BB - 1
Department of Physics, Indiana University (HOM 2/1/00) [Rev. MRS: 10/4/11]
Black-Body Radiation
Goal:
Test Planck’s law and the Stephan-Boltzmann law
Equipment:
Tungsten lamp with power supply, Ocean Optics spectrometer, pyrometer
1. Introduction
The Planck distribution law states that a “black” body at temperature T emits radiation with a
spectral distribution
f(
λ
)
given by
)
,
(
1
8
)
(
5
T
e
c
h
f
T
k
c
h
λ
ε
π
⋅
−
=
−
.
(1)
where
λ
is the wavelength, T the temperature in K,
h
=6.626•10
-34
Js is Planck’s constant,
k
=1.381•10
–23
J/K is the Boltzmann constant,
c
=2.998•10
8
m/s, and
ε
(
λ
,T)
<1, called the emissivity,
is a correction function that takes into account that ideal black bodies (for which
ε
=1) do not exist in
reality. For visible light, the exponential term in eq.1 is much larger that 1, so we can replace the
denominator of eq.1 by
exp(–hc/
λ
kT).
We will use a commercial spectrometer and a computer to
measure
f(
λ
).
The intensity
I
measured by the spectrometer is given by
I
(
,
T
)
=
b
(
)
(
,
T
)
⋅
8
⋅
hc
−
5
e
−
hc
kT
,
(2)
where
b
(
λ
) is a function, ideally unity, that accounts for absorption of light between the filament and
spectrometer.
When one integrates the Planck distribution to get the total power radiated,
P
R
, one obtains
the law of Stephan-Boltzmann,
4
T
A
P
eff
R
⋅
⋅
⋅
=
σ
,
(3)
where
σ
=5.64•-8 J/m
2
K
4
s is the Stephan-Boltzmann constant,
A
is the surface area, and
ε
eff
is the
weighted average of the wavelength dependent emissivity,
ε
(
λ
,T)
.
TASK 1: