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Ex p e r i m e n t  # 2 :  A n g s t r o m ’ s  M e t h o d

10

According to Angstrom’s method

where n is the harmonic, 

ω

 is the driving frequency, and 

x is 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 T

n

 is the period of the harmonic. Thus 

Combining these four equations yields

Note that 

α

 is 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:

α

n

ω

x

( )

2

2

φ

ln

A

c

A

f

------

 

 

 

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

=

ω

2

π

T

------

=

φ

2

π

t

T

n

-----

=

T

n

T

n

---

=

α

x

2

ln

A

c

A

f

------

 

 

 

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

=

k

c

ρα

=

k

c

ρα

x

( )

2

ln

A

c

A

f

------

 

 

 

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

=

Summary of Contents for TD-8513

Page 1: ...Heat Conduction Apparatus TD 8513 Instruction Manual 012 09189A...

Page 2: ...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 Techni...

Page 3: ...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 pos...

Page 4: ...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 w...

Page 5: ...mistors 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 thermist...

Page 6: ...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...

Page 7: ...2 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 bet...

Page 8: ...The speed of any wave is related to its frequency and wavelength by Calculate the wavelength of this wave How does compare to the length of the entire bar 5 Create another graph showing temperatures...

Page 9: ...ors 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...

Page 10: ...ay t between the two waves is measured directly The relative phase is calculated using where Tn is the period of the harmonic Thus Combining these four equations yields Note that is independent of the...

Page 11: ...e driving wave stop record ing 3 On the graph measure the amplitudes of both waves Ac and Af and the time dif ference between corresponding peaks of the two waves t Make a copy of the table below and...

Page 12: ...nty for all data runs and compare your answer to the accepted value of k for aluminum B Brass Record two more data runs with a 50 second triangle wave so that you have a total of five Repeat the analy...

Page 13: ...ws the pulse arriving at the close thermistor 5 2 s before the far thermistor The distance between the ther mistors is 30 mm The pulse speed is 30 mm 5 2 s 5 8 mm s The temperature differences between...

Page 14: ...shows the temperatures increasing with the switch set to HEAT before the switch starts alternating The apparatus is driven with a square wave At the first close thermistor upper trace on the graph the...

Page 15: ...A Aluminum B Brass Wide brass bar Period s Ac Af t k W m K Average k W m K 30 0 671 0 206 5 38 165 172 0 673 0 214 5 22 174 0 673 0 219 5 28 176 40 0 912 0 341 6 21 171 166 0 909 0 339 6 28 169 0 903...

Page 16: ...Af t k W m K Average k W m K 50 0 578 0 142 10 2 103 102 0 599 0 150 9 9 108 0 571 0 142 10 8 98 0 577 0 147 10 8 100 0 589 0 151 10 5 103 Period s Ac Af t k W m K Average k W m K 100 0 800 0 051 37...

Page 17: ...classrooms and are not sold for profit Reproduction under any other circumstances without the written con sent of PASCO scientific is prohibited Trademarks PASCO PASCO scientific DataStudio and PASPO...

Page 18: ......

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