Examination cover sheet

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1 Examination cover sheet (to be completed by the examiner) Course name: Physics of New Energy source Course code: 3DEX1 Date: 05/04/2016 Start time: 18:00 End time: 21:00 Number of pages: 8 (incl. this) Number of questions: 4 Maximum number of points/distribution of points over questions: 100 (Q1: 15, Q2: 15, Q3: 35, Q4: 35) Method of determining final grade: xnumber of points Answering style: formulation, order, foundation of arguments, multiple choice: formulation Exam inspection: tbd Other remarks: Instructions for students and invigilators Permitted examination aids (to be supplied by students): Notebook x Calculator Graphic calculator Lecture notes/book One A4 sheet of annotations Dictionar(y)(ies). If yes, please specify: Important: examinees are only permitted to visit the toilets under supervision it is not permitted to leave the examination room within 15 minutes of the start and within the final 15 minutes of the examination, unless stated otherwise examination scripts (fully completed examination paper, stating name, student number, etc.) must always be handed in the house rules must be observed during the examination the instructions of examiners and invigilators must be followed no pencil cases are permitted on desks examinees are not permitted to share examination aids or lend them to each other During written examinations, the following actions will in any case be deemed to constitute fraud or attempted fraud: using another person's proof of identity/campus card (student identity card) having a mobile telephone or any other type of media-carrying device on your desk or in your clothes using, or attempting to use, unauthorized resources and aids, such as the internet, a mobile telephone, etc. using a clicker that does not belong to you having any paper at hand other than that provided by TU/e, unless stated otherwise visiting the toilet (or going outside) without permission or supervision Associated with the Central Examination Regulations

2 Re-Exam 3DEX1: Physics of new energy from 18:00-21:00 M. Creatore & R.J.E. Jaspers PLEASE READ THESE INSTRUCTIONS FIRST! Solve each exercise on separate sheet of paper and make sure they all have your name on it! In this exam we would like to summarize with you the issues discussed in this class by 4 exercises: 1. Energy in general: the energy problem, consumption and storage. 2. Thermodynamics: how thermodynamics imposes a limit on the maximum efficiency to convert heat into work. 3. Fusion power: the basic principles and its challenges to realise a fusion power plant 4. Solar cells: its structure and operating principle All four questions are posed in English. You can choose yourself to answer in either English or Dutch. We also provide an indicative time needed to complete the exercise (just our own estimate, maybe it helps you to check whether your pace is sufficient). For each of the sub questions the number of points that can be scored is indicated. The total number of points is 100. The final result F is calculated according to F= x (number of points score) and rounded to 1 decimal. The use of calculators is allowed, but any other books, phones, laptops, internet access, formulary is strictly prohibited. Below you find some constants, which you might need for solving some exercises. (Note that you do not necessarily need all of them, it is just a standard list). Constants e = electron charge = 1.6x10-19 C m e = electron mass = 9.1x10-31 kg m p proton mass = 1.67x10-27 kg c = speed of light = 2.99x10 8 m/s ε 0 = vacuum permittivity = 8.85x10-12 F/m μ 0 = magnetic permeability = 1.26x10-6 Vs/Am h = Planck constant = 6.63x10-34 Js k B = Boltzmann constant = 1.38x10-23 J/K g = gravitation of Earth = 9.81 m/s 2 N A = Avogadro s number = 6.02x10 23 mol -1 R = Gas constant = 8.31 J/(mol K) (= 8.31 Pa m 3 /(mol K) atm = atmosphere = 1.01x10 5 Pa ρ air = density of air = 1.3 kg/m 3 ρ water = density of water = 1000 kg/m 3 k w = thermal conductivity wood= 0.1 W/(m K) k r = heat conductivity rubber= 0.15 W/(m K) c h2o = specific heat capacity water= kj/(kgk) atomic mass (amu): hydrogen=1, helium=4, carbon=12, oxygen=16

3 1. Energy General 15 pts estimated time: 25 minutes a) [5 pts] Energy Problem: One of the big issues with the present and forecasted energy use in the next decades, is the impact on the climate. For simplicity assume that presently 1/3 of the world population is living in the rich countries. Here the population and energy usage stay constant in the next 50 years, but the contribution of CO 2 free energy production increases from 20 to 80 %. The other 2/3 of the world population (in 2016) will in the next 50 years increase by 50 %, the energy use per person will increase from 10 to 50 % of the average rich person and the contribution of CO 2 free energy production increases from 0 to 50 %. [3 pts] By which factor will the CO 2 emission increase/decrease in 50 years? [2 pts] What obstacles do you foresee that in 50 years from now we will not have a complete CO 2 free energy production? b) [5 pts] Energy Use: Just to get an idea on the energy use, we will look to ourselves. How much energy does it take our own body to do work. Assume we will climb the Eiffel tower in Paris by taking the stairs. The viewing platform where we arrive is located at an height of 115 m. Our body has an efficiency of 30 %. Just take as your mass 75 kg (even if this might in your case be different in reality!). Also assume that each stair is 20 cm high and you take 3 stairs per second. (1 pt) How much work did your body do? (2 pts) What was the power your body had to produce? (2 pts) In the electrically driven elevator (500 kg, efficiency 80 %) 10 people of each 75 kg fit. Is it energetically more favourable to take this elevator? Explain. c) [5 pts] Energy storage: The disadvantage of wind energy is its intermittency. A possible solution to this could be that one uses the energy produced by the windmill to first pump up water into a lake and use the potential energy of this lake as energy storage. Assume the water level can rise by 10 meter in a lake of 700 km 2 (following a former idea for the Markerwaard in the Netherlands). [3 pt] How much energy can be stored in this lake? [2 pt] To see this in perspective: in the Netherlands we have about 8 million households. They use on average 400 W electricity (per household). For how many hours can we produce all this electricity from the lake (assuming a conversion efficiency of 80 %)?

4 2. Thermodynamics 15 pts estimated time: 25 minutes A heat engine allows 2 moles of a mono-atomic gas (CV=12.47 J/(mol K) and CP=20.78 J/(mol K)) to carry out the thermodynamic cycle indicated in the figure below. The temperature reaches a maximum value of 327 C. The pressure Pa is 10 5 Pa and the pressure Pb is Pa. The step b-c is isothermal. a) [6 pts] Calculate the heat exchanged between the gas and the environment in each step. b) [6 pts] Calculate the work done by the gas or by the environment in each step. c) [3 pts] Calculate the efficiency of this heat engine.

5 3. Fusion 35 pts estimated time 50 minutes Fusion Energy is a very promising new energy source: The fuel is abundantly present for thousands of years No CO 2 emission Inherent safe Large scale Nevertheless, we still do not have a working fusion reactor yet. Before this will be realised many challenges have to be overcome. Let s have a closer look at a few of those. Figure 1: bindings energy per nucleon versus mass of the nucleus a) (6 pts) Challenge 1: The fuel: the easiest fusion reaction is the one between deuterium (D) and tritium (T) nuclei. Other fusion reactions are possible as well with a combination of p, D, T, and 3 He, see Figure 1 & 2. The reaction between D+ 3 He has the advantage of not producing a neutron (so: no radioactivity). [2 pt] What are the reaction products of this fusion process? [ 2 pt] Estimate how much energy is released in one such fusion reaction. [ 2 pt] What is the main reason why ITER will not use D+ 3 He as a fuel.

6 Fusie cross-sectie σ [m 2 ] Figure 2: fusion cross-section versus collision energy b) (6 pts) Challenge 2: The Burn Condition. To have net fusion power we need to fulfil the following condition: More power should be produced by fusion reactions than we need to provide to heat the plasma. a. [2 pt] Give an expression for the fusion power (or fusion power density), using the parameters density (n), reaction rate (<σv>), Fusion energy (E f) b. [1 pt ]Give a definition of the energy confinement time (τ E) c. [3 pt] Derive the fusion condition using the above parameters and the temperature T. c) (4 pts) Challenge 3: Magnetic confinement. We need to confine the hot plasma with a magnetic field B of 5T. Charged particles will gyrate around this magnetic field line with a fixed frequency. Take a tritium ion at 15 kev. [2 pt] calculate this gyration frequency (in Hz!!) for the tritium ions [2pt] calculate the radius at which this ion gyrates around the magnetic field line. d) (5 pts) Challenge 4: Temperature. Fusion of the D-T reaction is easiest at 15 kev (equal to approximately 165 Million K). This can be done by for instance injecting energetic particles. Explain this heating principle in a few sentences, addressing the following issues: which particles need to be injected (and why)? Which energy do these particles need to have (and why)? How can we give energy to these particles? How is the plasma heated by these particles? Make a sketch of the geometry (showing the reactor vessel, the plasma and the particle path) e) (5 pts) Challenge 5: Wall power load. The aim of a fusion power plant is to produce electricity. Assume we have a fusion power reactor of the type tokamak, producing 4 GW of fusion power (from the D-T reaction). The major radius is 6 meter, the minor radius = 2 meter. Assume the torus has a circular cross-section. [3 pts] Calculate the power wall load (in MW/m 2 ) as a result of the neutrons. [2 pts] A fraction of the fusion power is in the kinetic energy of the alpha particles ( 4 He ions). Where does this power go to?

7 f) (5 pts) Challenge 6: control. To control the plasma we need to measure in real time some plasma parameters, like the plasma density. [3 pt] Describe a measurement technique (physics principle) to do this. [2 pt] Use a sketch to illustrate this and indicate the main hardware component. g) (4 pts) Challenge 7: Fusion is just one of the possible new energy sources. Give two advantages and two disadvantages of fusion power compared to wind power. (assume that we will have a working reactor in about 25 years).

8 4. Solar Cells 35 pts estimated time 50 minutes Analyse and carefully describe in your own words the structure of a crystalline silicon solar cell by addressing the following questions: a) (4 pts) Make a complete sketch of a c-si solar cell and indicate its components. b) (2 pts) The main component of a solar cell is the so-defined p-n semiconductor junction. Sketch the energy band diagrams for a p-type and an n-type semiconductor and explain the difference. c) (4 pts) A p-n junction in equilibrium (and under dark condition) does not allow any transport of charges. How can the application of an external voltage to the junction perturb this equilibrium? Explain it by making use of the current-voltage diagram for a p-n junction. d) (4 pts) How does the current-voltage diagram for a p-n junction modify when exposure to sun-light occurs? Motivate your answer. e) (6 pts) The current-voltage equation for a solar cell clearly indicates that it is not possible to convert all the photocurrent (i.e. all the photo-generated charges) in useful electrical current. Write down the equation and motivate this statement. f) (3 pts) Explain the criteria to follow when selecting an anti-reflection layer for a solar cell. Which anti-reflection layer is chosen for a crystalline silicon cell? g) (3 pts) Explain the criteria to follow when selecting a back-contact for a solar cell. Which back-contact is chosen for a crystalline silicon cell? h) (5 pts) Several loss mechanisms can take place in a commercial solar cell. Spectral mismatch is the major loss mechanism. Explain it and provide technical solution to solve it by making use of sketches. i) (4 pts) Another loss mechanism in a solar cell is related to electron-hole recombination. Where do recombination processes occur? Can we prevent them and how?

M. Creatore & R.J.E. Jaspers

Re-Exam 3DEX1: Physics of new energy 05-04-2016 from 18:00-21:00 M. Creatore & R.J.E. Jaspers PLEASE READ THESE INSTRUCTIONS FIRST! Solve each exercise on separate sheet of paper and make sure they all