= (fundamental constants c 0, h, k ). (1) k

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1 Introductory Physics Laboratory, Faculty of Physics and Geosciences, University of Leipzig W 12e Radiation Thermometers Tasks 1 Measure the black temperature T s of a glowing resistance wire at eight different powers P el using a filament pyrometer and the voltage U TP of a thermopile by Moll! Calculate the object (true) temperature. Analyze the data of the sensor in a diagram lnu TP vs lnt to check Stefan-Boltzmann s law graphically. 2 Determine the true temperature of a tungsten lamp at two different powers P el 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 P el. Determine Planck s constant! Additional task: Measure the object temperature T obj 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 lnp el vs lnt obj! Literature Physics, P. A. Tipler, 3rd Edition, Vol. 1, pp Physikalisches Praktikum, 12.Auflage, Hrsg. D. Geschke, Wärmelehre 1.0.1, 1.0.4, 1.4, Optik 5.0, (5.2) 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 P el (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: 1 1 λ c0 h = + lnε, c2 = (fundamental constants c 0, h, k ). (1) T Ts( λ) c2 k T s : 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

2 voltage U TP and the total radiant exitance M: M = const. U TP. The output signal (U TP ) of the thermopile follows the equation UTP ( T TU ) for T T U! Remark: ( T T ) = ( T + T ) ( T T ) 2 T ( T T ) 4 T ( T T ) U U U U U U U 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 lnε ( 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 ( ). The photo diode must work in reverse-biasing to comply with the linear relationship between the photodiode current I FD and the absorbed light intensity. From the slope of the plot lni FD vs 1/T using lni FD =const-(hc 0 /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 P el, 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 R 293 at T=293K and the equation R / Ω R / Ω T K = / 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; ) ten measurements have to be performed. Before switching on the pyrometers a short introduction is given by the demonstrator! 2

3 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 Fig. 3 Single-Waveband Thermometers / Filament Pyrometer (schematic) multimeters Fig. 4 Thermopile by Moll distribution of thermopiles on the detector surface and on the massive brass case (external thermocouples) 3

4 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 4

5 Radiation Thermometers (Definitions and Symbols) Radiometric quantities Quantity Symbol Definition Unit symbol Radiant energy Q Energy propagated as electromagnetic waves or photons J Radiant flux Φ Rate of flow of radiant energy Φ = dq/dt W Radiant intensity I Flux per unit solid angle from a source I = dφ / dω Radiant exitance M Flux per unit area leaving a surface M = dφ /da W sr -1 W m -2 Radiance L Flux propagated in a given direction, per unit solid angle about that direction and per unit W m -2 sr -1 area projected normal to the direction L = d 2 Φ /(da cosθ dω) Irradiance E flux per unit area incident on a surface 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 Symbol Definition Absorptance Absorption Reflectance Reflectivity α ρ Ratio of absorbed flux to incident flux Ratio of reflected flux to incident flux Transmittance τ Ratio of transmitted flux to incident flux Emittance Emissivity ε 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 For opaque materials (τ = 0) we get α + ρ + τ = 1. 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. 5

6 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. 4 4 Stefan-Boltzmann law: M = σ ( T Tu ), where M is the total radiant exitance in W m -2, T is the absolute temperature, and T u the ambient temperature. The quantity σ W m -2 K -4 is the Stefan-Boltzmann constant. c1 λ Planck s Law: M λ =, exp( c 2 / λ T ) 1 where M λ is the spectral radiant excitance in W m -2 per unit wavelength interval, λ is the wavelength in vacuum, and c Wm 2 and c m K are the so-called first 2 h c and second radiation constants, respectively: c1 = 2π h c, c 2 =. kb To express Planck s law in terms of spectral radiance, the term on the right-hand side must be divided by π. Wien s approximation of Planck s law (valid for low values of λ T ): M λ = c λ exp( c2 / λ T Wien s displacement law: λ m T = 2898 μm K, where λ m is the wavelength at which the maximum occurs of the Planck s curve at temperature T. - Lambert s cosine law: I = cosθ θ I 0 I θ is the directional radiant intensity in W sr -1 of a plane source in the direction θ and I 0 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 5 c1λ thermometry, is given by L λ = ε λ ( θ, T ), exp( c / λ T ) 1 2 where ε λ (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, 6

7 radiative heat transfer is the mode of heat exchange between the Sun and Earth; hence the term solar radiation. Radiation Radiation Incident Reflected, ρ G Emitted, ε G Radiation, G Fig. 4 Radiative properties of a surface Radiation Transmitted, τg Figure 4 shows that when radiant energy G (W/m 2 ) 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: 4 E = ε σ AT In this equation, σ is called the Stefan-Boltzmann constant and is equal to W/m 2 K; 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 = 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 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. 7

8 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) 8