1Flux and the ‘inverse-square’ lawRadiation flux is the amount of energy passing through anarea perpendicular to the radiation beam per unit time. Units: Joules per second per square meter = J s-1 m-2 = Watts per sq. meter = W m-2(Because 1 J s-1 = 1 W, by definition)Flux, S, from a stardrops off with increasingdistance. In fact, it decreaseswith the square of the radialdistance, r, from the star, asS µ 1/ r2.e.g., Sun’s flux at the planet MarsSolar flux=Distancefrom Sun= 1.5 A.U.MarsSolar flux=1370 Wm-2Distancefrom Sun= 1 A.U.EarthReducedby a factorof 1/(1.5)2= 2.25compared toEarth608.9 Wm-2Radiation Recap - 11. Electromagnetic radiation: - propagates through space at speed of light, c- has a characteristic wavelength (l) and frequency (n)- useful to talk about two parts of the spectrum: SW: shortwave (mostly visible; also UV, near-IR) from SunLW: longwave (mostly infrared) from planet2. Radiation and matter interact in 4 ways: - Radiation can be:(i) absorbed(ii) transmitted(iii) reflected (or scattered) - All matter emits radiation(iv) emission by matter2Radiation Primer - 23a. Absorption of radiation causes matterto warm up (or gain heat) 3b. Emission of radiation causes matterto cool down (or lose heat)Radiation Primer - 34. Temperature of matter is crucial because both the wavelength and the total energy of radiation emitted by matter depend upon its temperature.4a. Hotter matter emits shorter wavelengths [Wien’s Law]- Sun: “SW” [ultraviolet (UV), visible, near-infrared]- Earth: “LW ” [infrared (IR)]ground, ocean, atmosphere, clouds, etcalso, moon and other planets4b. Hotter objects emit more total energy. [Stefan-Boltzmann Law]Fig. 3-3Radiation vsWavelength0.3 2.0305Fig. 3-8SunEarthEarthSunStefan-Boltzmann LawHotter objects emit more total energy:Stephan-Boltzmann Law: F = s T40.3 2.0305s= 5.67 ¥10-8 W m-2 K-4 = a constant of natureT is temp in Kelvin, theabsolute temperature scaleT(K) = T(C) + 273.15Applies to an ideal materialknown as a "blackbody".This just means that theemission curve depends only ontemperature.3Kelvin (absolute) Temperature ScaleWhat is the meaning of "absolute zero" temperature?T(K) = T(C) + 273.150-273.15Absolute zero273.150water freezes373.15100water boils(at sea level)Kelvin Scale(K)Celsius Scale(°C)ReferencePointConsider...• Hotter objects emit more total energy• Can there be a negative temperature on the Kelvin scale?• What is the meaning of "temperature", anyway?Kelvin/Boltzmann applicationsStephan-Boltzmann Law: F = s T4where s = 5.67x 10-8 , F is in W/m2, and T is in Kelvin (K)Kelvin vs. Celsius scale: T(K) ≈ T(°C) + 273Qu. 2) An object warms from 0°C to 10 °C.What is the fractional increase in temperature?What is the fractional increase in emitted, radiative energy?Qu. 3) If the Sun’s emitting surface layer (the “photosphere”) were to warm up by10%, by how much would the solar flux increase (as a fractional increase)?Qu. 1) The average surface temperature of the Earth is 15°C. What is this in
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