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Introductory Physics Laboratory, Faculty of Physics and Geosciences, University of Leipzig
W 12e
Radiation Thermometers
Tasks
1 Measure the black temperature Ts of a glowing resistance wire at eight different powers Pel using
a filament pyrometer and the voltage UTP of a thermopile by Moll! Calculate the object (true)
temperature. Analyze the data of the sensor in a diagram lnUTP vs lnT to check Stefan-Boltzmann′s
law graphically.
2 Determine the true temperature of a tungsten lamp at two different powers Pel using a filament
pyrometer!
3 Measure the intensity of photodiode current in dependence on temperature of the heated filament
in a tungsten lamp at the wavelength λ=750 nm at eight different powers Pel . Determine Planck’s
constant!
Additional task:
Measure the object temperature Tobj of a resistance wire in dependence on the electrical power
using an alternating light pyrometer! Check the validity of the Stefan-Boltzmann′s law of radiation
creating a plot lnPel vs lnTobj!
Literature
Physics, P. A. Tipler, 3rd Edition, Vol. 1, pp. 530-534
Physikalisches Praktikum, 12.Auflage, Hrsg. D. Geschke, Wärmelehre 1.0.1, 1.0.4, 1.4, Optik 5.0,
(5.2)
http://csep10.phys.utk.edu/astr162/lect/light/radiation.html
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html
Accessories
thermopile sensor by Moll, filament pyrometer, laboratory power supplies, digital multimeter, test
wire, reflection diffraction grating, photodiode, alternating light pyrometer, tungsten bulb
Keywords for preparation
- radiation laws, Planck′s radiation law, displacement law of Wien, Stefan-Boltzmann law,
Kirchhoff ′s law, Wien’s radiation law, Rayleigh-Jeans’ radiation law
- black body radiation, black temperature
- principles of pyrometers, principles of thermocouples
- Conditions for the calculation of the (true, object) radiation temperature
- heat transport processes, conduction, radiation, convection
Remarks
In task 1 about 8 different values of electrical power Pel (currents 7 … 10 A) have to be adjusted
dissipated by the glowing resistance wire. The thermopile sensor voltage (thermopile by Moll) is
measured by an analog voltmeter and the black temperature is determined by a filament pyrometer.
In order to determine the (true, object) temperature T in task 1 the following equation has to be
used:
c h
1
1
λ
=
+ ln ε , c2 = 0 (fundamental constants c0 , h , k ) .
(1)
T Ts (λ ) c2
k
Ts: measured (black) temperature, effective pyrometer wavelength λ = 655 nm or hν = 2 eV using
the red filter in the filament pyrometer, emissivity ε=0,35.
The equ.(1) can be derived using Planck′s law at the condition hν kT and Kirchhoff’s law; do it!
To evaluate the Stefan-Boltzmann law it can be assumed the linear relationship between thermopile
voltage UTP and the total radiant exitance M: M = const. U TP .
The output signal (UTP) of the thermopile follows the equation U TP ∝ (T − TU ) for T ≈ TU !
Remark: (T 4 − TU4 ) = (T 2 + TU2 ) ⋅ (T 2 − TU2 ) ≈ 2 TU2 (T 2 − TU2 ) ≈ 4 TU3 (T − TU )
In task 2 measure the black temperature by the filament pyrometer analogous to task 1 of the
glowing spiral in a tungsten lamp and determine the average (object) temperature by iteration using
a diagram representing emissivity vs object temperature (see below). The corresponding equation
for iteration is
hν ⎡ 1 1 ⎤
ln ε ( λ , T ) =
.
(1)
⎢ − ⎥
k ⎣ T Ts ⎦
In task 3 measure the photo diode current produced by thermal radiation of a tungsten bulb at 750
nm. The white light spectrum of the tungsten bulb is separated using a diffraction grating spectral
photometer with which it is possible to choose different wavelength turning a barrel to change the
angle of incidence ( http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/grating.html ).
The photo diode must work in reverse-biasing to comply with the linear relationship between the
photodiode current IFD and the absorbed light intensity. From the slope of the plot lnIFD vs 1/T
using lnIFD=const-(hc0/λkT) you can determine Planck’s constant h.
The temperature of the glowing tungsten wire (R(T)= U/I) is determined from current and
voltage measurements with the use of a voltage correct circuit (Fig. 1). The current source of
the tungsten lamp comes from the laboratory power supply. After the build-up of the electric
circuit, that is supervised by the demonstrator, switch on the power supply (the voltage
controller at the front to the left is to be set up). Using the voltage controller the selected
voltage (current) is set up after one another and the product from the displayed voltage and
current values must be calculated constantly so that the given maximum value of Pel, max at
workstation is not to be exceeded. The temperatures of the tungsten helix that are necessary for
further evaluation can be determined by using the measured electric resistances R(T), the given
value R293 at T=293K and the equation
⎡
⎤
R/Ω
+ 0.486
⎢
⎥
R /Ω
T / K =1000 ⎢ 44.37 + 293
− 6.661⎥ .
⎢
⎥
0.3526
⎢
⎥
⎣⎢
⎦⎥
Fig. 1
Voltage correct circuit (R tungsten lamp, RSt internal resistance of ammeter, RSp
internal resistance of voltmeter)
In the additional task using the so-called alternating light pyrometer (it is a radiation pyrometer,
where a chopper disc interrupts periodically the received thermal radiation and a pyroelectric
sensor transforms the radiation into an electrical signal (chopped radiation method;
http://www.wintron.com/Infrared/guideIR.htm ) ten measurements have to be performed. Before
switching on the pyrometers a short introduction is given by the demonstrator!
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Fig. 2 Experimental setup for task 1 (schematic)
1 observer
2 filament pyrometer
(built-in red filter)
3 millivoltmeter
4 thermopile by Moll
5 heat radiation source
(flat metal wire)
6 laboratory power
supply and digital
multimeters
Fig. 3 Single-Waveband Thermometers / Filament Pyrometer (schematic)
Fig. 4 Thermopile by Moll
distribution
of
thermopiles on the
detector
surface
and on the massive
brass case (external
thermocouples)
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Fig. 5 Experimental setup for task 3 (schematic)
1 tungsten lamp
2 lamp casing
3 casing
4 condensor lens
5 entrance slit
6 collimator lens
7 reflection grating
8 objective lens
9 exit slit with closure
damper
10 photo diode
11 connectors
12 power supply
13 ammeter (digital
multimeter)
14 sensor casing
15 barrel
Diagram for task 2
ε (T) - dependence ( tungsten, λ = 655 nm ) for iteration
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Radiation Thermometers (Definitions and Symbols)
Radiometric quantities
Quantity
Symbol
Definition
Radiant energy
Q
Energy propagated as electromagnetic waves
or photons
Radiant flux
Φ
Radiant intensity
I
Radiant exitance
M
Radiance
L
Rate of flow of radiant energy Φ = dQ/dt
Flux per unit solid angle from a source
I = dΦ / d ω
Flux per unit area leaving a surface
M = dΦ /dA
Flux propagated in a given direction, per unit
solid angle about that direction and per unit
area projected normal to the direction
L = d2Φ /(dA cosθ dω)
flux per unit area incident on a surface
Irradiance
E
Unit
symbol
J
W
W sr-1
W m-2
W m-2 sr-1
W m-2
dA element of surface; dt element of time; dω element of solid angle; θ angle between direction of
propagation and normal to emitting surface
Note: The symbol λ will be used to indicate reference to a given wavelength (spectral quantities).
Radiation properties
Property
Absorptance
Absorption
Reflectance
Reflectivity
Transmittance
Emittance
Emissivity
Symbol
Definition
α
Ratio of absorbed flux to incident flux
ρ
Ratio of reflected flux to incident flux
τ
ε
Ratio of transmitted flux to incident flux
Ratio of the radiant exictance of a body at a given
temperature to that of a block body at the same
temperature and under the same viewing conditions
Interrelationships of Properties
The radiative properties integrated over the whole spectrum of a black-body radiation (total
properties) of a specimen of any kind are related by the equation
α + ρ +τ = 1 .
For opaque materials (τ = 0) we get
α + ρ =1 .
Emissivity is introduced into the above relationships by referring to Kirchhoff′s law. This states in
simple terms that any body which is a good absorber of radiation is also a good emitter, and just
the same amount. Kirchhoff′s law leads to α = ε .
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Black-Body Laws
A black-body radiator is an ideal body having the following properties:
- It absorbs all radiant energy incident on it, irrespective of wavelength, direction, and state of
polarization.
- It emits at any temperature the maximum amount of radiant flux per unit area, and this applies to
both integrated and spectral fluxes.
- The emission is independent of direction. This property is described as a perfectly diffuse
radiator.
Stefan-Boltzmann law: M = σ (T 4 − Tu4 ) , where M is the total radiant exitance in W m-2 , T is the
absolute temperature, and Tu the ambient temperature. The quantity σ ≈5.67⋅10-8 W m-2 K-4 is the
Stefan-Boltzmann constant.
c1 λ−5
,
exp ( c2 / λ T ) − 1
where Mλ is the spectral radiant excitance in W m-2 per unit wavelength interval, λ is the
wavelength in vacuum, and c1 ≈ 3.742⋅10-16 Wm2 and c2 ≈ 1.439⋅10-2 m K are the so-called first
hc
and second radiation constants, respectively:
c1 = 2π h c 2 , c2 =
.
kB
To express Planck′s law in terms of spectral radiance, the term on the right-hand side must be
divided by π.
Mλ =
Planck′s Law:
Wien′s approximation of Planck′s law (valid for low values of λ T ):
M λ = c1 λ−5 exp ( −c2 / λ T )
Wien’s displacement law: λmT = 2898 μm K, where λm is the wavelength at which the maximum
occurs of the Planck′s curve at temperature T.
-
Lambert′s cosine law: I θ = I 0 cosθ
Iθ is the directional radiant intensity in W sr-1 of a plane source in the direction θ and I0 is the
intensity in the direction normal to the source.
Real bodies
The spectral radiance of real bodies, which is the quantity of main interest in the radiation
c1λ−5
,
thermometry, is given by Lλ = ε λ (θ , T )
exp( c2 / λ T ) − 1
where ελ (θ,T ) is the directional spectral emissivity at the observation angle θ and temperature T.
Properties of Thermal Radiation
Thermal radiation is the energy emitted by a body as result of its finite temperature. In contrast to
heat transfer through convection and conduction, radiation heat transfer does not require a medium
and can occur in a vacuum. This is because thermal radiation energy is a type of electromagnetic
(E-M) radiation and like other types of E-M radiation it can travel can travel through vacuum at the
speed of light. Since it is the only mode of heat transfer that can take place through vacuum,
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radiative heat transfer is the mode of heat exchange between the Sun and Earth; hence the term
solar radiation.
Radiation
Reflected, ρ G
Incident
Radiation, G
Radiation
Emitted, ε G
Radiation
Transmitted, τG
Fig. 4 Radiative properties of a surface
Figure 4 shows that when radiant energy G (W/m2) is incident on a surface, portions of it can be
reflected, absorbed and/or transmitted. The relative fractions that are reflected, absorbed and
transmitted are determined by the radiative properties ρ, α and τ, the reflectivity, absorptivity and
transmissivity, respectively, of that surface. From conservation of energy we also know that:
ρ+α+τ=1
In addition to the above, the surface also emits energy via radiation where the amount of energy
emitted by the surface is given by the Stefan-Boltzmann Law:
E = ε σ AT 4
In this equation, σ is called the Stefan-Boltzmann constant and is equal to 5.67⋅10-8 W/m2K; A is
the surface are, ε is the emissivity of the surface, a surface property similar to ρ, α and τ and T is
the absolute temperature of the body in degrees Kelvin. The emissivity of a body can vary
between 0 and 1. A surface with ε = 1 is a perfect radiator and is referred to as a black body
radiator; for all real surfaces, ε < 1.
Thermal Radiation Spectrum
Electromagnetic radiation, like all other forms of radiation, travels at the speed of light, which is
related to its wavelength, λ, and frequency ν by c = ν λ , where c = 3⋅108 m/s is the speed of light.
Thermal radiation spans only a portion of the entire electromagnetic spectrum, which ranges from
X-rays to Microwaves.
Fig. 5 Thermal radiation portion of the Electromagnetic Spectrum
The thermal spectrum spans a range of 0.1 μm - 100 μm, which, as shown in Fig. 5 includes the
entire visible spectrum. Whether thermal radiation is visible, and at what color, is a function of the
portion of the radiation that falls within the visible spectrum. Not only is the total amount of
thermal radiation emitted by a surface − described by the Stefan-Botzmann’s law − a direct
function of temperature, how this energy is distributed over the thermal spectrum as a function of
wavelength, is also a related to the surface temperature.
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The Planck Distribution gives the spectral distribution of thermal radiation of a Black Body as a
function of temperature. This distribution function can be found in any standard undergraduate heat
transfer text. Using Planck’s Distribution, the spectral distributions from black bodies at various
temperatures are shown in Figure 6. The figure shows that energy radiated varies continuously
with wavelength at any given temperature. It also illustrates that at lower temperatures most of the
energy the energy is outside the visible spectrum. However, as the temperature rises, more and
more energy is shifted to shorter wavelengths and into the visible spectrum region. The
dependence of spectral distribution on temperature also explains why the color of a body changes
as it is heated: from black to dark red to bright red to yellow and finally to white hot. The overall
intensity of the visible light from an object also increases with temperature since a larger
percentage of the total energy radiated is in the visible spectrum.
Solar radiation has a spectrum very similar to that of a black body at 5800K. As a result, a large
portion of solar radiation is visible. The reflectivity, absorptivity and transmissivity of most
materials are also a function of wavelength of the incident radiation. Hence they may transmit
radiation from sources above (or below) certain temperatures, i.e. within a certain range of
wavelengths, while blocking light from sources at temperatures outside that range. This
wavelength dependence of material transmission properties is responsible for the greenhouse
effect.
Fig. 6 Spectral distribution of a Black body emissive power using Planck’s Distribution
Fig. 7 Spectral Sensitivy of optoelectronic sensors
(a Photodiode, b CCD-Sensor)
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