Physical Meteorology ESCI 340
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This 4 page Class Notes was uploaded by Cordie Miller on Thursday October 15, 2015. The Class Notes belongs to ESCI 340 at Millersville University of Pennsylvania taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/223519/esci-340-millersville-university-of-pennsylvania in Earth Sciences at Millersville University of Pennsylvania.
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Date Created: 10/15/15
ESCI 340 Physical Meteorology Radiation Lesson 2 Radiation Laws Dr DeCaria References Atmospheric Science An Introductory Survey Wallace and Hobbs An Introduction to Atmospheric Radiation Liou A First Course in Atmospheric Radiation Petty Reading Petty Chapter 6 up through Section 63 PLANCK S LAW 0 A blackbody is a perfect emitter and absorber of radiation 0 The monochromatic intensity emitted by a blackbody is described by the Planck function BA 2 5 2hc2 xi exphck1T 1 0 k is the Boltzmann constant and is 138gtlt103923 J K 1 0 h is Planck s constant and is 6626x10 34 J s 0 c is the speed of light in a vacuum and is 29979gtlt108 m s l 0 NOTE B lis monochromatic intensity and has units of W m 2 sr391 um 1 I Blackbody radiation is isotropic 0 In a prior lesson we showed that for isotropic radiation that ux and intensity are related by F 7r Therefore the monochromatic ux emitted by a blackbody is FEB1 52 h02 a xi exphck1T 1 where the subscript BB reminds us that this is for a blackbody 0 If we define two new constants c1 2711ic2 and cz hck then Planck s law can be written in a more concise way as F 01 BM lsexpc21T 1 WIEN S DISPLACEMENT LAW 0 Wien s displacement law gives the wavelength of maximum emission for a blackbody O Wien s displacement law is found by setting 8F 881 0 and solving for xi see exercises to get 1m 2 2897 um K i T STEFANBOLTZMANN LAW 0 The StefanBoltzmann law gives the total ux emitted from a blackbody It is found by c F 1 dl BB 15 expcZ1T 1 O This integral is see exercises FEB 0T4 where 039 is the StefanBoltzmann constant and is 567X10 g Wm ZK 4 ABSORPTIVITY AND EMISSIVITY O Nonblackbodies emit less radiation than do blackbodies O The ratio of emitted monochromatic ux to blackbody monochromatic ux is known as the monochromatic emissivity 61 51 E F 1 F 331 0 Emissivity is always between 0 and 1 O The ratio of emitted ux to blackbody ux is known as the graybody emissivity s 8 E F FEB O The ux emitted from a gray body is F sFBB 039T4 Nonblackbodies absorb less radiation than do blackbodies The ratio of absorbed monochromatic ux to blackbody absorbed monochromatic ux is known as absorptivilfy a 1 0 Absorptivity is always between 0 and 1 The ratio of emitted flux to blackbody absorbed ux is known as the graybody absorptivity a KIRCHOFF S LAW 0 Kirchoff s law states that an objects emissivity equals its absorptivity a1 81 0 Objects that are good emitters at a particular wavelength are good absorbers at that wavelength EXERCISES 1 Starting with F 01 BM is expcZ1T 1 make the variable substitution x 2 1T Then nd the value of x that maximizes FEB to show that C 2m 7 where C 2897 umK 2 Starting with m 01 FEB 1156Xpcz1T 1d1 make the variable substitution toget 4 3 F61 J x dx expx l 20 and then evaluate the integral to obtain the StefanBoltzmann Law What is the blackbody ux of the Sun s surface T 6000K 5quot What is the blackbody ux of the Earth s surface T 288K 5 5quot Are the graybody and monochromatic emissivities related via 8 Sid1 0
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