Documents

10.pdf

Categories
Published
of 94
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Description
Chapter 10: Radiation Section 10.2: Emission of Radiation by a Blackbody 10.2-1 (10-1 in text) Radiation that passes through the atmosphere surrounding our planet is absorbed to an extent that depends on its wavelength due to the presence of gases such as water vapor, oxygen, carbon dioxide and methane. However, there is a relatively large range of wavelengths between 8 and 13 microns for which there is relatively little absorption in the atmosphere and thus, the tr
Transcript
  Chapter 10: Radiation Section 10.2: Emission of Radiation by a Blackbody  10.2-1 (10-1 in text) Radiation that passes through the atmosphere surrounding our planet is absorbed to an extent that depends on its wavelength due to the presence of gases such as water vapor, oxygen, carbon dioxide and methane. However, there is a relatively large range of wavelengths between 8 and 13 microns for which there is relatively little absorption in the atmosphere and thus, the transmittance of atmosphere is high. This wavelength band is called the atmospheric window. Infrared detectors on satellites measure the relative amount of infrared radiation emitted from the ground in this wavelength band in order provide an indication of the ground temperature. a) What fraction of the radiation from sun is in the atmospheric window? The sun can  be approximated as a blackbody source at 5780 K.  b) Prepare a plot of the fraction of the thermal radiation emitted between 8 and 13 microns to the total radiation emitted by the ground for temperatures between -10°C to 30°C. c) Based on your answers to a) and b), indicate whether radiation in the atmospheric window can provides a clear indication of surface temperature to satellite detectors.  10.2-2 A new stove top uses a halogen lamp that is placed under a glass surface as the heat source for each burner. The advantages of this design are that the lamp delivers instant heat and responds very quickly to changes in the temperature setting. The heating element of the lamp is a circular disk that is insulated on its back and has a diameter of  D l  = 2.4 cm. The design specification for the stove top requires that it be capable of heating V  w  = 2 liters of water from T  ini  = 25°C to boiling in less than t  b   = 8 minutes at a location that is at sea level. Assume that the heating element radiates a blackbody and that all of the radiation emitted by the heating element is absorbed by the water. Ignore convection for this problem. a) If the efficiency of the burner is 100% (i.e., all electrical power provided to the halogen heating element is transferred to the water) then what is the minimum required electrical power input to the unit in order to meet the design specification?  b) Estimate the temperature of the heating element required. c) Will the radiant energy from this stove top unit be visible? What is the fraction of the radiation emitted by the element that is visible?  10.2-3 The solar constant, G sc  ,  is the energy from the sun per unit time that would be received on a unit area of surface perpendicular to the direction of the propagation of the radiation at the mean earth-sun distance if there were no atmosphere surrounding earth. We know that the diameter of the sun is approximately    D sun  = 1.39x10 9  m and that the surface of the sun is at an equivalent temperature of approximately T  sun  = 5780 K. The diameter of the earth is  D earth  = 1.276x10 7  m and the mean earth-sun distance is  R  = 1.497x10 11  m. a.) Estimate the value of the solar constant.  b.) In 2003, the amounts of primary energy consumed in the world as a result of combustion of coal, natural gas, and oil was 140x10 9  GJ/yr, 95x10 9  GJ/yr and 190x10 9  GJ/yr, respectively. Compare the amount of energy that is radiated to earth from the sun to the annual energy consumed by combustion of these fossil fuels. c) The first law of thermodynamics indicates that energy cannot be destroyed. If you answer to part (b) indicated that more energy strikes the planet in year than we use then explain why we are experiencing an energy shortage.  10.2-4 (10-2 in text)  Photovoltaic cells convert a portion of the radiation that is incident on their surface into electrical power. The efficiency of the cells is defined as the ratio of the electrical power produced to the incident radiation. The efficiency of solar cells is dependent upon the wavelength distribution of the incident radiation. An explanation for this behavior was srcinally provided by Einstein and initiated the discovery of quantum theory. Radiation can be considered to consist of flux of photons. The energy per photon ( e ) is: / e hc  λ  =  where h  is Planck’s constant, c  is the speed of light, and λ   is the wavelength of the radiation. The number of photons per unit area and time is the ratio of the spectral emissive power, , b  E  λ   to the energy of a single photon, e . When radiation strikes a material, it may dislodge electrons. However, the electrons are held in place by forces that must be overcome. Only those photons that have energy above a material-specific limit, called the band-gap energy limit (i.e., photons with wavelengths lower than bandgap λ  ) are able to dislodge an electron. In addition, photons having energy above the  band-gap limit are still only able to dislodge one electron per photon; therefore, only a fraction of their energy, equal to λ   / bandgap λ  , is useful for providing electrical current. Assuming that there are no imperfections in the material that would prevent dislodging of an electron and that none of the dislodged electrons recombine (i.e, a quantum efficiency of 1), the efficiency of a photovoltaic cell can be expressed as: 00 bandgap b,bandgapb,  E d  E d  λ λ λ  λ λ λ η λ  ∞ = ∫∫  a.) Calculate the maximum efficiency of a silicon solar cell that has a band-gap wavelength of bandgap λ  = 1.12 µm that is irradiated by solar energy having an equivalent blackbody temperature of 5780 K.  b) Calculate the maximum efficiency of a silicon solar cell that has a band-gap wavelength of bandgap λ  = 1.12 µm that is irradiated by incandescent light produced by a  black tungsten filament at 2700 K. c) Repeat part (a) for a gallium arsenide cell that has a band-gap wavelength of bandgap λ  = 0.73 µm, corresponding to a band gap energy of 1.7 ev. d) Plot the efficiency versus bandgap wavelength for solar irradiation. What bandgap wavelength provides the highest efficiency?
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks