Take away concepts. What is Energy? Solar Energy. EM Radiation. Properties of waves. Solar Radiation Emission and Absorption

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1 Take away concepts Solar Radiation Emission and Absorption 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. V Climate and Society What is Energy? Energy: The ability to do work. Energy measured in Joules (1 J = 0.24 calories). Power measured in Watts (1 J/s) Energy is always conserved (1st law of TD). Energy can be changed from one form to another, but it cannot be created or destroyed. EM Radiation 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) Properties of waves Amplitude (A) Wavelength (µm) Period (sec) Frequency (1/sec) c is constant Since c is constant, frequency of EM wave emission related to electron vibration Warm things have more energy than cold things, so.? 1

2 Wein s Law Blackbody Radiation λmax = a / T A blackbody absorbs and emits radiation at 100% efficiency (experimentally, they use graphite, or carbon nanotubes) Where: λmax a T = 2898, constant emitter temperature (in K) Recall that K = T C Across all wavelengths Sun s temperature is 5800K What s its wavelength? The Sun s temperature is 5800 K, that is the wavelength of its radiation? λmax = a / T 5000 µm 50 µm 0.5 µm 2 µm 20µm is wavelength of emitted radiation (in µm) energy in = energy out a. b. c. d. e. emission wavelength and temperature λmax is wavelength of emitted radiation (in µm) a T = 2898, constant emitter temperature (in K) What s your wavelength? λmax = a / T (a = 2898) Your body is 37 C or = 310K Recall that K = T C λmax =? 9.4 µm (far infrared) Earth as we see it (visible) Earth s Infrared Glow : 15µm 2

3 Electromagnetic spectrum Visualizing emission temperatures hot 9 µm cold Sunny day: 6000K Sunset: 3200K Candlelight: 1500K 0.5 µm Blackbody applet: 1 µm = 1000 nm The effect of distance on radiation the 1 / r 2 rule Mars is 1.52 AU (1 AU = earth-sun distance = 1.5 x m) Using 1/ r 2 rule 1 / (1.5*1.5) = 0.44 Mars receives ~44% of the Earth s solar radiation. Sun emission decreases in proportion to 1 / r 2 of the Sun-Planet distance Jupiter is roughly 5 AU from the Sun, what fraction of Earth s solar radiation does it get? a. 1/2 b. 1/5 c. 1/10 d. 1/25 e. 1/125 Summary so far Wein s Law (emission freq. and temperature) The 1 / r 2 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 3

4 Stefan - Boltzmann Law Energy emitted by a black body is greatly dependent on its temperature: I = (1-α) σ Calculating the Earth s Effective Temperature Easy as T4 Where: I = Black body energy radiation σ = (Constant) 5.67x10-8 Watts/m2/K4 T = temperature in Kelvin 1. Calculate solar output. 2. Calculate solar energy reaching the Earth. 3. Calculate the temperature the Earth should be with this energy receipt. α = albedo ( reflectivity ) Example: Sun surface is 5800K, so I = 6.4 x 107 W/m2 1. Calculate solar output. Calculate Sun temperature assuming it behaves as a blackbody (knowing that λsun= 0.5µm). 2. Calculate solar energy reaching the Earth. Simple Geometry. (recall the inverse square law..) From S-B law: Isun = 6.4 x 10 7 W/m2 Earth-Sun distance (D): 1.5 x 1011 m Area of sphere = 4π r 2 We need surface area of sun: Area = 4πr2 = 4π (6.96x108 m) = 6.2 x m2 So, 3.86 x Watts / (4π (1.5 x 1011 m)2 ) Total Sun emission: 3.86 x 1026 Watts (!) Earth s incoming solar radiation: 1365 W/m2 Solar Emission Power 3. Earth energy in = energy out You have Iearth, solve for Tearth Stefan - Boltzmann law: Iearth = (1-α) σ 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 Solve for 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 natural greenhouse effect. that is: (0.7)*(0.25)*1365 = energy that reaches Earth surface Energy in = 239 W/m2 = σ T4 4

5 So what Earth s radiation wavelength? Emission Spectra: Sun and Earth λ max = a / T Where: λ max is wavelength of emitted radiation (in µm) a = 2898, constant T emitter temperature (in K) 0.5 µm 9 µm 15 µm If Earth effective temperature is 255K What s the wavelength? Radiation and Matter Emission Spectra: Sun and Earth Also dependent upon the frequency of radiation! (next lecture) Blackbody emission curves and absorption bands Why is the Sky blue? Rayleigh scattering of incoming, short wavelength radiation (photons with specific energy) Radiation scattered by O 3, O 2 in stratosphere (10-50 km) 5

6 Why are sunsets red? Blue wavelengths are scattered/ absorbed Red and orange pass through to surface 6

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