10 April, 2014 The Sun Blackbody radiation and the greenhouse effect Keywords 1. Radiation: Law of Stefan-Boltzmann 2. Radiation and the Earth atmosphere 3. Greenhouse effect (simple models) Ronald Griessen 2008 Vrije Universiteit, Amsterdam 1 2 What heats the 564 million tons of hydrogen are converted into 560 million tons of helium per second (0.42 MeV) E=mc2 3.8 x 1026 W 1 MeV=1.6 x 10-13 J 63 MW/m2 3 1. Measuring the Sun’s temperature 564 million tons of hydrogen are converted into 560 million tons of helium per second 3.8 x 1026 W Planck’s Law 30000 Spectral Irradiance (W/m /eV)) E=mc2 4 2 But how do we know this? dE 2 2 h 2 h d c e k BT 1 25000 63 MW/m2 20000 5800 K 15000 10000 T = 5800 K 5000 0 0 2 4 6 8 Photon energy [eV] 5 6 1 10 April, 2014 2. Calculating the total power World Total Primary Energy Supply 2005 3.8 x 1026 W 3.8 x 1026 W T = 5800 K Stefan–Boltzmann law = 5.67x10-8Wm-2K-4 17.2 TW 8 7 http://www.iea.org/textbase/nppdf/free/2007/Key_Stats_2007.pdf IEA: KeyWorld2013.pdf Solar area Sahara 1368 W/m2 1.5 x 1011 m Future world power consumption 1010 persons 5 kW/person = 50 TW 148 m2/person R2 63 MW/m2 Solar constant: 1350 W/m2 50% reaches the Earth’s surface 25% due to R2/4R2 Efficiency of photovoltaics: 20%. 1.48 106 km2 R2 7 x 108 m 10 9 50 TW Heat transfer through radiation 1200 x 1200 km2 1200 x 1200 km2 63 MW/m2 63 MW/m2 0.8 km2 gives 50 TW 0.8 km2 gives 50 TW 11 12 2 10 April, 2014 Summary heat transfer by radiation You are radiating, too Stefan–Boltzmann law Spectral energy density dE/df S = 5.67 x 10-8 T4 [W/m2] Planck’s Law 1.5 dE 2 2 h 2 h d c e k BT 1 1.0 300 K 600 K 900 K 1200 K 0.5 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Photon energy [eV] 13 Some constants Planck's constant: h 6.626 0693(11)×10-34 Js = 4.135 667 43(35)×10-15 eVs Wien's displacement constant b = 2.897 7685(51)×10–3 mK max Tb 1.380 6505(24)×10−23 J/K = 8.617 343(15)×10−5 eV/K Boltzmann constant: kB Stefan–Boltzmann constant: 5.670 400(40)×10−8 Wm-2K-4 Speed of light: c 299 792 458 m/s 14 Spectral irradiance on Earth dE 2 2 h 2 h d c e k BT 1 15 16 Incoming and reflected solar energy 70% absorbed 100 % The Greenhouse effect Atmosphere: 6% Clouds: 20 % Earth’s surface: 4 % 17 18 3 10 April, 2014 Without atmosphere 5600 K Absorption by the atmosphere 260 K 5600 K 260 K 19 Why water and CO2 ? 20 Earth without an atmosphere equilibrium: O H O + ASSun _ _ H + SSun C O R 2 S Sun 1 A 4 R 2 S Earth 4 1 A S Sun 4S Earth 4 TEarth 1 − 0. 31366 W m−2 4 5. 67 10 −8 W m−2 K −4 T 4 T Earth 255 K SE _ (1-A)SSun _ + _ + e.m. wave e.m. wave 21 Earth with totally absorbing atmosphere: Greenhouse effect Sa ASSun SSun T Earth −18 o C 2 Sa S Earth R 2 S Sun 1 A 4 R 2 Sa 4 R 2 S Earth SE (1-A)SSun Sa S Sun 1 A 4S a 4S Earth 4 S Sun 1 A 2S Earth 2 TEarth T Earth 303 K T Earth 30 o23C 22 Direct Global Warming Potentials (mass basis) relative to carbon dioxide GAS Pre-1750 Current concentra tropospheric -tion concentration GWP *) (100-year time horizon) Atmospheric lifetime (years) variable Carbon dioxide (CO2) 280 ppm 377.3 ppm 1 Methane (CH4) 730 ppb 1847 ppb 23 12 Nitrous oxide (N2O) 270 ppb 319 ppb 296 114 Tropospheric ozone (O3) 25 ppb 34 ppb n.a. hours-days CFC-11 (CCl3F) zero 253 ppt 4600 45 HFC-23 (CHF3) zero 14 ppt 12000 260 Perfluoroethane (C2F6) zero 3 ppt 11900 10000 *) Global Warming Potential GWP T 0 Igas Mgas dt T 0 ICO 2 MCO 2 dt I = radiative forcing M = amount of gas at time t 24 4 10 April, 2014 Radiative forcing Radiative forcing conc ppmv warming effect (oC) H2O vapour 5000 20.6 CO2 360 7.2 O3 0.03 2.4 N2O 0.3 0.8 CH4 1.7 0.8 TOTAL sun spots 33.0 without atmosphere 25 warmer more H2O feedback ! in reality T Earth 288 K (15 o C) T Earth 255 K 26 Effect of change in solar “constant” axial tilt (nutation): 41 ky Stefan–Boltzmann law P T4 excentricity: 95,125,400 ky longitude of perihelion precession: 19,22,24 ky P T 4 dP dT 20% variation! insolation 4T 3 dP P 4T 3 dT T 4 dT T 1 dP 4 P 4dT T dP 4T 3 dT Will the temperature also change by 20%? 27 Radiative forcing dP P 20% dT T 5% ΔT 15 K Real past variability is < 15 K. The 20% in dP/P is for 65oN, average over earth is much smaller. 28 Non-linear relation: warming vs conc. 100% CO2 increase 280386 ppm gives S = 1.66 0% W/m2 Clouds increase greenhouse effect by S = 30 W/m2 Clouds reduce solar absorption by S = 48 W/m2 Total atmospheric greenhouse effect is S = 140 W/m2 1 dP 4 P total greenhouse dT 1 dP 4 P T 1 4 CO2 increase dT 1 dP 4 P T 1 4 dT T 140 1 1366 4 1.66 1 1366 4 289 29. 619 K ΔF CO2 lnC/C0 with 5. 3 289 0. 351 2 K 29 30 5 10 April, 2014 Sunspots and temperature More Sun spots: (1) More irradiance (2) More ozone More greenhouse 31 Conclusions 32 What can we do? CO2 and Temperature CO2 Find sources of energy that do not produce CO2 400 CO2 (ppm) [75 years smoothed] 350 • geothermal heat • chemical (CO2) • gravitational (tides) flow • nuclear we don’t do this • solar solar heat heat photovoltaics semiconductor bioenergy we don’t do this hydropower flow wavepower flow Law Dome Ice Core Mauna Loa 300 250 1000 1200 1400 1600 Date 1800 2000 http://cdiac.ornl.gov/ftp/trends/co2/lawdome.combined.dat CO2 is certainly rising fast It is 40% higher now that it was during the past 106 y politics The temperature seems to be rising heat flow/fluid dynamics semiconductor What will we do? Introduction of new energy vectors, CO2 regulations etc. YOU 33 How does it work? How much energy can we get from it? 34 Leerdoelen Isolatie woning isolatie Pipelines Bulk Straling: satelliet (microgolf Elektisch Chemisch: Energieopslag Energietransport Chemisch ‐ fuelcells Warmte – phase change Electrisch: batterij, condens Mechanisch: vliegwiel, wate Windmolens Fotovoltaisch Fotolytisch Solarthermal Solar ponds Solar chimney Warmtepomp Getijden, golfkracht Waterkracht OTEC Geothermal Omgekeerde osmose / blue Paleotemperatuur + oorzak Wat doet CO2, wat is het gr Klimaat aarde en IPCC Energieopwekking Warmte balans aarde Klimaatmodellen solar irradiance (Wm-2) Sunspots and solar input to Earth Thermodynamica Temperatuur (TiplerMosca p 564) x Ideale gaswet (TiplerMosca p 569) – nodig voor Maxwell-Boltzman distributie (TiplerMosca p 582 Thermal energy + Carnot – gasturbine voor elektr Warmtepomp Latent heat (TiplerMosca p 594) – warmte opslag Heat capacity (TiplerMosca p 606, 611) Straling x Geleiding x x x x x x x x x x x x x x x x Gibbs Free energy, (Electro+)Chemical potential Equipartitie en kinetische gastheorie (TiplerMosca Wet van Wien x x x x x x x x x x x x Stromingsleer Continuiteitsvergelijking (AndrewsJelly 54) x Diffusie van warmte en atomen x Bernouilli - windmolen Pitot/Venturi (TiplerMosca p 443) Lift (AndrewsJ Magnus effect (AndrewsJelly 64) Betz (windmolens) Turninevergelijking (AndrewsJ Snelheisprofiel in buizen - waterkrachtopslag bijv. Poiseuille Wet van Archimedes - getijdekracht boeien Stability of ships (Stephenson) - getijdekracht boe The force on a water dam (TiplerMosca p 427) Drukverdeling in de atmosfeer (TiplerMosca p 43 Viscositeit (TiplerMosca p 446) x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Vaste Stof Bandstructuur PN – junctie met/zonder licht Basic electrochemistry Nernst equation (for Erwin) x x de tol x x x Mechanica x x x x x 35 6