VIEWS: 14 PAGES: 26 POSTED ON: 9/16/2009
Solar Radiation: Emission and Absorption Qu ickTime™ an d a TIFF ( U comp ress ed) dec ompr esso r n are n eeded to see this pic tur e. QuickTime™ and a TI FF (Uncompres sed) decompressor are needed to s ee this picture. QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. V1003 - Science and Society Take away concepts 1. 2. 3. 4. 5. 6. 7. Conservation of energy. Black body radiation principle Emission wavelength and temperature (Wein’s Law). Radiation vs. distance relation Black body energy flux (Stefan-Boltzmann Law) Effective temperature calculation, differences from actual temperature. Why there are seasons. What is Energy? Energy is an abstract quantity that matter or a waves possess. “The ability to do work”. Energy measured in Joules (1 J = 0.24 calories). Power measured in Watts (1 J/s) (what’s a “kilowatt hour”?) Energy is always conserved (1st law of TD). Energy can be changed from one form to another, but it cannot be created or destroyed. Types of Energy ･Kinetic Energy ･Chemical energy ･Gravitational energy ･Electrical energy ･Mass energy ･Thermal energy ･Elastic energy ･Nuclear energy ･Radiant energy Solar Energy Nuclear fusion: H to He Emits Electromagnetic radiation (radiant E) EM waves behave like particles and waves EM travels at c (3 x 108 m/s) Quick Time™ and a TIFF (Unc ompres s ed) dec ompres s or are needed to see this pic ture. EM Radiation QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. Since c is constant, frequency of EM wave emission related to electron vibration Warm things have more energy than cold things, so ….? Properties of waves Amplitude (A) Wavelength (µm) Period (sec) Frequency (1/sec) c is constant QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. Blackbody Radiation A “blackbody” absorbs and emits radiation at 100% efficiency. QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. energy in = energy out Across all wavelengths Wein’s Law emission wavelength and temperature max = a / T Where: max a T is wavelength of emitted QuickTime™ and a TI FF (Uncompres sed) decompressor are needed to s ee this picture. radiation (in µm) = 2898, constant emitter temperature (in K) Recall that K = T°C - 273.15 Sun’s temperature is 5800K What’s its wavelength? What’s your wavelength? max = a / T (a = 2898) Your body is 37°C or 37+273 = 310K max = ? 9.4 µm (far infrared) Earth’s Infrared “Glow”: 15µm Electromagnetic spectrum 9 µm “hot” “cold” 0.5 µm 1 µm = 1000 nm Visualizing emission temperatures Sunny day: 6000K Sunset: 3200K Candlelight: 1500K QuickTime™ and a TI FF (LZW) decompressor are needed to see this picture. Blackbody applet: http://qsad.bu.edu/applets/blackbody/applet.html The effect of distance on radiation “the 1 / r2 rule” QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. Sun emission decreases in proportion to 1 / r2 of the Sun-Planet distance Mars is 1.52 AU (1 AU = earth-sun distance = 1.5 x 1011 m) QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. Using 1/ r2 rule… QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. 1 / (1.5*1.5) = 0.44 Mars receives ~44% of the Earth’s solar radiation. QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. Summary so far… Wein’s Law (emission freq. and temperature) The “1 / r2” law (radiation amt and distance) Now let’s calculate the total radiative energy flux into or out of a planet using the: Stefan - Boltzmann Law Stefan - Boltzmann Law Energy emitted by a black body is greatly dependent on its temperature: I = T4 Where: I = Black body energy radiation = (Constant) 5.67x10-8 Watts/m2/K4 T = temperature in Kelvin Example: Sun surface is 5800K, so I = 6.4 x 107 W/m2 Calculating the Earth’s “Effective Temperature” Easy as 1-2-3… 1. Calculate solar output. 2. Calculate solar energy reaching the Earth. 3. Calculate the temperature the Earth should be with this energy receipt. 1. Calculate solar output. Calculate Sun temperature assuming it behaves as a blackbody (knowing that sun= 0.5µm). From S-B law: Isun = 6.4 x 10 7 W/m2 We need surface area of sun: Area = 4r2 = 4(6.96x108 m) = 6.2 x 10 18 m2 Total Sun emission: 3.86 x Solar Emission Power 1026 Watts (!) QuickTime™ and a TI FF (Uncompres sed) decompressor are needed to s ee this picture. 2. Calculate solar energy reaching the Earth. Simple Geometry. (recall the inverse square law..) Earth-Sun distance (D): 1.5 x 1011 m Earth radius (r): 6.7 x 108 m So, 3.86 x 10 26 Watts / (4 (1.5 x 1011 m)2 ) Earth’s incoming solar radiation: 1365 W/m2 3. Earth energy in = energy out You have Iearth, solve for Tearth Stefan - Boltzmann law: Iearth = Tearth4 Incoming solar radiation: 1365 W/m2 About 30% is reflected away by ice, clouds, etc.: reduced to 955 W/m2 Incoming on dayside only (DISK), but outgoing everywhere (SPHERE), so outgoing is 1/4 of incoming, or 239 W/m2 QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. 239 W/m2 = T4 Teffective = 255K Earth Effective temp: 255 K, or -18°C Earth Actual temp: 288K, or +15°C … the difference of +33°C is due to the greenhouse effect! QuickTime™ and a TI FF (Uncompres sed) decompress or are needed to s ee this picture. Qu ickTime™ an d a TIFF ( U comp ress ed) dec ompr esso r n are n eeded to see this pic tur e. So what Earth’s radiation wavelength? max = a / T Where: max a T is wavelength of emitted QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. radiation (in µm) = 2898, constant emitter temperature (in K) If Earth effective temperature is 255K What’s the wavelength? Emission Spectra: Sun and Earth QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. 0.5 µm 9 µm 15 µm Radiation and Matter QuickTime™ and a TI FF (Uncompressed) decompressor are needed to see this picture. Also dependent upon the frequency of radiation! (next lecture)