1!Lecture Ch. 3a!• Types of transfers!• Radiative transfer and quantum mechanics!– Kirchoff’s law !– Blackbody radiation!– Planck’s radiation law!– Wien’s displacement law!– Stefan-Boltzmann law!Curry and Webster, Ch. 3 pp. 74-85!For Thursday: Read Ch. 3 and Ch. 12 pp. 331-337 !For Tuesday, 10/14: Homework Ch. 3, pp.94-95:#1,2,3; Read Ch. 4!What are the 3 ways heat can be transferred?!• Radiation: transfer by electromagnetic waves. !• Conduction: transfer by molecular collisions. !• Convection: transfer by circulation of a fluid.!Image from: http://www.uwsp.edu/geo/faculty/ritter/geog101/uwsp_lectures/ lecture_radiation_energy_concepts.html#Radiation Curry and Webster:!• Energy!– Radiation!– Conduction!– Advection !• Scalars!– Diffusion!– Advection!Scalar Transport!• Mass conservation!– A continuity equation expresses a conservation law by equating a net flux over a surface with a loss or gain of material within the surface. !– Continuity equations often can be expressed in either integral or differential form.!• Transport!Energy Transport!• Thermodynamic changes with time!• Thermodynamic changes with transport!Sun - our star – the source of most of our energy!For the entire earth, climate can be explained by: 1) the amount of sunlight received and 2) the character of the surface receiving it. Solar Spectrum!2!Peak!Area Under Curve!Planck’s Radiation Law!• Direct consequence of quantum theory!Solar Radiation!• Luminosity of the sun L0 ~ 3.9x1026 W (p. 331)!• Irradiance F=Luminosity/Area=L0/(4πr2)= 6.44x107 W/m2!– rsun=6.96x108 m [p. 437]!• Estimate blackbody radiation TBB,sun=(F/σ)0.25~ 5800K!– σ=5.67x10-8 W m-2 K-4 [p. 437]!• Use Wien’s law to evaluate λsun ~ 0.5 µm (visible)!• Similarly, λearth ~ 10 µm (infrared) for Tearth ~ 300K!Radiance and Irradiance!Radiant energy !per unit time!Surface area!I [W m-2 sr-1 ]!Q!F [W m-2]!Q!From one direction!From all directions!Wavelength Dependence!• Shortwave!– Solar!– Wavelengths 0.3-4 µm!• Longwave!– Terrestrial!– Wavelengths 4-200 µm!Wien’s Displacement Law!• Inverse dependence of wavelength on temperature!This is the location of the peak!!3!Radiation Laws - Wien's Displacement Law!• Although all known objects emit all forms of electromagnetic radiation, the wavelength of most intense radiation is inversely proportional to the T. ( 1/T) • Implications: • Sun emits @ ~ 6000 deg Kelvin • Earth emits @ 288 deg Kelvin, • Which will emit radiation at the longer wavelength? • Earth • The peak of Solar output is in the visible (light, shorter) part of the electromagnetic spectrum while the Earth, emits most of its energy in the infrared (heat, longer) portion of the electromagnetic spectrum Radiation Laws - Wien's displacement law!• What does this mean in terms of the Earth and the Sun? • Warm objects, Sun (6000°K) emit peak radiation at relatively short wavelengths (0.5 micrometers ( 1 millionth of a meter) = yellow-green visible) • Colder objects Earth-atmosphere (average T of 288 °K, 15°C, 59°F) emit peak radiation at longer wavelengths ( 10 microns – infrared part of the spectrum) • Most of the sun's energy is emitted in a spectrum from 0.15 µm to 4 µm. 41% of it is visible, 9% is uv, 50 % infra-red. • Earths radiant energy, stretches from 4 to 100µm, with maximum energy falling at about 10.1 µm (infrared). Stefan-Boltzmann Law!• Describes T4 dependence of emission!This is the area under the curve!!Blackbody Radiation!• Maximum possible emission of radiation!Comparison -Earth & Sun Radiation!• Sun – more energy & shorter wavelength • Earth-lower energy and longer wavelength Radiation Laws - Black Body Radiation!• Several physical laws describe the properties of electromagnetic radiation that is emitted by a perfect radiator, a so-called black body. • By definition, at a given temperature, a black body absorbs all radiation incident on it at every wavelength and emits all radiation at every wavelength at the maximum rate possible for a given temperature; • No radiation is reflected. • A blackbody is therefore a perfect absorber and a perfect emitter.4!Radiation Laws - Black Body Radiation!• The term black body can be misleading because the concept does not refer to color. • Objects that do not appear black may none the less be be blackbodies, perfect radiators. • Most gases are not blackbodies (see instead Kirchoff’s Law) • Both the Sun and the Earth closely approximate perfect radiators, so that we can apply blackbody radiation laws to them. • We'll discuss 2 laws for blackbody radiation, 1) Wien's displacement law 2) Stefan-Boltzmann law. Radiation Laws - Stefan-Boltzmann law !• Would you expect the same amount of electromagnetic radiation to be emitted by the Earth and Sun? • No. The total energy radiated by an object is proportional to the fourth power of it's absolute T • F = k (T4) = Stefan-Boltzmann law. • F (rate of energy emitted) • k = Stefan-Boltzmann constant ( 5.67 x 10-8 Wm-2 K-4) • Sun radiates at a much higher temperature than Earth.- • Sun’s energy output/m2 = 160,000 that of Earth Radiant Energy!• Direct!– Parallel beam!– One direction !• Diffuse!– Isotropic!– All directions!Radiative Transfer!• Absorption, Transmission, Reflection!Energy Balance!From Cunningham & Cunningham, 2004, Fig. 9.2 Reflected = 25 + 5 = 30 Absorbed = 25 + 45 = 70 Sun’s energy is emitted in the form of electromagnetic radiation (Radiant Energy)!• Radiant energy can interact with matter in 3 ways. !• Most often its behavior is a combination of two or more of these modes !• Reflection - there is no change in the matter because of the radiant energy that strikes it and it does not let the energy pass through it (i.e. it is opaque to the radiant energy), then it reflects the energy. Reflection only changes the direction of the beam of radiant energy, not its wavelength or amplitude. !• Transmission - matter allows radiant energy to pass through it unchanged. Again, there is no change in any of the properties of the radiant energy. !• Absorption –energy is transferred from the radiant beam to the
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