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  Lecture notes forDuurzame Energie: Zon, Wind en WaterRenewable Energy: Sun, Wind and Water(for 2SBI) dr. R.J. WijngaardenMarch 7, 2018  Contents 1 Energy: units and orders of magnitude 1 1.1 GETTING A FEELING FOR ENERGY . . . . . . . . . . . . . . . . . 11.2 HUMAN POWER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 USE OF ENERGY BY MANKIND . . . . . . . . . . . . . . . . . . . . 2 2 The Climate and Energy crisis 3 2.1 PALEOCLIMATOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 PRESENT CHANGES . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Earth’s climate and the Sun 8 3.1 Solar Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 THE SUN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3.1 The energy source in the Sun . . . . . . . . . . . . . . . . . . . 93.3.2 The solar spectrum . . . . . . . . . . . . . . . . . . . . . . . . 123.4 BLACK BODY RADIATION . . . . . . . . . . . . . . . . . . . . . . . 143.5 THE GREENHOUSE EFFECT . . . . . . . . . . . . . . . . . . . . . 163.5.1 Earth without atmosphere . . . . . . . . . . . . . . . . . . . . . 163.5.2 Earth with a totally absorbing atmosphere . . . . . . . . . . . 183.5.3 Intermezzo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.6 TRENDS IN CO 2  EVOLUTION . . . . . . . . . . . . . . . . . . . . . 21 4 Transport of heat 24 4.1 transport of heat by conduction . . . . . . . . . . . . . . . . . . . . . . 244.2 transport of heat by convection . . . . . . . . . . . . . . . . . . . . . . 26 5 Thermal energy and thermodynamics 31 5.1 THE IMPORTANCE OF THERMODYNAMICS . . . . . . . . . . . . 315.2 THE IDEAL GAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32ii  CONTENTS5.2.1 The ideal gas law . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2.2 Pressure as the result of the impact of particles on the containerwalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2.3 The root-mean-square (rms) speed of a molecule in an ideal gas 375.2.4 Heat and speci fi c heat . . . . . . . . . . . . . . . . . . . . . . . 385.2.5 Mechanical equivalent of heat . . . . . . . . . . . . . . . . . . . 405.3 THE FIRST LAW OF THERMODYNAMICS . . . . . . . . . . . . . 415.3.1 First law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.3.2 Application 1 of the  fi rst law: Speci fi c heat of an ideal gas revisited 435.3.3 Application 2 of the  fi rst law: Closed cycle steam power plant . 475.3.4 Carnot cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.4 ENTROPY AND THE SECOND LAW OF THERMODYNAMICS . . 565.4.1 The second law of thermodynamics and Carnot’s theorem . . . 565.4.2 Entropy: a new thermal potential . . . . . . . . . . . . . . . . 575.5 ENGINES DESCRIBABLE WITH IDEAL GASES . . . . . . . . . . . 645.5.1 Stirling engine . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.5.2 Otto engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.5.3 Gas turbine: Joule cycle . . . . . . . . . . . . . . . . . . . . . . 685.5.4 Heat pumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.5.5 Heat pumps: evaporation-condensation cycle . . . . . . . . . . 755.6 REAL GASES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.6.1 Van der Waals gases . . . . . . . . . . . . . . . . . . . . . . . . 775.6.2 Heating of water at constant pressure . . . . . . . . . . . . . . . 805.6.3 Steam turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.7 CO 2  sequestration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.8 Fuel cells: Engines not subject to Carnot cycle limitations . . . . . . . 865.8.1 Principle of operation of a fuel cell . . . . . . . . . . . . . . . . 865.8.2 Useful thermodynamic potentials . . . . . . . . . . . . . . . . . 895.8.3 Theoretical e ffi ciency of a fuel cell . . . . . . . . . . . . . . . . 905.8.4 E ffi ciency of real fuel cells. . . . . . . . . . . . . . . . . . . . . 90 6 Introduction to  fl uiddynamics for energy 92 6.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.2 BASIC FLUID DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . 926.2.1 Stationary  fl uids . . . . . . . . . . . . . . . . . . . . . . . . . . 926.2.2 Fluids in motion . . . . . . . . . . . . . . . . . . . . . . . . . . 966.2.3 Lift and drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7 Water energy: rivers, reservoirs and tides 107 7.1 FLUID DYNAMICS FOR WATER POWER APPLICATIONS . . . . 107iii  CONTENTS7.1.1 Euler’s turbine equation . . . . . . . . . . . . . . . . . . . . . . 1077.1.2 Hydropower from a dam . . . . . . . . . . . . . . . . . . . . . . 1087.1.3 Tidal power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1107.1.4 Energy from waves . . . . . . . . . . . . . . . . . . . . . . . . . 118 8 Wind energy 123 8.1 Wind energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1238.2 Wind turbines: the Betz limit . . . . . . . . . . . . . . . . . . . . . . . 1238.2.1 Power from kinetic energy of the wind . . . . . . . . . . . . . . 1248.2.2 Change in kinetic energy . . . . . . . . . . . . . . . . . . . . . 1268.2.3 Thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1278.2.4 Extracted power . . . . . . . . . . . . . . . . . . . . . . . . . . 1288.2.5 Is Betz limit valid for water  fl ow? . . . . . . . . . . . . . . . . . 1308.3 Optimal design of turbine blades . . . . . . . . . . . . . . . . . . . . . 1318.4 Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1398.4.1 Too large induction factor    . . . . . . . . . . . . . . . . . . . . 1398.4.2 E ff  ect of drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1398.4.3 Rotation of the air . . . . . . . . . . . . . . . . . . . . . . . . . 1408.5 Turbine design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1448.6 Wind properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1458.7 Wind farms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1478.8 Other ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 9 Quantum mechanics 150 9.1 Basic Quantum Physics for Solar Energy . . . . . . . . . . . . . . . . . 1509.2 WAVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1509.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1509.2.2 The wave equation for a rope . . . . . . . . . . . . . . . . . . . 1549.2.3 Fourier generator . . . . . . . . . . . . . . . . . . . . . . . . . . 1609.2.4 Waves in 2D and 3D (can be skipped in a  fi rst reading) . . . . . 1609.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1649.3 LIGHT BEHAVING LIKE PARTICLES . . . . . . . . . . . . . . . . . 1669.3.1 The Blackbody radiation . . . . . . . . . . . . . . . . . . . . . . 1669.3.2 The Photoelectric E ff  ect . . . . . . . . . . . . . . . . . . . . . . 1679.3.3 The Production of X-Rays . . . . . . . . . . . . . . . . . . . . . 1699.3.4 The Compton E ff  ect . . . . . . . . . . . . . . . . . . . . . . . . 1719.3.5 Is it a Wave, or a Particle? . . . . . . . . . . . . . . . . . . . . . 1729.3.6 A Two-Slit Experiment . . . . . . . . . . . . . . . . . . . . . . . 1749.3.7 Di ff  raction: Uncertainties in Particle Properties . . . . . . . . . 1779.3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177iv
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