PASCO TD-8513 Manuel utilisateur

Heat Conduction Apparatus

TD-8513

Instruction Manual

012-09189A

Heat Conduction Apparatus Table of Contents

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

Safety. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Specifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

Material Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Experiment #1: Heat Conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Experiment #2: Angstrom’s Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Sample Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Heat Conduction Apparatus

TD-8513

®3

Introduction

The PASCO Heat Conduction Apparatus demonstrates the difference in the rate of heat conduction through bars

of different materials and cross-sectional areas. The apparatus has four metal bars: one aluminum, one stainless

steel, and two brass with different cross-sections. One end of each bar is heated or cooled by a Peltier device.

Each bar has two 10 kΩ thermistors embedded about 3 cm from each other. A cable is supplied to connect the

thermistors to a PASPORT Temperature Array (PS-2157) so data can be recorded from all eight sensors simulta-

neously. Foam insulators cover the bars to minimize heat exchange with the environment.

The embedded thermistors are labeled T1 through T8; these labels correspond to the Temperature Array channels

(1 through 8) on which data is collected. The lines printed on the board indicate the lateral positions of the ther-

mistors within the bars.

Temperature

Port Power Input

Ports

Heat/Cool

Switch

Narrow Brass Bar

Stainless Steel Bar

Wide Brass Bar

Aluminum Bar

Peltier

Device Heat

Sin ThermistorsThermistors

Included Equipment Part Number

Heat Conduction Board TD-8513

Heat Sink 624-005

Thumbscrew 617-013

Foam Insulators (qty. 2) 648-09185

Temperature Array Cable 514-09162

Required Equipment Part Number

PASPORT Temperature Array1

1Temperature Array requires a PASPORT interface; see PASCO catalog or www.pasco.com

PS-2157

DC Power Supply PI-98772

2Or similar power supply capable of supplying at least 5 volts and 1 amp.

4 mm Banana Patch Cords (qty. 2) SE-9750, SE-9751, or similar

Heat Conduction Apparatus Connections

The Heat/Cool switch changes the polarity of the voltage applied to the Peltier device

so that the lower surface of the device either heats or cools the bars. When the switch

is set to Cool, the device pumps heat from the lower surface to the upper surface; the

heat sink helps to dissipate this heat.

Connections

Use the included cable to connect the temperature port of the Heat Conduction Appa-

ratus to the multiport of a PS-2157 Temperature Array. Connect the Temperature

Array to a PASPORT interface. Connect the interface to a computer and start

DataStudio.1

Connect a PI-9877 DC Power Supply (or similar) to the power input ports of the

apparatus with the positive terminal of the power supply connected to the red input

port, and the negative terminal connected to the black input port. Set the voltage to

zero.

Safety

The Peltier device and metal bars can be hot. Do not touch them while the appa-

ratus is in use. When applying power to the device, always monitor the temper-

atures and do not allow them to exceed 80 °C. After use, do not leave the apparatus

unattended until all parts have cooled.

Do not apply more than 15 V or 2 A to the apparatus.

Specifications

Material Properties

1If your PASPORT inter-

face is an Xplorer GLX,

you can use it without a

computer or DataStudio.

Aluminum, stainless steel, and wide brass bar

dimensions

9 × 1.2 × 0.4 cm

Narrow brass bar dimensions 9 × 0.7 × 0.4 cm

Maximum input voltage 15 VDC

Thermistors Eight embedded 10 kΩthermistors

Brass (360 Alloy) Aluminum (6063-T5) Stainless Steel (304)

Density ρ (kg/m3)8520 2800 8000

Specific Heat

(J/kg·K) 385 830 400

Conductivity

(W/m·K) 115 150 14

Model No. TD-8513 Experiment #1: Heat Conduction

Experiment #1: Heat Conduction

Set-up

1. On the power supply, turn the Function switch to SET MAX and set the voltage

limit to 8 V; this will prevent accidental overload during the experiment. Turn the

Function switch to constant DC mode ( ).

2. Use two banana patch cords to connect the power supply to the Heat Conduction

Apparatus. Connect the positive (+) terminal of the power supply to the red input

jack of the Heat Conduction Apparatus; connect the negative (−) terminal of the

power supply to the black input jack of the Heat Conduction Apparatus.

3. Use the included cable to connect the temperature port of the apparatus to the

multiport of the Temperature Array. Connect the Temperature Array to the

PASPORT interface. Connect the interface to a computer and start DataStudio.

4. Measure the distance between the two thermistors embedded in each bar; their

positions are marked by the white lines on the board.

5. Make a drawing showing the layout of the apparatus including the Peltier device,

the four bars, and the thermistors. Label each thermistor with the following des-

ignations:

T1 Wide Brass (far)

T2 Wide Brass (close)

T3 Narrow Brass (close)

T4 Narrow Brass (far)

T5 Aluminum (far)

T6 Aluminum (close)

T7 Stainless (close)

T8 Stainless (far)

A. Heat Conduction Race

Set-up

1. Set the switch to HEAT and place the insulators over the bars.

2. In DataStudio, set the sampling rate of the Temperature Array to 5 Hz. Set up a

graph display to show the temperatures measured by all four “far” thermistors

(T1, T4, T5, and T8).

3. Collect a test run of data to make sure that all four bars are all at room tempera-

ture. Delete the data.

Equipment Required Model

Heat Conduction Apparatus TD-8513

DC Power Supply PI-9877

Temperature Array1

1Temperature Array requires a PASPORT interface; see PASCO catalog or www.pasco.com

PS-2157

DC Power Supply PI-9877

4 mm Banana Patch Cords (qty. 2) SE-9750, SE-9751, or similar

Heat Conduction Apparatus Experiment #1: Heat Conduction

Procedure

1. Set the power supply to 5 V (constant DC) and simultaneously start recording in

DataStudio. Watch the graph of “far” temperatures and allow them to increase for

about 5 minutes. Stop recording.

2. Set the power supply voltage to zero. Remove the insulators to allow the bars to

cool.1

Analysis

1. Look at the final temperature measured by the “far” thermistor of each bar.

Which material is the best conductor? Which is the worst? Is there a difference

between the two brass bars?

2. Create a graph showing data from both thermistors in the wide brass bar (T1 and

T2). Zoom in on the area of the graph where the temperatures start to increase.

Notice that the temperature at the close thermistor (T2) starts to increase before

the temperature at the far thermistor (T1). Measure this time difference.

3. Calculate the speed of the heat pulse down the brass bar. At this speed, how long

would it take for the pulse to travel the length of the bar?

4. In DataStudio, create a calculation for the temperature differ-

ence (∆T) between the close and far thermistors in the wide

brass bar. Create similar calculations for the other three bars

(be sure to subtract the “far” temperature from the “close”

temperature). Display all four calculations in a graph.

Which bar has the largest ∆T? Which bar has the smallest?

What is the correlation between ∆Tand how good a

conductor each material is?

5. Why does ∆Tpeak and then decrease? Why does this peak occur at different

times for the four bars?

6. Notice that ∆T in each bar approaches a final equilibrium value. Estimate this

final value for each bar.

7. The rate of heat flow (∆Q/∆t, in joules per second) is given by

where k is the thermal conductivity of the material, Ais the cross-sectional area

of the bar, and x is the distance between the thermistors.

See page 4 for the conductivities of brass, aluminum, and stainless steel. Measure

the dimensions of the bars. Calculate the final heat flow rate in each bar.

8. Which bar has the highest heat flow rate? Is there a correlation between ∆Tand

heat flow rate? Why is the heat flow lower in the narrow brass bar than in the

wide one?

Further Study

Repeat the previous experiment with the switch set to COOL. Which direction does

heat flow in this case?

1To cool the bars faster,

you can set the switch to

COOL and apply 5 volts

for a few minutes; then

wait a few more minutes

with the apparatus

un-powered for the bars

to come to equilibrium.

Q∆

t∆

--------kA T∆

--------------=

Model No. TD-8513 Experiment #1: Heat Conduction

B. Heat Pulse

Set-up

1. Set the switch to HEAT and place the insulators over the bars.

2. In DataStudio, set the sampling rate of the Temperature Array to 2 Hz. Set up a

graph display to show the temperatures measured by both thermistors in the wide

brass bar (T1 and T2).

3. Collect a test run of data to make sure that all four bars are all at room tempera-

ture. Delete the data.

Procedure

1. Set the power supply to 5 volts (constant DC) and start recording in DataStudio.

Wait until the “close” temperature (measured by T2) reaches about 40 °C. 2

2. Change the switch to the COOL position and start timing with a clock or stop-

watch. Change the switch every 30 seconds. In this way the end of the bar is

alternately heated and cooled with a period of 60 s.

3. Continue for several minutes until the temperature wave at each thermistor has

stabilized with a constant amplitude.

4. Stop data recording and set the power supply to 0 V. 3

Analysis

1. Observe the shape of the two waves (it helps to zoom in on the last few cycles).

What is the shape of the wave that you applied to the bar by switching between

heating and cooling? What is the shape of this wave when it reaches the close

thermistor (T2)? How has it changed when it reaches the far thermistor (T1)?

2. Notice that there is a time lag between the two waves. What causes this? Measure

the time lag. How is the time lag related to the distance between the thermistors?

3. Why is there an amplitude change between the two waves? Are these really two

different waves?

4. Create a new graph showing data collected by the thermistors in the aluminum

bar (T5 and T6). Repeat analysis steps 1 through 3 for the aluminum bar.

5. Compare the shape of the waves in the aluminum and brass bars. Why are they

different? Compare the amplitude of the waves. Which material is the better con-

ductor?

6. Compare the time lags in the aluminum and brass bars? What does this tell you

about the speed of the pulse in each bar?

C. Heat Waves

Theory

In this part, the power supply will apply a triangle wave voltage to the Peltier device.

This heating and cooling of one end of each bar causes a thermal wave to travel down

the bar. The wave on each bar is measured by two thermistors. You will investigate

the relationship between wave speed, period, and wavelength.

2You can decrease the

wait time by applying a

higher voltage (8 V), but

reduce the voltage back

to 5 V before the temper-

ature reaches 40oC.

3If you are going to do

part C of this lab, set the

power supply now. This

will allow the system to

come to equilibrium while

you perform the follow-

ing analysis. See the

Set-up section for part C

below.

Heat Conduction Apparatus Experiment #1: Heat Conduction

Set-up

1. Set the switch to COOL.

2. Place the insulators on the bars.

3. Set the power supply to output an 8 V positive triangle wave with a 50 s period,

as shown in the diagram. See the PI-9877 DC Power Supply manual for detailed

instructions.

4. In DataStudio, set the sampling rate to 2 Hz. Create a graph to show data col-

lected by both thermistors in the wide brass bar (T1 and T2).

5. Start recording data. Wait for several minutes until the thermal wave at each ther-

mistor has stabilized with a constant amplitude. Stop recording data and delete

the data run.

Procedure

Start recording data again. After two full cycles, stop recording.4

Analysis

1. Measure the time lag between the wave measured by the “close” and “far” ther-

mistors.

2. Calculate the speed (V) of the wave using the distance between the thermistors

and the time lag between the waves.

3. Calculate the frequency (f) of the wave in Hz.

4. The speed of any wave is related to its frequency and wavelength (λ) by

Calculate the wavelength of this wave. How does λcompare to the length of the

entire bar?

5. Create another graph showing temperatures measured in the aluminum bar.

Repeat analysis steps 1 through 4. Do the same for the narrow brass bar and the

stainless steel bar.

Questions

1. Is the wave speed different in each material? Which has the highest speed? How

is the wave speed related to the conductivity of the material?

2. Notice the decrease in amplitude (attenuation) of the wave measured at the far

thermistor compared to the close thermistor. How is this related to the material

and the conductivity? Which material has the most attenuation.

Further Study

Repeat the experiment for a wave with a period of 100 Hz. How are the wave speed,

wavelength, and attenuation affected by the frequency of the wave?

8 V

0 V

50 s

Power Supply Settings:

Max. Voltage 8 V

Min. Voltage 0 V

Period 50 s

Auto-repeat −0

4If you are going to do

the Further Study part of

this section, change the

period of the triangle

wave to 100 s now and

allow the system stabilize

while you do the following

analysis.

Vλf=

Model No. TD-8513 Experiment #2: Angstrom’s Method

Experiment #2: Angstrom’s Method

Set up

1. On the power supply, turn the Function switch to SET MAX and set the voltage

limit to 8 V; this will prevent accidental overload during the experiment. Turn the

Function switch to constant DC mode ( ).

2. Use two banana patch cords to connect the power supply to the Heat Conduction

Apparatus. Connect the positive (+) terminal of the power supply to the red input

jack of the Heat Conduction Apparatus; connect the negative (−) terminal of the

power supply to the black input jack of the Heat Conduction Apparatus.

3. On the Heat Conduction Apparatus set the switch to COOL.

4. Use the included cable to connect the temperature port of the apparatus to the

multiport of the Temperature Array. Connect the Temperature Array to the

PASPORT interface. Connect the interface to a computer and start DataStudio.

5. Measure the distance between the two thermistors embedded in each bar; their

positions are marked by the white lines on the board.

6. Make a drawing showing the layout of the apparatus including the Peltier device,

the four bars, and the thermistors. Label each thermistor with the following des-

ignations:

T1 Wide Brass (far)

T2 Wide Brass (close)

T3 Narrow Brass (close)

T4 Narrow Brass (far)

T5 Aluminum (far)

T6 Aluminum (close)

T7 Stainless (close)

T8 Stainless (far)

Theory

In this experiment, you will measure the thermal conductivity of the metal bars using

Angstrom’s method. A periodic wave travels down the bar and the resulting tempera-

ture wave is measured at two points using thermistors. The thermal diffusivity, α, can

determined by measuring the amplitude of the temperature wave at the close ther-

mistor (Ac) and the amplitude at the far thermistor (Af) as well as the relative phase

(φ) between these two waves.

Equipment Required Model

Heat Conduction Apparatus TD-8513

DC Power Supply PI-9877

Temperature Array1

1Temperature Array requires a PASPORT interface; see PASCO catalog or www.pasco.com

PS-2157

DC Power Supply PI-9877

4 mm Banana Patch Cords (qty. 2) SE-9750, SE-9751, or similar

Heat Conduction Apparatus Experiment #2: Angstrom’s Method

According to Angstrom’s method

where nis the harmonic, ωis the driving frequency, and ∆xis the distance between

the thermistors.

In this experiment, the driving frequency is very small so it is easier to consider the

period (T) of the wave, where

The time delay (∆t) between the two waves is measured directly. The relative phase,

(φ), is calculated using

where Tnis the period of the harmonic. Thus

Combining these four equations yields

Note that αis independent of the harmonic (n) and of the driving frequency (ω).

A more commonly used quantity that is related to the thermal diffusivity, but includes

the specific heat (c) and density (ρ) of the material, is the thermal conductivity (k).

This gives the final expression:

αnωx∆()

2φln Ac

------







------------------------=

ω2π

------=

φ2πt∆

-----

TnT

---

αx2

∆

2tln Ac

------







∆

---------------------------

kcρα=

kcρα x∆()

2tln Ac

------







∆

---------------------------

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