®
H e a t C o n d u c t i o n Ap p a r a t u s
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
∆
2 t ln
A
c
A
f
------
∆
---------------------------
=
k
c
ρα
=
k
c
ρα
x
∆
( )
2
2 t ln
A
c
A
f
------
∆
---------------------------
=
