Lecture notes Renewable Energy sources

what renewable energy source is the fastest growing and lecture notes on renewable energy technology. how renewable energy became unstoppable pdf free downlaod
AlexSwift Profile Pic
AlexSwift,Singapore,Professional
Published Date:14-07-2017
Your Website URL(Optional)
Comment
Lecture notes for Duurzame Energie: Zon, Wind en Water Renewable Energy: Sun, Wind and Water (for 2SBI) dr. R.J. Wijngaarden March 9, 2017Contents 1 Energy: units and orders of magnitude 1 1.1 GETTINGAFEELINGFORENERGY ................. 1 1.2 HUMANPOWER ............................. 2 1.3 USEOFENERGYBYMANKIND.................... 2 2 The Climate and Energy crisis 3 2.1 PALEOCLIMATOLOGY.......................... 3 2.2 PRESENT CHANGES........................... 5 2.3 SOLUTIONS ................................ 7 3 Earth’s climate and the Sun 8 3.1 SolarEnergy................................. 8 3.2 INTRODUCTION ............................. 8 3.3 THESUN.................................. 9 3.3.1 TheenergysourceintheSun ................... 9 3.3.2 Thesolarspectrum ........................ 12 3.4 BLACKBODYRADIATION....................... 14 3.5 THEGREENHOUSEEFFECT ..................... 16 3.5.1 Earthwithoutatmosphere..................... 16 3.5.2 Earthwithatotallyabsorbingatmosphere ........... 18 3.5.3 Intermezzo ............................. 19 3.6 TRENDS IN CO EVOLUTION ..................... 21 2 4 Transport of heat 24 4.1 transportofheatbyconduction ...................... 24 4.2 transportofheatbyconvection ...................... 26 5 Thermal energy and thermodynamics 31 5.1 THEIMPORTANCEOFTHERMODYNAMICS ............ 31 5.2 THEIDEALGAS ............................. 32 iiCONTENTS 5.2.1 Theidealgaslaw.......................... 33 5.2.2 Pressure as the result of the impact of particles on the container walls ................................. 35 5.2.3 The root-mean-square (rms) speed of a molecule in an ideal gas 37 5.2.4 Heat and specificheat....................... 38 5.2.5 Mechanicalequivalentofheat................... 40 5.3 THE FIRST LAW OF THERMODYNAMICS ............. 41 5.3.1 Firstlaw .............................. 41 5.3.2 Application1ofthefirstlaw: Specificheatofanidealgasrevisited 43 5.3.3 Application 2 of the first law: Closed cycle steam power plant . 47 5.3.4 Carnot cycle ............................ 49 5.4 ENTROPY AND THE SECOND LAW OF THERMODYNAMICS . . 56 5.4.1 The second law of thermodynamics and Carnot’s theorem . . . 56 5.4.2 Entropy:anewthermalpotential ................ 57 5.5 ENGINESDESCRIBABLEWITHIDEALGASES........... 64 5.5.1 Stirlingengine ........................... 64 5.5.2 Ottoengine............................. 67 5.5.3 Gasturbine:Joulecycle...................... 68 5.5.4 Heatpumps ............................ 73 5.5.5 Heatpumps:evaporation-condensationcycle .......... 75 5.6 REALGASES ............................... 77 5.6.1 VanderWaalsgases........................ 77 5.6.2 Heatingofwateratconstantpressure............... 80 5.6.3 Steamturbines........................... 82 5.7 CO sequestration ............................. 85 2 5.8 Fuelcells:EnginesnotsubjecttoCarnotcyclelimitations ....... 86 5.8.1 Principleofoperationofafuelcell ................ 86 5.8.2 Usefulthermodynamicpotentials................. 89 5.8.3 Theoretical efficiencyofafuelcell ................ 90 5.8.4 Efficiencyofrealfuelcells. .................... 90 6Introductionto fluiddynamics for energy 92 6.1 INTRODUCTION ............................. 92 6.2 BASICFLUIDDYNAMICS ........................ 92 6.2.1 Stationary fluids .......................... 92 6.2.2 Fluidsinmotion .......................... 96 6.2.3 Liftanddrag ............................ 106 7 Water energy: rivers, reservoirs and tides 107 7.1 FLUID DYNAMICS FOR WATER POWER APPLICATIONS . . . . 107 iiiCONTENTS 7.1.1 Euler’sturbineequation ...................... 107 7.1.2 Hydropowerfromadam ...................... 108 7.1.3 Tidalpower............................. 110 7.1.4 Energyfromwaves ......................... 118 8 Wind energy 123 8.1 Windenergy................................. 123 8.2 Windturbines:theBetzlimit ....................... 123 8.2.1 Powerfromkineticenergyofthewind .............. 124 8.2.2 Changeinkineticenergy ..................... 126 8.2.3 Thrust................................ 127 8.2.4 Extractedpower .......................... 128 8.2.5 Is Betz limit valid for water flow? ................. 130 8.3 Optimaldesignofturbineblades ..................... 131 8.4 Losses .................................... 139 8.4.1 Too large induction factor .................... 139 8.4.2 Effectofdrag ............................ 139 8.4.3 Rotationoftheair ......................... 140 8.5 Turbinedesign ............................... 144 8.6 Wind properties............................... 145 8.7 Windfarms ................................. 147 8.8 Otherideas ................................. 147 9 Quantum mechanics 150 9.1 BasicQuantumPhysicsforSolarEnergy ................. 150 9.2 WAVES ................................... 150 9.2.1 Introduction............................. 150 9.2.2 Thewaveequationforarope ................... 154 9.2.3 Fouriergenerator .......................... 160 9.2.4 Waves in 2D and 3D (can be skipped in a firstreading)..... 160 9.2.5 Summary .............................. 164 9.3 LIGHTBEHAVINGLIKEPARTICLES ................. 166 9.3.1 TheBlackbodyradiation...................... 166 9.3.2 The Photoelectric Effect ...................... 167 9.3.3 TheProductionofX-Rays ..................... 169 9.3.4 The Compton Effect ........................ 171 9.3.5 IsitaWave,oraParticle?..................... 172 9.3.6 ATwo-SlitExperiment....................... 174 9.3.7 Diffraction:UncertaintiesinParticleProperties ......... 177 9.3.8 Summary .............................. 177 ivCONTENTS 9.4 PARTICLESBEHAVINGLIKEWAVES................. 179 9.4.1 ATwo-SlitExperimentwithparticles............... 179 9.4.2 MatterWaveinterference:EvidenceandApplication ...... 183 9.4.3 PropertiesofMatterWaves .................... 186 9.4.4 TheFree-ParticleSchrödingerEquation.............. 189 10 Photovoltaic energy 192 10.1TheFree-ParticleSchrödingerEquation.................. 192 10.1.1 Freeparticleinabox........................ 192 10.1.2 Particle in a finitepotentialwell ................. 196 10.2Simulatingmoleculesandsolids ...................... 197 10.2.1 Singleelectronapproximation ................... 197 10.2.2 The ground state of an-electronsystem............ 200 10.3 Semiconductors............................... 200 10.3.1 Impuritystates:doping ...................... 207 10.3.2 p-njunctions ............................ 208 10.3.3 Photovoltaiccells .......................... 220 11 Final Remarks 226 12 Appendices 227 12.1Appendix:theKingHubbertmethod................... 227 12.1.1 TheVerhulstequation ....................... 227 12.1.2 Verhulstandconsumption ..................... 228 12.1.3 Hubbardlinearization ....................... 229 12.2LISTOFSYMBOLS ............................ 230 vCONTENTS viChapter 1 Energy: units and orders of magnitude 1.1 GETTING A FEELING FOR ENERGY In this chapter we try to develop a feeling for various energy quantities. This is nec- essary, because an energy intuition is missing because (1) energy is ubiquitous in the industrialized nations (2) there is a zoo of units (3) energy and power are mixed up and (4) energy is very cheap. We illustrate our bad intuition by two examples. The energy to climb the Kilimanjaro is just   which is for a typical person roughly −2 80kg× 10ms × 5700m = 46MJ. The energy for heating a bathtub is roughly ∆ with the heat capacity of water per kilogram. Thus we find typically −1 −1 300kg×4200Jkg K ×25K = 315MJ We need nearly 7 times more energy for heating the bath Actually, the amount of energy released when 1 kg of oil is burned is 42MJ about what is needed for heating the bath. With an error of ±30% most hydrocarbons have the same energy content per kilogram. This is, of course because upon burning both the carbon and hydrogen are oxidized and for all hydrocarbons the ratio C : H ' 1 : 2. The shorter hydrocarbons have a larger fraction of hydrogen atoms (becausethe ends of themoleculeshave more relativecontributionof themiddle is shorter) and thus (because the heat of combustion of hydrogen is 120MJkg and of pure carbon is 32MJkg) have a larger heat of combustion. Actually, upon com- bustion water vapor is formed. If this condenses, the heat of condensation is released. Due to this, a higher heating value (HHV) is defined, where the heat of condensation is added to the heat obtained, and a lower heating value (LHV) is defined, where the heat of condensation is not taken into account (e.g. because the water vapor escapes 3 through the chimney). Since the volume of a gas at ambient conditions is roughly 10 3 thevolumeofasolidofthesamecompound,1m of natural gas corresponds roughly 1CHAPTER 1 to 1 kg of gas and thus one expects an energy content of about 40MJkg In fact, for 3 the Groningen gas it is 35MJm (because it contains quite some nitrogen), while for 3 Algerian gas it is 42MJm . Units that are often used are MWh (mega watt hour) 6 9 and toe (tonne of oil equivalent). 1 MWh is 10 W×3600s=36×10 GJ while 1 toe corresponds to 41.868 GJ or 11.630 MWh. 1.2 HUMAN POWER There are many studies concerning the amount of heat and work that can be produced bythehumanbody. Thesenumbershaveofcoursearatherlargevariabilityduetothe variability of man. Typically, a human body in rest emits 50-100 W of thermal power as a consequence of the chemical processes in the body. The mechanical power can be estimatedfromtheruleofthumbofmountaineersthatonecanclimb300mperhour. For a typical person of 80 kg this implies a power of −2   80kg×98ms ×300m  = = '65W (1.1) ∆ 3600s usually, one takes 100W as a maximum for continuous work. For short duration the power can be much higher, say by a factor of 5. 1.3 USE OF ENERGY BY MANKIND In the developed countries, each person uses typically 5kW continuously. Note that this corresponds to each person using5kW65W'77 slaves The present total power consumption of the world is 15.8 TW, but if the total projected world population for 10 2050, that is 10 persons,wouldeachuse5kW the world would need 50 TW, more than three times as much in less than 40 years This is what Richard Smalley calls the terawatt challenge in his famous paper (MRS Bulletin 30 (2005) 412). 2Chapter 2 The Climate and Energy crisis 2.1 PALEOCLIMATOLOGY To try and predict the future, it can be very profitable to study the past. One can try yo predict the future climate based on the long climate history that is logged in the earth. There is a large number of data that has logged local weather: (1) tree rings (2) corals (3) stomatites (4) erosionpatterns etc. The scienceof paleoclimatology tries to extract the temperature, humidity, prevailing wind etc. from such data. Here we only briefly mention some results. Temperature is usually deduced from isotope 16 16 ratios. For example the average isotopic composition of water is H O : HD O: 2 18 H O = 997680 : 320 : 2000 ppm. The more heavy isotopes have a higher boiling 2 point and have a smaller diffusion constant. As a consequence, in the net transport through the atmosphere (driven by solar heating) of water, heavier isotopes tend to stay at the equator, while lighter ones are driven to the poles. If earth is warmer, this isotope separation is of course stronger. Empirically, a roughly linear relation was 18 found between O,defined as µ ¶ µ ¶ 18 18 O O − 16 16 O O sample standard 18  O= ³ ´ (2.1) 18 O 16 O standard and local temperature (at high latitude). Therefore such calibrations are also used for reconstructing paleoclimates. An example of such reconstruction is shown in Fig. 2.1. Clearly, the CO concentration in the past has been much higher that is is now, and 2 the same holds for the average global temperature. From the figure we also see that we now live in an epoch with ice ages. Lets zoom in to more recent times, see Fig. 2.2. Here we see a certain periodicity, withtemperatureandCO movinginparallelupanddown. Unfortunately, 2 3hominids Jurassic Carboniferous Cretasseous Permian Triassic CHAPTER 2 zoom in now hominids dinosaurs Figure 2.1: Past CO concentration and indication of temperature from amount of glaciation. 2 the data cannot resolve whether one precedes the other. All of this plot corresponds to the ice age epoch at the right hand side of Fig. 2.1, but the peaks correspond to period where there are few glaciers. Note that we are exactly living at such moment and from the plot it seems that we may soon see a decrease in temperature The variability in temperature etc. is now believed to be due to the so called Milankovich cycles. This is a variability in the insolation (the amount of sunlight arriving at earth), due to celestial mechanics. In particular, the earth is a spinning top with precession and nutation, and earth experiences forces by the other planets, mainly Jupiter and Saturn. Due to all these mechanisms, the ellipticity or eccentricity of the orbit changes, the obliquity (angle of the axis of earth with respect to the plane of orbit) changes and the axial precession changes, leading to the north pole or south polehavingsummeratthemomentofclosestapproachbetweenearthandsun. Infact, a Fourier transform (or rather power spectrum) of Fig. 2.2 clearly shows peaks at the frequencies corresponding to the effects just mentioned. Since the mechanism behind the variability of Fig 2.2 is now known, it can be used to predict the future. According to the IPCC-4 scientists, the next ice age is not to be expected before 30000 y (FAQ 6.1). Of course, the climate can be influenced by other mechanisms, in particular the CO2 concentration (see below) and albedo. Both of these are presently changed rather dramatically by mankind. 4CHAPTER 2 Figure2.2: ThepastclimateasrecontructedfromtheVostokicecoredata(fromAntarctica). 2.2 PRESENT CHANGES The last half century, human population has been growing extremely fast (super expo- 10 nential). For 2050 a population of 10 people is expected. Since the fuel consumption per capita is also increasing, the fuel consumption is increasing even faster More than 75% of this energy is currently generated by burning fossil fuels (coal, oil and gas), thus releasing CO into the atmosphere. M. King Hubbert predicted in 1956 that the 2 maximumoil productionwouldtakeplacearoundtheyear2000. Itseemsthatwehave now just experienced this peak, although this is still debated. It is, however, more relevant that such a peak exists. And that such a peak is highly problematic: the oil production is then decreasing while demand is increasing. This has recently led to fast increases of the price of crude oil. Clearly, we do need other sources of energy, apart fromfossil. Weshouldnote, however, thatthecoal reservesamounttoabout1000year of current coal use, so we will not run out of fossil fuels altogether very fast. The large scale burning of fossil fuels has ledto a continuous increases inCO 2 concentration in the atmosphere, see Fig. 2.3. As we will see in chapter 3, a higher CO concentrationleadstomoresolarenergybeingcapturedbyearthandthustoextra 2 heating. Indeed a rise in global temperature has been observed, see Fig. 2.4. Possibly asaconsequence, manyglaciersareretreating, theamountof meltwaterontheglaciers of Greenland has increased and the arctic sea ice volume is decreasing. If the decrease ofthearcticseaicevolumecontinuesatthesamerate,thearcticwillbecompletelyfree 5CHAPTER 2 400 Law Dome Ice Core 350 Mauna Loa 300 250 1000 1200 1400 1600 1800 2000 Date http://cdiac.ornl.gov/ftp/trends/co2/lawdome.combined.dat Figure 2.3: CO concentration during the past millenium. 2 ofseaiceby2050. IftheiceofGreenlandwouldmeltcompletely, globalsealevelwould rise by about 7 meter. The effect om northern Europe, however, will be very limited, because the ice on Greenland gravitationally attracts ocean water towards the Arctic. If the ice on Greenland melts, this effect disappears leading to a reduction in sea level in northern Europe. In addition, the mantle of earth experiences a reduced pressure and will move upwards. The total of these three effects could be a small reduction in sea level. Of course, for meting of land ice on Antarctica the opposite holds: the three effects there all contribute to an increase of sea level in Europe. Global average sea level has been observed to increase over the last century and currently increases by about 3 cm per decade. Part of this increase is due to thermal expansion of the oceans as a consequence of increasing global temperature. Theburningoffuelsisconsumingoxygenandindeedtheoxygenconcentration intheatmosphereisdecreasingatarateofabout20ppm/y. Wenowtrytounderstand 12−1 thisnumber. ThecurrentCO emissionis25×10 kgy . TheoxygeninthatCO was 2 2 12 taken from the atmosphere and hence about 16×10 kg O is consumed each year. 2 We now calculate the amount of oxygen in the atmosphere. Its volume is 88km× 2 18 3 3 4(6370km) =44872×10 m theweightof1 m air is about 12kg and 21% of 18 18 that is oxygen. Hence there is 12×45239×10 ×021kg =114×10 kg O in the 2 6 CO (ppm) 75 years smoothed 2 CHAPTER 2 Figure 2.4: Change in global average temperature. atmosphere. Thus the rate of change is: 12−1 O 16×10 kgy 2 −6−1 =140×10 y (2.2) 18 O 114×10 kg 2 −6−1 This is a bit smaller than the observed 20 ×10 y but for such a crude calculation, the result is not bad 2.3 SOLUTIONS Both problems, the effects of CO on climate and the increasing scarcity of fossil fuels, 2 can be solved by (1) changing to nuclear or renewable energy ’sources’ and (2) by energy conservation. These topics are subject of the remaining chapters. In particular theamountofsolarenergyarrivingatearthissolargethatevenwithcurrenttechnology 2 only 156 m of photovoltaic cells would be needed per person. This would require a 10 total area for 10 persons, that is much smaller than the Sahara. In view of the intermittencyofsolarradiation(day-night, summer-winter, clouds)alongtermstorage or long distance transport system is needed. 7Chapter 3 Earth’s climate and the Sun 3.1 Solar Energy 3.2 INTRODUCTION 2 The average solar power incident on the Earth is approx. 1000 W/m or about 100000 TW. This power is far larger than the current world power consumption of 15 TW. Currently, 12 % of the world’s power is supplied by biomass and renewables, while 85% is derived from fossil fuels. Both are the consequence of photosynthesis, in which plants use solar energy to convert water and carbon dioxide into carbohydrates. While biomass is not necessarily a net producer of CO , the burning of fossil fuels definitely 2 is. However, biomassisnotagoodconverterofsolarenergyastheefficiencyofbiomass production is low (0.2 to 2%). 8CHAPTER 3 Figure 3.1: The contribution of renewable energy sources has increased from (1.8%+10.6%+0.1%=12.5%) in 1973 to (2.2%+10%+0.5%=12.7%) in 2005. In percentage this is not impressive. One should however keep in mind that the total energy consumption doubled between 1973 and 2005. Amoreefficient conversion (15%) of solarenergy directly to electrical power is provided by photovoltaic (PV) cells. Currently (2004) these provide a peak power of 2.5 GWthat is predicted to rise to 1000 GWby 2030. The current price of PV cells is too high to be competitive with fossil or nuclear power, for electricity supply to a national grid, but is expected to decrease as new systems are developed. However, PV cells are already very competitive for applications in areas far from a grid. We shall introduce the physics needed to understand the functioning of PV cells in the second part of this course. In a third part we shall look at several types of PV cells and solar thermal collectors. In this firstpartofthecourse,welookatthesourceofenergyoftheSun,the solar energy spectrum and the Greenhouse effect. 3.3 THE SUN 3.3.1 The energy source in the Sun AtthetopoftheatmosphereoftheEarthonemeasuresthatthepowerradiatedbythe 2 8 Sun is 1366 W/m . As the distance between the Sun and the Earth is=15×10 km we conclude that the total power radiated by the Sun is 2 26 4 ×1366 =386×10 W (3.1) 9CHAPTER 3 Figure 3.2: The Sun is a star with a diameter of approximately 1390000 km, about 109 times the diameter of Earth. Per square meter at the Sun surface the power is 26 26 38×10 386×10 7−2 ∼ = 62×10 Wm (3.2) = 2 18 4 62×10  13 The present world power consumption is 15 TW= 1.5×10 W. We conclude 2 thus that an area of 500 × 500 m on the Sun produces enough energy to power the wholepopulationontheEarth. Thisenormousproductionofenergyisduetoanuclear process that converts approx. 564 million tons of hydrogen into 560 million tons of helium per second. This follows directly from Einstein’s famous relation between mass 2 and energy = . There are several processes responsible for energy production, but the most important one is the so-called proton-proton chain reactionexplainedinFig. 3.3. The proton-proton chain reaction is one of several fusion reactions by which stars convert hydrogen to helium, the primary alternativebeingtheCNOcycle(Carbon- Nitrogen-Oxygen cycle). The proton-proton chain dominates in stars the size of the Sun or smaller. Overcoming electrostatic repulsion between two hydrogen nuclei requires a 9 large amount of energy, and this reaction takes an average of 10 years to complete at the temperature of the Sun’s core. Because of the slowness of this reaction the Sun is still shining; if it were faster, the Sun would have exhausted its hydrogen long ago. Ingeneral,proton-protonfusioncanoccuronlyifthetemperature(i.e. kinetic 10CHAPTER 3 1 1 2 H H→ H e e − e e→ 2 (1.02 MeV) 2 1 3 H H→ He (5.49 MeV) 3 3 4 1 1 He He→ He H H 12.86 MeV Proton  Gamma ray Neutron  neutrino Positron Figure 3.3: The proton-proton chain reaction is the main source of energy production in the Sun. energy) of the protons is high enough to overcome their mutual Coulomb repulsion. The theory that proton-protonreactions were the basic principle by whichthe Sunand otherstarsburnwasadvocatedbyArthurStanleyEddingtoninthe1920s. Atthetime, thetemperatureoftheSunwasconsideredtoolowtoallowforprotonstoovercome theirCoulombbarrier. Afterthedevelopmentofquantummechanics, itwasdiscovered that tunneling of the protons through the repulsive barrier allows for fusion at a lower temperature than the classical prediction. 1. The first step in the proton-proton chain reaction involves the fusion of 1 2 two hydrogen nuclei (1 proton) into deuterium (the lower index says 1 proton; 1 1 theupperindexindicatesthenumberof nucleons, inthiscase1protonand1neutron), releasing a positron and a neutrino as one proton changes into a neutron. 1 1 2 +  +→+ + +042MeV  1 1 1 This first step is extremely slow, because both protons have to tunnel through their Coulomb barrier and because it depends on weak interactions. 2. The positron immediately annihilates with an electron, and their mass energy is carried off by two gamma ray photons. − +  +→2+102MeV 3. After this, thedeuteriumproducedin thefirst stagecanfuse withanother hydrogen 3 to produce a light isotope of helium, , i.e. 2 protons and 3 nucleons, in this case 2 2 protons and 1 neutron),: 11CHAPTER 3 2 1 3 +→ ++549MeV 1 1 2 4. From here there are three possible paths to generate helium isotope 4He. The most important is 3 3 4 1 + → +2+1286MeV 2 2 2 1 The complete chain reaction releases a net energy of 26.7 MeV. Important is to note that this energy cannot be used in totality to heat up the Sun. Only the photons can couple to ions and shake them. This happens because photons are light and light is an electromagnetic wave. The electric field couples to the charges of the ions. 3.3.2 The solar spectrum BymeansofaprismonemaydividetheSunlightintoabroadspectrum,whichdisplays the intensity of the light  as a function of wavelength. More precisely the quantity 2   is the energy entering per second per square meter W/m with a wavelength between and+d. The solar radiation  as a function of wavelength has thus 2−9 W/m /nm as unit. Note that one nanometer l nm = 10 m, and that Id has the 2 2 unit W/m /nm× nm = W/m , i.e. a power per unit area. The solar spectrum measured on the ground and high above the Earth’s at- mosphere are quite different as can be seen in Fig. 3.4. This figure contains a lot of information. We therefore will read the graph in detail and first focus on the yellow curve, which represents the solar irradiation measuredoutside the Earth atmosphere. The solar light that arrives at the top of the atmosphere has a very broad spectrum ranging from the ultra violet, (. 400 nm) abbreviated as UV, to the deep infrared ( 800 nm ) abbreviated as IR. In between is the visible region. An appreciable part oftheincomingSunlighthaswavelengthsinthevisibleregion. Theradiationatthetop of the Earth’s atmosphere has travelled through empty space between Sun and Earth and is thus unchanged. It is consequently a fingerprint of the solar spectrum when it leaves the surface of the Sun. It is reasonable to assume that the structure in that spectrum is determined by the specific composition of the Sun’s outer layer. In case the Sun would just be a perfect hot black body (see below) its spectrum would be as indicated by the black curve. The difference between the black curve and the yellow one reflects thus the composition of the Sun’s outer layer. In particular, free atoms may be around of which it is known that they emit and absorb radiation at specific wavelengths. The little dip at=400 nm in the spectrum is for example due to free Ca atoms at high temperature that emit or absorb at=393 nm and 397 nm. This is close enough to the observed 400 nm in the figure. 12CHAPTER 3 Figure 3.4: Spectral irradiance of incident solar radiation outside the atmosphere (yellow) and at sea level (red). The visible region of the spectrum is indicated with UV (Ultra Violet) on the left and Infrared on the right. Major absorption bands of some of the important atmospheric gases are indicated. The emission curve of a black body at 5523 K is shown for comparison, with its peak adjusted to fit the actual curve at the top of the atmosphere. A similar dip, a little to the right, at 420 nm is also due to Ca atoms in the outer solar atmosphere. The red curve in Fig. 3.4 is the solar irradiation curveat sea level.Thefact that it is lower is due to absorption by the atmosphere and the scattering of Sunlight by the atmosphere back into space. Only about 70 percent of the incoming Sunlight reaches sea level. At sea level the solar spectrum exhibits much more structure than at the top of the atmosphere as a result of absorption by molecules such as HOand 2 CO , which absorb over a broad region of wavelengths and particularly in the regions 2 which are indicated. Note that HOandCO molecules do not absorb in the visible 2 2 region, but in many regions in the Infrared. Finally,wedrawattentiontothearrowsindicatedasO ozone. Undernatural 3 circumstances, there is not much ozone at low altitudes, but there is a thin ozone layer at an altitude of 20 to 30 km. There it does no harm but, on the contrary, protects living organisms on the Earth from harmful solar UV radiation, as it absorbs Sunlight with a wavelength shorter than 295 nm. This can be seen on the very left in Fig. 3.4. A decrease in the ozone layer in the upper atmosphere does not only increase the total amount of UV light of a particular wavelength reaching the Earth, but it also allows the transmission of increasingly shorter UV radiation. This has important implications for bio-molecules such as DNA proteins, which are essential for life. They do absorb Sunlight with wavelengths 300 nm if not blocked by the ozone layer, and, as a consequence, they are destroyed or malfunctioning. With the thinning of the 13CHAPTER 3 Figure 3.5: Spectral irradiance spectra of the Sun measured at the top of the atmosphere The corresponding temperature is then 5777 K. This shows that the temperature of the Sun top layer is not exactly known but for all practical purposes, we will take it as 5800 K in this course. protectingozonelayer, thebio-moleculeswillbecomeincreasinglypronetoUVdamage in the future. 3.4 BLACK BODY RADIATION The black curve in Fig. 3.4 is that of a black body radiating at a temperature of 5523 K. If one fits the measured curve to the black body curve so that the area under both curvesisthesameoneobtainstheresultsshowninFig.3.5 The term ‘black body’ originates from experiments with a black cavity held at a certain temperature. It appeared to emit a smooth spectrum with the intensity  as a function of wavelength given by the shape of the grey curve. The position of the peak shifts to lower wavelengths for higher temperatures. At the beginning of the 20th century, attempts were made to calculate the spectral shape of black body radiation. In these calculations it was assumed that at each wavelength all energies could be emitted. There was no relation between wave- lengthandenergy. However,theresultingspectralintensityoftheblackbodyradiation did not correspond to experiment at all. In an historic contribution to quantum me- chanics, Planck solved the problem by making the assumption that the energies E of the electromagnetic field are restricted to 14

Advise: Why You Wasting Money in Costly SEO Tools, Use World's Best Free SEO Tool Ubersuggest.