractical since connecting terminals 1 and 2 to a voltmeter would result in the



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formation of new junctions between the copper (or whatever metal) leads in the voltmeter and materials A and B(the thermocouple). Suppose we connect two copper leads to the two wires shown in Figure 3 to produce the

configuration shown in Figure 4:

Figure 4: Wires of two different materials with copper leads attached

Writing the voltage drops for each wire segment we find that

− −

(9) − − − − 4 − 4 −

Adding all four equations yields:

4 − − + 4 − + − + − (10)

Since junctions 3 and 4 represent the Cu-Cu connections at the terminals of the voltmeter, 4. Furthermore,

if we force and to be at a common, known reference temperature, such as an ice bath maintained at 0oC,

then . Therefore, the first term on the right hand side of (10) vanishes and the equation simplifies

to:

4 − − ( − ) (11)

The left hand side of (11) is the voltage drop measured at the voltmeter. When the materials comprising the

thermocouple are known, e.g. iron and constantan, then and are known from a separate measurement. The

reference temperature, , is known by virtue of the fact that it is held fixed by an ice bath or similar standard.

Thus, (11) represents a single equation in the unknown temperature,

.

Prior to the modern era of electronics, ice baths were indeed used to provide the reference temperature for

thermocouples. However, since the reference temperature generates an equivalent voltage as can be seen from the − term in (11), reference junctions can be eliminated by electronic compensation which refers to

adding or subtracting an equivalent voltage electronically. This is exactly what some thermocouple amplifierchips such as the AD594 do – they provide what is called “cold junction compensation”, which is essentially

setting the reference temperature to a fixed value using an equivalent voltage. In addition, the AD594 provides aconstant reference temperature by anchoring the reference junctions, junctions 1 and 2 in Figure 4, to the circuit

board itself. Thus, provided the heat dissipated within the chip is small enough, the electronic compensation is



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related to the reference temperature or temperature of the chip’s circuit board itself (se e AD594 specificationsheet for further details). It is recommended that you read the AD594 specification sheet before the lab.

Test your understanding

1. Suppose all the wires, including the lead wires in the configuration in Figure 4 were made of the same

material. What would the voltmeter read for the potential difference

4

− ?

2.

Consider the thermocouple arrangement shown below:

Figure 5: Diagram for use with question 2, note that T1 is the temperature of the thermocouple.

a. The Seebeck coefficient of copper (Cu) and constantan are 1.52 V/K and -35 V/K, respectively.

If the temperatures at the voltmeter are equal, i.e. , and 0oC, what is the temperature

in terms of the potential difference − ?

b. If = 500oC, what is the potential difference recorded by the voltmeter?

c. What is the Seebeck coefficient of the thermocouple? See Appendix A for a table of Seebeck

coefficients of common materials.

EXPERIMENTAL EQUIPMENT

Per Person Per Group

1.5’ type J thermocouple

wire

1 prepared breadboard

(with chips)

1 set of jumper wires

2 banana plugs with leads

1 banana cable to BNC

connector

1.5’ type J thermocouple

wire(NOT WELDED)

2 glass beakers

Ice and water

5V fixed power

supply

Hotplate

Oscilloscope

LabVIEW

A

B

Voltmeter

Cu

Cu

Constantan

T1



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DELIVERABLES

See details on deliverables in sections to follow.

Deliverable Delivery Method Due Date

Pre-Lab Exercise Carmen dropbox Before scheduled lab time

Post-Lab Assignment Individual Hard Copy One week after lab

PRE-LAB EXERCISERead through and understand this document.

Download the example executable VI for this lab. Exercise the example VI to gain insight into how the VI works.Construct your own VI based on the provided example and the following description. (Hint: Place all the

components needed to construct the VI first. Then, figure out what is needed to wire everything together on yourblock diagram.) Once completed, submit your VI attempt through the Carmen dropbox. The VI will be graded

based on a combination of functionality and level of attempt.

Description of VI

The VI that you are being asked to construct is regarded as a preliminary VI because you will be simulating thethermocouple voltage instead of actually collecting data. Instructions are given in the “In-Lab Exercise” sectionsof how this VI will be modified to take actual data. The following description should help you to construct the VIin the correct manner.

1.

General description of VI operation a. The DC gain of the simulated voltage signal is controlled by the “Simulated Thermocouple

Voltage” slider. Voltage readings are being taken continuously and then output to the “RawWaveform Graph”

b. The “Thermometer Reading Input” box is where you will type the actual thermometer readingduring the lab so that it can be added to the table to aid in record keeping. However, you willwant to test its functionality during the preliminary VI.

c.

When the “OK Button” is pressed, all of the voltage readings plotted on the “Raw WaveformGraph” will be averaged. The gain you determine for the thermocouple is then applied to the

mean voltage to calculate the corresponding temperature. The mean voltage and calculatedtemperature and then added to the second and third columns of the “Data Table,” respectively.

d. The “OK Button” also controls the indexing of the data point num ber (first column of the data

table headed by “Point #”).

2. Tips on front panel objects a. Data table

Once your data table is placed, you will need to add column headers. To do this, rightclick on the table, and make sure that “column headers” is selected in the Visible Items

dropdown menu. b. Simulated thermocouple voltage slider

As is shown on the VI example, the voltage slider range differs from the default settings.You will want to range the voltage slider such that the minimum and maximum voltagescorrelate with the voltage produced by the thermocouple at room and boiling water

temperature, respectively. Once you have verified the voltage range needed, you candouble click on the default minimum and maximum slider values to edit them.

When you run the VI, you will need to click the slider’s pointer to initialize it to yourminimum value. Before you do this, it will be sending a DC signal at 0 V.



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3.

Hints and tips for block diagram objects a. After completing the front panel, you should see 7 objects on your block diagram – one for each

front panel object, except the table, which creates 2 block diagram objects. b. Continuous running of the VI

As with previous VIs you have made for this class, you will need to add a controlstructure that keeps the VI r unning until the “Stop Button” is pressed.

c.

Simulated signal Add the same simulate signal block as you have done in previous labs Under the signal type drop down menu, select “DC”

We know that the actual thermocouple is not a perfect voltage source. To simulate thiswe will add artificial noise to our simulated DC signal. To do this, check the “Addnoise” option. Set the noise type to “Uniform White Noise,” with an amplitude of 2 and

a seed number of -1. Set the sampling rate to 1000 Hz, the number of samples to 100. Make sure that “Run as

fast as possible” and “automatic” are selected. All other settings can be left at theirdefault values.

What will have to be done to the signal to get a single value for the table?d. Data point number indexing

There are several ways to do this. However, the easiest is to use a shift register, whichcreates something like a local variable that is stored between “OK Button” presses.

Shift registers are created by right clicking on the outer control loop, and selecting “add

shift register” off of the right-click-menu The blocks for connecting the circuitry of the shift register can be found in the arithmetic

and comparison section in express functions – a similar logic scheme was used in the

LabVIEW basics lab for the enable button. The “OK Button” will also be tied into this circuit.

e. Data table

You should have a “build table block” and “table” block from placing the front panelobject. If you do not see both of these blocks, replace the table with the “express table.”

After all of your other objects are wired together in the block diagram, you should have

data from four blocks, one piece of data per column, which needs to be sent to the table.After all of the calculations and inputs are ready for the table, they will be carried on thinorange wires, which indicate that they are double-precision scalars. However, the buildtable block requires a data array input. Therefore, you will have to merge all of the

scalars into a single array. You will need to send an enabling signal to the “Build Table” block, or the table will

display every array it is sent.

4.

Useful tips for working in LabVIEW a. When you place an object on the block diagram, they appear in the most condensed from

possible. To expand them, click and hold on the double arrow near the bottom edge. You canthen drag the edge down, which will reveal all the input and output names.

b. Colors are important in LabVIEW programming because they indicate the data types flowing

throughout the program. The color scheme of the block diagram is not limited to the wire color.It extends to block boarders (e.g. the “OK Button” is outlined in thick green because it is aBoolean output that cannot be changed, and the slider is outlined in thick orange because it is ascalar output in all cases) and the text of input and output names on a block ( e.g. after configuring

the “Simulate Signal” block, the outputs name will appear in blue because it is a dat a array).

However, certain blocks will automatically convert the data type. An example of this is the“mean” block. When you try connecting the simulated signal output to the “mean” block,LabVIEW will automatically place an array-to-double conversion block before it. Other blocks

will accept data types other than their default requirement. For example, the waveform graph is



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initially outlined in a thin orange line, which indicates that its default requirement input is anarray of scalars, but it will accept other data structures as well. When you connect the “waveform

graph” block to the simulated signal, the outline turns blue, which indicates that waveform arraysare acceptable. It is important to note that if you try and connect an unacceptable data type to a

block, a broken wire will appear.c. Order of “operations” for making this VI

Start by placing all front panel objects While working on the block diagram, begin with general considerations such as the outer

control loop

Figure out and place the blocks needed to process the data from input to output.

Finish wiring the block diagram.

IN-LAB EXERCISE

This lab is divided into two parts. In the first part you will measure temperatures using a reference bath and in thesecond part, you will measure temperatures using an AD594 chip.

Part 1: Use thermocouple in conjunction with a reference bath.

The TA will review with the entire class on how to weld their thermocouple. Listen carefully as you and your partner will be required to do the welding on your own while the TA helps other students with circuit board

design. After the class demo, each student will weld one thermocouple. To do this, follow the ThermocoupleWelding Procedure outlined below. While waiting to weld thermocouples, students should read the power supply

and AD594 chip specifications sheets, and the sections describing how to use a breadboard. You can save time

by starting the first step of Part 2 of the experiment (building the breadboard circuit) while others are

welding their thermocouple.

Thermocouple Welding Procedure

Weld a thermocouple junction using separate segments of iron and constantan wire. This type of thermocouplemade out of Iron-Constantan is called a "Type J Thermocouple". Pure white wire is iron and, wire with red

stripe is constantan.

Use extreme caution when operating the welder, as there is a high risk of shock, burn, or death if proper procedures are not followed. Remember that there is a very large electrical potential stored in the welder, and itwill use any route available to it to get to ground, including going through your body.

1. Prepare the wire to be welded.

a.

Unroll a length of thermocouple wire from the reel; a foot of wire will be more than sufficient. The

thermocouple wire is white and red and is on a spool located near the welder.

b.

Strip about half an inch from the end of each wire. The wire with the plain white insulation is the iron

and the one with the red stripe is the constantan. Constantan is a copper-nickel alloy often used in

thermocouples and strain gauges. You may cut the wires from the spools or unwind to have slack in order

to manipulate the wire near the machine.

c.

There are two methods of which one can prepare the wire ends for welding.

Method 1 (a bit harder to get right the first time):

a. Bend both wire ends towards each other about 45o.

b. Grip the wires so that the ends are just touching.



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Method 2 (a bit easier for first time welders):

a. Grip the ends of both wires with the pliers close to the insulation/bare wire edge, but leave a little space

between the pliers and the insulation.

b. Use the needle-nosed pliers to twist ends of wires. Cut any un-twisted wire off the end so that the two

wires are touching at the tip. Leave about one and a half to two turns, excess twists or large junction

bead will cause the thermocouple to respond slowly to a temperature change.

2. Prepare the welder for use.

a.

Check to ensure that pliers/electrode is plugged into the machine (lower right, front).

b. Place foot switch on floor.

c.

Turn main valve on regulator of argon cylinder counter-clockwise until it cannot be turned any further. At

that point the valve will be seated against the stop.

Whether opening or closing the argon cylinder, always seat the valve in the position desired. The valve is

a double-seat valve which will leak past the stern if not seated in the open or closed position. Set theoutput pressure to 3-4 psi.

d. Turn welder switch on. The power switch is on the back of the machine, above the power cord on the left

side.

Do not touch the pliers or the cone electrode with your fingers, hands, tongue, or other body parts unless youwant to be nominated for a Darwin award! It will cause shock, burn and/or death! Also, do not touch the coneelectrode with the pliers! The welder passes a high current through the cone and thermocouple tip to weld it.

Normally this current travels back into the welder via the blue-handled electrode pliers, but if you provide analternate route to ground (such as through your body via your fingers or another set of pliers, etc) the current will

take advantage of it and you will not be happy!

e.

Set toggle to “Arc”.

f. Set the level dial to “Medium”.

g. Test the foot switch or weld toggle to be sure that argon is flowing (the copper cone in the middle of the

machine front is going to be the powered electrode, your junction between the two wires is the other

electrode; Argon is dispensed through the center of the cone, defining the weld region at the tip of the cone).

h. Turn the power setting to 2/3-3/4 of maximum.

3.

Weld the thermocouple junction.a. When the ready light turns green, the machine is ready to weld.

b. Put on the green safety goggles.

Make sure you wear the green safety goggles before welding – the flash from the welder can damage youreyes.

c. Grip the bare thermocouple wires with the welder pliers so that there is some space between the pliers and

the junction, and also between the pliers and the wire insulation. If you place the pliers too close to the

twist, they may be welded to the junction, requiring you to break the weld and start over.

Do not use a second pair of pliers while welding your junction. This can cause arcs to appear where they are

not intended.

d. Press the weld toggle or foot switch. Slowly move the junction closer to the cone while continuing to

depress the weld toggle or foot switch. The weld is completed when there is a flash of light accompanied by a pop sound. Immediately move the junction away from the weld cone.

e. Remove your finger from the weld toggle or your foot from the foot switch, and remove the thermocouple

junction from the pliers.

Do not touch the junction bead immediately after welding – it is very hot, but should cool down fairly

quickly.

f.

Check your welded junction. Use the magnifying glass to check it visually or use the pick and pull on the

small loop created by the junction to check its strength. If the weld looks or feels strong enough, cut the



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length of wire needed from the spool (if it has not already been cut) and you are done! If the weld appears

incomplete or broken, cut the ends and repeat the Wire prep and Welding steps above.

4. Shut down the welder

a. Repeat all steps for Wire prep in reverse and place all tools and devices where they were found. Close the

main valve on the regulator of the argon cylinder.

b.

Depress the toggle or foot switch to release the trapped argon from the lines. This will ensure that the argon

regulator is closed.

Use thermocouple to make temperature readingsIn this lab procedure you have been provided space to write notes as you run through the lab. You should have

something written in each of these boxes before you leave the lab for the day. Use these notes to answer thequestions in the lab assignment. Students will work in their regular lab groups for the rest of the lab, using one of

the welded thermocouples. The remaining thermocouples will be used later for a time constant comparison.

You know that the thermocouple junction creates a voltage proportional to the temperature of the junction. Sowhy not plug the thermocouple right into a multi-meter, get a calibration curve, and call it a day? Let's do some

tests to make sure this is a good plan.

5.

Use some alligator clips to connect the non-welded ends of your thermocouple to the banana clips and cables

directly to the multimeter. The iron wire should be connected to the positive terminal of the multimeter. These

junctions will be termed as reference thermocouple junctions (clip to non-welded wire) and will be used as a

reference thermocouple junction. The end where iron and constantan wires are welded will be termed as welded

junction. The welded end is the thermocouple you will use to measure temperatures. Enter all measurements

in to Table A on datasheet.

a. With the reference junctions suspended in the air, measure the room temperature with the welded junction.

Record this voltage and the temperature of the room according to a thermometer. Based on how this

thermocouple works, does this voltage make sense?

b. Again with the reference junctions suspended in the air, measure the temperature of the ice water bath using

welded junction.c. Use the two points above to calculate the ΔV/ΔT value for the thermocouple.

d. Now hold one reference junction tightly in each hand and wait for them to get warm. While the reference

junctions are still in your hands, measure the room temperature and ice water temperature with the welded

junction (as was done in 5a and 5b). Using a thermometer, take updated measurements of the room

temperature (ambient air) and the ice water temperature. Using these new data points with the reference

junctions in your hands, calculate the ΔV/ΔT value.

Note: It is important to note that the reference junction is actually just another thermocouple that is not welded.

1.2 Were your twoΔ/Δ values calculated above the same in both cases? What did you change between the

two sets of measurements? Does your answer agree with Equation 10? How would this impede your ability

to accurately measure the temperature of the machine parts using the thermocouple?



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Use reference thermocouple junction as an ice water bath reference

6. Use an ice water bath to create a standard reference temperature for the reference thermocouple junctions and

get an estimate of the ΔV/ΔT value for the thermocouple. Enter measured values in to Table B on datasheet.

a. Insert the reference thermocouple junctions into a beaker containing ice and water, and let the welded

junction dangle in ambient air.

b.

Convert the voltage that you measure into an ambient temperature using the values given for a Type Jthermocouple in Table I (AD594 595) of the specification sheet located on Carmen.

c. Use a thermometer to record the ambient temperature and compare that value with the one you determined

from your thermocouple using Table I (AD594 595) in the specification sheet.

1.3 Record both values and note their difference. Comment on possible reasons why they are not equal.

d. Immerse the welded junction into the beaker containing ice water, being careful to make sure that the

welded junction does not touch the reference thermocouple junctions.

e. Measure the voltage on the multimeter, and use Table I (located within the specification sheet) to determine

the temperature. Measure the temperature of the ice water in the beaker with a thermometer, and record

the temperatures. Be sure to place thermometer in water to the immersion line marked on the

thermometer

1.4 Using the results from the ambient temperature and ice water bath measurements, calculate Δ/Δ. How

well does this comare with theΔ/Δ value for a Type J thermocouple as determined from Table I?

1.5 Comment on the performance of the thermocouple when using the ice water reference bath. What are some

disadvantages of this method, especially regarding the use of thermocouples in the milling machine scenario?

1.6 You are planning on using an AD converter to record the temperatures of the temperatures of the parts over

time. Assuming a 12-bit conversion for a ±5 volt range, what is the minimum resolvable voltage? Howdoes this compare to the voltage being generated by your thermocouple? What is the approximate

minimum resolvable temperature with this measurement scheme? Is this scheme suitable to themeasurements done in lab? Hint: Look up resolution and quantization error.



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Part 2: Use thermocouple in conjunction with AD594 amplifier chip

A circuit chip can be used to amplify and linearize the thermocouple voltage to a more useful scale. This chip has

been designed specifically for this purpose. As a bonus, the chip has an internal reference point, doing away withthe need for the ice water bath.

7. Read the AD594 and Power Supply specs sheets. You will be using the AD594 chip in a basic configuration

with a single power supply. Remember that pin layouts for IC chips are conventionally drawn with the notchfacing left (pin #1 is located by notch). Complete the breadboard layout diagram shown in Figure 6 using the

specification sheet found on Carmen. Remember to include your power supply voltage. Note that you will

not use the op amp in this experiment. It will be used next week in the Stirling Engine experiment.

8.

Have your TA approve the breadboard layout before building the circuit.

Figure 6: Breadboard for planning circuit layout

The AD594 chip is very sensitive to static electricity, and can be zapped if it is not handled carefully. Be

sure to ground yourself before touching the chip or any part of the circuit that the chip is in.

9. Build your circuit. Double check that it matches your approved diagram before you connect the power supply.

Take note that one of your wires for the thermocouple is grounded.

Check the output of the power supply with the multi-meter before connecting it to your circuit. You can

destroy the AD594 chip by supplying it with too much power.10. Modify the VI you made for the pre-lab exercise to take input from the PCI-6321 at your lab station. This is

done by configuring the DAQ assistant, as we have done previously. You will also need to change the gain

applied to your thermocouple voltage signal according to the AD594 chip specifications. Take care to check

your input and output units.

11.

After ensuring that the constantan end of your thermocouple is connected to pin 14 and the iron end is

connected to pin 1, connect the output from the AD594 (pin 8 or 9) and the ground to your PCI-6321 via AI0

using a banana-to-BNC adapter (as pictured in Figure 6).

Power Supply

5V Fixed

Black

(Ground)Red

Banana to BNC Adapter

To LabVIEW or OscilloscopeBlack with bump

indicates ground

AD594 LM324

Iron - Ground

(White)

Constantan

(Red)

Hint: Make this row a common

ground between all instrumentation



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12.

Measure ambient temperature and the temperature of a heated bath.

a. Once your DAQ system is assembled, take a few test points to make sure that the system is working

correctly.

b. Using your VI, collect 8 to 10 different temperature readings from room temperature to near boiling. Your

first measurement should be taken before your turn on your hotplate – this will be considered your baseline.

After taking your baseline reading, turn on your hot plate to the max setting. Make sure to stir the water

bath well and often to ensure an even temperature distribution. (Hint: while taking your data, the person

should set the thermometer entry, and then wait until the set “trigger level” is reached.) Compare the

voltages that you measure at the different temperatures with the values listed in Table I on page 3 of the

AD594 spec sheet.

13.

Connect the output from the AD594 chip to the oscilloscope, while your thermocouple junction is measuring

a specific temperature.

1.7 How does the thermocouple signal seen on the scope differ from the one you observed by looking at the

multimeter readout? How could you later the signal to make it more usable?

14. Obtain step responses of each thermocouple made using the oscilloscope. Before starting, twist the end of

your un-welded thermocouple. You will include this as one of your trials in this section. However, do not

use the twisted thermocouple for your data sheet sketch for part 14e.

a. Top off the hot water bath and bring it to a rolling boil. Adjust your oscilloscope to accommodate for the

voltage change between room temperature and boiling water, and a 1 second window.

b. Make a few notes regarding the characteristic of the weld. Some examples of what to look for:

i. The weld is smooth and regular

ii. The wires are overlapping, thereby creating a weld with a larger surface area

iii.

The weld is a messy blob.iv. Twisted.

c. Plunge a thermocouple into the boiling water as quickly as possible. Once the full response is collected,

another team member should hit the Run/Stop button on the oscilloscope.

The result should resemble the diagram in Figure 7, where is the ambient temperature in the room, is

the temperature as you are approaching the hotplate and water, and is the temperature of the boiling

water. As you can see, there are actually two first order step responses captured. However, we are only

interested in the step from to ; therefore, you will base your calculations on the second step collected.

Figure 7: Diagram of Step Response Data

Time

T e m p e r a t u r e

T R

T A

T W



14

d.

Save your step response data to a jump drive for later use. This is done with Save/Recall button on the

oscilloscope.

e. Calculate the time constant, , and label the points used in your calculations. The time constant is defined

as the time it takes for the measurement signal to reach 63.2 % of its final value.

f. Repeat steps b and d with your group’s remaining thermocouple(s).

1.8 Draw a sketch of the step response from one of your thermocouples on your data sheet. List your observations

about the appearance of the weld bead. Comment on the system response. List any useful quantities that you

have determined from the response. Give an example of how someone may use this thermocouple in industry.

Do not use the examples given in lab.

15. You will keep your circuit and thermocouple built in this lab for the lab the next week. Be sure to record the

number of your breadboard before leaving class.

POST LAB ASSIGNMENT

This assignment is to be completed individually. Please type the assignment with 1” margins, size 12 or 14font, and 1.15 line spacing. Make sure that all questions are clearly and correctly numbered. The pre-labquestions should be numbered 1.1, 1.2, etc., matching the question numbers in the manual. Any tables or figuresused to answers should have labels and units for the axes, a legend (if needed), and be appropriately captioned.

Also, if you choose to print in black and white, your plots must be readable in black and white.

1. Summarize all 8 questions encountered during the lab. Must type out all answers, you may not just hand in

worksheet. Expand your answers if need be.

2. Plot static calibration of your thermocouple/AD594 measurement device by plotting voltage versus

temperature. Use linear regression (see Appendix B) to fit a straight line to the data. Obtain the best fit values

of the slope (static sensitivity) and y-intercept. Determine the standard deviation of these quantities. Compare

these values with those listed on Table I of the AD594 spec sheets, page 3. Do you see any differences? What

do you think is responsible for any differences?

3. Using the values obtained from your linear regression (question 2) determine the precision (95% Confidence

Interval) of a temperature measured in the approximate mid-range of your experimental data. Refer to Figliola

and Beasley, page 131, for a table of t -values.

4.

Calculate the theoretical time constants for a thermocouple. Based on the differential equations governing afirst order system response, the expression for the time constant is

̅ ̅ℎ , where is the mass of the weld bead, ̅ and ̅ are the average is the average specific heat and density,

respectively, of the thermocouple’s materials, and are the volume and surface area of the weld bead, andℎ is the heat transfer coefficient.



15

For these calculations, we will assume that the weld bead is a sphere which has the same diameter as the wire

( = 0.511 mm). We will also need to assume an appropriate value for ℎ. The expression for is predicated

on the assumption that the heat transfer between the water and thermocouple is limited by convection.

Therefore, in line with this assumption, we will assume that the heat transfer occurring at the boundary of the

thermocouple control volume is due to either natural or forced convection. Thus, we can find published typical

heat transfer coefficients are in the following ranges:

ℎ [ WmK] Low High

Free convection 50 500

Forced convection 500 15000

The precise value for the heat transfer coefficient is largely dependent on the physical geometry of the system,

as well as the fluid and thermocouple material and surface characteristics of the objects involved. For our

purposes, we are only looking for comparative values. In other words, we only need the bounding values for

the time constant for both of the heat transfer mechanisms.

5. Plot the step response data from all of the thermocouples your group tested. Calculate and compare the time

constants form each of the tested thermocouples. Do you see a correlation between your weld observations

and the different time constants? Based on your observations of the measuring junctions, and your time

constants determined from the collected data, which physical factors do you think effect the response time of

the system? Also, specifically comment on the performance characteristics of the twisted thermocouple when

compared to the welded thermocouples. Make sure to explain your reasoning with calculations or examples

from your data for each question.

How do your experimentally determined time constants compare with the bounding values you calculated in

question 4? Were the assumed heat transfer mechanisms reasonable in your opinion? Which of the

mechanisms is dominating the system? Make sure to explain your reasoning with calculations or examplesfrom your data for each question.

Applying knowledge gained to experimental objective problem…

6. Write a short summary of your final conclusions that you will present to your boss before wiring up the

prototype for testing. Include only information that you think is necessary for her to know, presented in a

clear, concise manner.



16

Appendix A – Seebeck Coefficients of Common Materials

Table A-1: Data from: L. Loeb, Fundamentals of El ectri city and Magnetism , 2nd Ed., Wiley, New York, 1938.

Material T[ oC ]

, Seebeck coefficient at T[ V/K ]

Temperature dependence[ T in oC, in V/K ]

Al (Aluminum) 20 - 0.68 - 0.76 + 0.0039T

Ag (Silver) 20 2.41 2.12 +0.147T

Au (Gold) 20 3.0 2.8 + 0.0101T

Bi (Bismuth, commercial) 20, 0 - 97, - 72 -

Bi (Bismuth, pure) 20 - 89 -

C (Carbon) 0 3.0 -

Cd (Cadmium) 20 3.48 2.63 + 0.0424T

Constantan* 100, 0 - 47.0, - 35.0 -

Cu (Copper) 20 1.52 1.34 + 0.0094TFe (Iron)* 20 16.2 17.15 – 0.0482T

Ge (Germanium) 100 375.0 -

Hg (Mercury) 0 0.6 -

K (Potassium) 0 - 9.0 -

Na (Sodium) 0 - 2.0 -

Ni (-18oC to 175oC) 20 - 22.8 - 21.8 – 0.0506T

Nichrome 0 25.0 -

Pb (Lead) 20 0 0

Pt (Platinum, hard) 20 2.42 2.57 – 0.007T

Pt (Platinum, malleable) 20 - 0.818 - 0.6 – 0.0109T85%Pt-15%Ir (Platinum-Iridium alloy) 20 8.03 7.9 + 0.0062T

Rh (Rhodium) 0 6.0 -

Se (Selenium) 20 807 -

Si (Silicon) 100 455.0 -

Steel 20 10.62 11.27 – 0.0325T

Sb (Antimony) 20 6.0 -

Sn (Tin) 20 - 0.33 - 0.43 + 0.0055T

Ta (Tantalum) 0 4.5 -

W (Tungsten) 0 7.5 -

Zn (Zinc) 20 2.79 2.32 + 0.0238T

Sb (Antimony) 20 6.0 -

Sn (Tin) 20 - 0.33 - 0.43 + 0.0055T

Ta (Tantalum) 0 4.5 -

W (Tungsten) 0 7.5 -

Zn (Zinc) 20 2.79 2.32 + 0.0238T



17

Appendix B – Least Squares Curve Fitting

Defini tions and Procedure

Linear regression, also known as “Least Squares” curve fitting, is discussed in greater detail in the ME 3870Lectures. The appendix is intended to be a “quick reference” summary of the information contained in section 4.6of Figliola & Beasley (5th edition). The brief summary presented here will be sufficient for purposes of this lab.

Linear regression is the statistical process by which experimental data points are “fit” to the best smooth curve .

Typically, the data points are fit to a polynomial, but this is not a requirement. The criteria for accomplishing this

fit is that the residual , , is minimized. The analysis for our purposes will be restricted to fitting the experimental

data to a straight line in standard form ( + ). Therefore, we may define the residual as

+ − =

, (B1)

where , is the current experimental data point, is the total number of experimental data points, and and

are the best values of slope and

-intercept, respectively. The slope and

-intercept of the fit are calculated

using the entire data set. This process is start by calculating the following intermediate quantities.

= (B2)

= (B3)

= (B4)

= (B5)

Using the intermediate quantities determined from (B2)-(B5), the slope and -intercept of the fit can bedetermined using (B6) and (B7), respectively.

− − (B6)

− − (B7)

After calculating and , you can now plot the line of best fit over the range of your experimental data using

+ , (B8)

where , are the points along the line of best fit. The resulting curve may be regarded as the estimated

mean of the collected data set. Note that runs over the entire range of the experimental data; however, it does

not need to be the identical to the points of .



18

Standard Deviations Standard deviations are a measure of how tightly grouped a data set is around its mean value, or fitted curve,

where low values indicate a tightly grouped data set, and a high value indicates a data set that is spread out.Standard deviations may also be calculated in a point-wise fashion to determine the relationship of the individualswithin a data set to the mean of the data set. Here, we will use them to assess the quality of the fit, and todetermine how much uncertainty there is in our measurements.

We will begin by assessing the quality of the fit with respect to the original data. This is done using three

quantities: the standard deviation of the output (shown in (B9)), the standard deviation of the slope (shown

in (B10)), and the standard deviation of the -intercept (shown in (B11)). It should be noted that (B9) is

assumed to be independent of .

√ ∑ + − = , where degrees of − 2 (B9)

√

− (B10)

√ − (B11)

In order to determine the spread of the data about the fitted curve , we can calculate the standard deviation of

the data with respect to . Thus,

√ 1

+ − ̅

Σ − ̅ . (B12)

Likewise, we can calculate the standard deviation of an individual reading by

√ 1 + 1 + − ̅Σ − ̅. (B13)

It is also important to note that (B9), (B12), and (B13) are related by

+ , (B14)

where is the combined variance of the curve fit variance, , and the variance of the data, .

Using , we are able to find the standard deviation of an individual reading, in the units of the input, by using

the slope as a conversion. Thus,

(B15)



19

Uncertainties

Uncertainties are calculated using standard deviation of a quantity and a probability from the Student’s-Distribution (found on page 131 in Figliola and Beasley). The -value is found from the data using the desired

confidence level, , and the number of degrees of freedom . For example, if we would like to know the

uncertainty for an individual reading measured, in input units, with a 95% confidence interval in a system where

there are 15 degrees of freedom, we need to find

95,5 from the table. Thus,

±95,5 ±2.131 . (B16)

This same methodology can be adapted for any of the previously calculated uncertainties. Table B1, gives thedescription of each calculated uncertainty.

Table B1: Description of Uncertainties

Uncertainty (all are ±) Description

, Uncertainty of the estimated slope

, Uncertainty of the estimated

-intercept

,

Uncertainty in due to slope and -intercept being based on a sample of

data rather than the population;

therefore, it is based on and

, Uncertainty associated with an

individual reading

, Uncertainty for an individual reading

measured in input units

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Thermocouple Exercise