The Physics of Energy 1st edition Robert L. Jaffe, Washington Taylor - Solutions

Real photo diodes do not precisely obey the ideal photo diode equation (25.17) A more realistic model is the non-ideal photo diode equation where m > 1 is the ideality factor. Consider a non ideal photo diode with m = 2, Voc = 0.7 V. Compute Iphoto/I0 and the fill factor. Compare the
Given a silicon photovoltaic solar cell with open-circuit voltage Voc = 0.7V that operates at an overall 20% efficiency under 1000 W/m2 of normal illumination, (a) compute the current density from the collecting surface. (b) How many cells must be connected in series to make a 12 V
Compute the Shockley–Queisser bound on Voc for a silicon cell with band gap 1.1 eV at temperature T = 300 K. Model the Sun as a black body at 6000 K.
Consider a single-junction solar cell with Voc = 0.7 V under one sun illumination conditions. Estimate the increase in Voc and the increase in overall efficiency if the incoming light is concentrated by a factor of 400.
Download the AM 1.5 solar spectrum from [135] and numerically compute the maximum collection efficiency expected for a silicon PV cell through a computation analogous to eq. (25.11) .2 (Si) Pmax Si7 dx x²/(e* – 1) .17 E 0.439. 2.17 So dx x³/(e* – 1) max %D Ncollection Ptotal
Numerically compute the maximum collection efficiency for a single-junction PV cell under 6000 K blackbody conditions as a function of the band gap. Estimate the maximum possible collection efficiency and the associated band gap. Repeat for double junction and triple-junction cells, confirming the
Estimate the collection efficiency of a triple junction solar cell where the first layer is an indium gallium phosphide alloy In0.53 Ga0.47P, with band gap EIGP = 1.87 eV, the second layer is gallium arsenide, and the third layer is germanium.
Given four materials, with band gaps 0.2 eV, 0.7 eV, 1.5 eV, and 3 eV, which two are likely to make the best double-junction solar cell? Explain your answer.
Perovskites are a promising new class of materials for thin-film PV. Perovskites include a wide range of compounds, such as CH3NH3PbI3 , characterized by a crystal structure first observed in the mineral perovskite (CaTiO3). Perovskite solar cells have reached ~20% efficiency under laboratory
Suppose a PV with gap Egap were illuminated by a laser that produces monochromatic light with frequency v0. How would the collection efficiency of the PV vary with?
Why does the efficiency of a silicon PV drop as it heats up? eq. (25.25). E- kBT In dE Egap Voc < SE dE gap E2 eE/kgT e
Following the logic of Figure 25.6, sketch (no calculation necessary) the wave functions of the energy basis states at the top of the second energy band and the bottom of the third energy band in a periodic square well potential with high barriers. First establish that these wave functions are
Discuss qualitatively the origins of the three terms in the Shockley– Queisser bound on PV efficiency and, in particular, explain why they are independent.
Show that for each unit cell in the crystal shown in Figure 25.1? there are eight atoms, all identical in the case of the diamond and four of each kind in the zincblende case. Each atom at a corner is shared among eight cells, etc. (a) (b)
For a concentrator with concentration C = 100, and incident sunlight at intensity I0 = 1000W/m2, compute the temperature T of the absorber at which solar to electric conversion efficiency is optimized, assuming Carnot efficiency. How does your answer change if the system has an additional rate of
Consider a parabolic dish concentrator built from a dish with radius 3 m, height equal to the focal length, and an absorber at the focus with spherical shape and radius 0.1 m. Compute the concentration and acceptance angle of this concentrator, and check that the Rabl bound is satisfied.
Consider a linear 2D compound parabolic concentrator built from parabolas tilted at 10◦ to the vertical, with a trough of width 3 m, and an absorber width of 0.5 m. Compute the concentration C of the concentrator. If the incoming radiation has intensity I0 = 1000 W/m2 and the (blackbody) absorber
Prove that for the compound parabolic concentrator depicted in Figure 24.11 the line containing points Q and A is parallel to the axis of parabola 2. consider the incoming ray that is reflected along Q?A?. D Q (a) (b) P. parabola 2 axis 1 collector axis axis 2 parabola 1
Consider a parabolic trough where the height of the reflector is identical to the height of the center of the absorber, as depicted in the figure? The concentrator width is 8 m and the absorbing tube of radius 0.5 m is centered along the focal line at a height of 2 m above the bottom of the
Compare the total (integrated daily) insolation on a flatplate collector located in Chicago, Illinois (latitude λ = 41.98◦) on February 1 when the collector is (a) tilted at an angle θ = λ to the south, (b) tilted at an angle θ = λ + 15◦ to the south.
Discuss some of the possible advantages or disadvantages of the different approaches to solar thermal electricity production: parabolic trough, power tower, parabolic dish. Can you imagine other approaches that might be worthwhile pursuing?
Solar thermal collectors powering small off-grid electric generators have been proposed for the developing world. Research and discuss the advantages and disadvantages of this proposal. Topics might include efficiency, reliability, versatility, and water requirements and availability.
The eccentricity of Mars’ elliptic orbit is roughly 0.0935. Estimate the range over which the solar constant and average surface temperature (in the uniform temperature blackbody approximation) vary during the year.
Estimate the energy used for space and water heating in your home. How feasible would it be to get all of this energy from simple low temperature solar thermal collectors?
The radius of Mars’ orbit around the Sun averages roughly RMars ≅ 2.28 × 108 km. Assuming that the surface temperature is roughly uniform over the planet’s surface and constant over a Martian day, that the surface is a perfect black body, and that there is no atmosphere, estimate the average
Verify the estimates of global land use per tera watt in the two scenarios outlined in §23.6.
The absorption coefficient for crystalline silicon at 300K for a photon of energy 1.3 eV is roughly 70 cm−1.Compute the thickness of silicon needed to absorb 75%of incoming photons at this energy
Compute the integrated daily insolation at several different latitudes on July 30 and compare with Figure 23.6. 10 1= 0° d= 20° A= 40% A = G0% A = 80 %3D Mar 22 June 22 Sept 22 Dec 22 Mar 22 (a) time of year 20 40 60 80 latitude average daily insolation (hours of perpendicular sunshine) daily
The thickness of Earth?s ozone layer at any location is measured in Dobson Units (DU), where 1 DU corresponds to a gas layer of thickness 10 ?m if the gas pressure were raised to 1 atm. Show that 1 DU corresponds to 2.69 ? 1016 molecules/cm2. Data on the absorption cross section for ozone are given
Investigate the distribution of insolation and population in China or another country of your choice, and discuss (in general terms) the prospects for solar power in that country.
In many (Northern Hemisphere) locations, solar PV panels are oriented toward the southwest rather than south. Discuss aspects of electricity demand that might motivate this choice.
A flat panel solar collector is to be tilted at an angle θ to the horizontal to maximize the amount of sunlight it can collect over the whole year. Once tilted, it is oriented toward the south (in the Northern Hemisphere). One might think that θ should be chosen to equal the latitude λ of the
In §23.3 we describe the effect of Earth’s axial tilt, or obliquity on insolation and, indirectly, on the seasons. Discuss qualitatively how Earth’s seasons would change if its obliquity were ∼90°(as is the case for Uranus) or ∼0° (as is the case for Mercury or Jupiter).
As a source of black body radiation becomes hotter, the peak in its radiation spectrum moves from the visible to the ultraviolet and beyond. Does this imply that the object can no longer be seen by the unaided human eye?
The interior of a glass blower’s furnace may contain shelves and other objects of various shapes and colors. As the furnace is heated, objects in the interior become more and more difficult to discern through a small opening, until finally, when the furnace is hot enough, the interior objects are
Derive the results of Box 21.1 (the last two equations)by using the Schrödinger equation for the time derivative of ψ(x) and ψ∗(x) and integrating by parts.
Think of some physical systems in which energy appears not to be conserved. Can you identify a coupling of the system to external processes that add or remove energy from the system? Can you characterize the dynamics of the system quantitatively in a way that makes manifest the flow of energy
According to relativity, the clocks of an object moving with speed v = ?c are slowed down by a factor ? The total(relativistic) energy of the object is given by .mc2? The mean energy of cosmic ray muons at creation is about 6 GeV. How far can such a muon travel on average before decay? y = 1/ V1 -
There is some controversy about the effects of moderately increased radiation levels on ecosystem health. Following the Chernobyl disaster in 1986, and the resulting human evacuation of the area,animal populations in the area increased both in size and in diversity.Some evidence has suggested,
According to Einstein?s theory of relativity, the kinetic energy of a particle with mass m and speed is First, verify that when v kin = ? mv2 . Then compute ? for an electron and an ?-particle with 5 MeV kinetic energy. v = Bc
An alternative technology for ultimate disposal of spent nuclear fuel,known as deep borehole disposal, envisions using well-understood drilling technologies to confine SNF in stable geological formations far below ground water. Investigate and evaluate the pros and cons of this proposal.
The government of Free donia claims to be developing nuclear reactors for peaceful purposes using enriched uranium they have produced from their own isotope separation plants. The IAEA (International Atomic Energy Agency), which tracks nuclear proliferation, observes that Free donia’s engineers
Why do you suppose the author of chose Bordeaux wine for his measurements. Can you suggest other candidates?
What are TENORMs? Discuss some examples such as coal ash,water treatment wastes, or mine tailings. What causes their radioactivity? How significant are the hazards?
Investigate and discuss the physics and public health issues raised by the radium watch-dial painters of the 1920s, the Daghlian criticality accident in 1945, the contamination accident that occurred in Goiânia, Brazil in 1987, or another incident you choose.
Consider the pros and cons of the public health response, including mandatory evacuations, to low levels of environmental radiation following the Fukushima-Daiichi incident. Find estimates of the cost, in terms of both money and human life, of the evacuation.Estimate the expected additional cancer
Choose one of the Gen IV reactor designs and investigate its advantages and disadvantages. Is there active research and/or development on this design? What is your judgment on its future prospects?
Can you figure out a series of reactions in a neutron-rich environment that would lead from 232Th to 232U? See §20.6.3 for discussion of the role of in possible weaponization of 233U produced 232U in a thorium-fueled reactor. Hint: there is a n + AZ → 2n + A-1Z reaction involved.
The energy amplifier uses a particle accelerator to feed neutrons into a sub critical reactor. Find suitable sources and give a concise summary of this novel type of reactor, its advantages such as inherent safety and capacity to breed fuel and/or reduce the burden of nuclear waste, and its
Some designs for breeder reactors use liquid metals such sodium or lead as a coolant. Discuss some of the advantages and disadvantages of such a coolant.
Explain why the optimal ratio of moderator to fuel is so much larger for a graphite-moderated (infinite, homogeneous) reactor than for a water-moderated reactor at the same enrichment.
Explain why the resonance escape probability grows and the thermal utilization factor falls with increasing ratio of moderator to fuel at fixed enrichment.
Some medical radioisotopes – nuclides that produce specific forms of radiation used for medical purposes – are obtained as fission products from thermal-neutron-induced fission of 235U. A particularly important example is technetium-99 m, 99 mTc, which is a meta stable nuclide with a half-life
Check that the nuclides 239Pu, 233U, and 241Pu satisfy the four conditions listed in §18.3.3 for being fissile. A few other actinides Z > 92– nuclei with – produced in reactors are also fissile. See if you can find one or two. Check out the isotopes of curium (Z = 96) and/or californium (Z
234U decays primarily by α-emission. It has rarely been observed to decay by spontaneous fission or by emitting a neon or magnesium nucleus. In what sense are all of these decays different examples of the same phenomenon?
When exposed to a flux of thermal neutrons, most common materials absorb one or more neutrons and many become radioactive (β- -emitters). Explain how this is compatible with energy conservation. Can you name a naturally occuring nucleus that cannot absorb a neutron?
The decay chain of 238U is described in some detail in the text. The other naturally occurring heavy nuclide whose decay initiates a decay chain is 232Th. Look up the 232Th decay chain. At what nuclide does it end? How many -particles and how many electrons are emitted in the entire chain?
Radium-226 is a decay product of 238U . 226Ra has a half-life of 1600 years and is found in uranium ores. When it was first discovered and before radioactive decay was well understood, some mineral prospectors claimed to have discovered a rich deposit of radium (a few percent by mass) in a cave in
Consider the decay chain for 238U shown in Figure 17.13 Why are there -decays, but no electron captures, interspersed among the - decays? U (92) 238 92 Th (90) Ra (88) Rn (86) Po (84) Pb (82) 124 126 128 130 132 134 136 138 140 142 144 146 N
Sketch a curve similar to those of Figure 17.12? for a value of A that results in three isobars that are stable against decay and electron capture. On the basis of the SEMF explain why the number of stable isotopes per element increases with Z. A = 121 A = 122 even-even | even-odd odd-odd stable
For small A, where the symmetry energy overwhelms the Coulomb energy, the most stable nuclei with even A have Z = N A/2. For odd–even nuclei in the same range of A, which is more stable, Z = N + 1 or N = Z + 1? Why? Check your answer for some nuclei in the range.
Discuss the ways in which the assumptions behind the SEMF may fail when A is very small.
How can the neutron be unstable in free space, but stable when inside a nucleus?
A possible way to evaluate the extent of uranium resources is to build a probabilistic model that includes both known resources and possible unconventional sources of uranium and their relative cost of extraction, and then to project the cost of uranium as a function of the number of nuclear power
Research the present cost of fuel for nuclear fission power plants (in $ per MWhe) and compare with the cost of coal and natural gas for conventional fossil fuel power plants. What are the implications for expanding utilization of nuclear power?
Investigate the proposed mechanisms for recovering uranium from seawater. What do you think are the prospects for this source of uranium?
It is not hard to balance a (brand new) ordinary pencil vertically upon its eraser. This is a configuration of stable classical equilibrium. Explain why in principle, even under the best of conditions (flat surface, symmetric pencil, no wind currents), the pencil is unstable due to quantum
The scanning tunneling microscope (STM) makes use of quantum tunneling to obtain resolutions down to the scale of individual atoms. Investigate the operating principles and applications of STMs.
Classical systems also decay. The decay or failure rate of many systems follows a bathtub curve. Look up and consider this type of decay and contrast it with the decay pattern of a quantum system.
The tauon τ decays often to a muon μ, which in turn decays to an electron. How many neutrinos, and of which type are produced in this sequence of weak decays.
A baryon frequently encountered in particle physics experiments is known as the Λ (“Lambda”). Its quark content is uds. Sometimes the Λ decays by the process Λ → nγ, where n is a neutron (ddu) and γ is a photon. What interactions must be active in this decay?
Two possible nuclear fusion reactions are d + d → 4He + γ and d + d → 4He + p , where d is deuterium, an atom with a nucleus composed of a proton bound to a neutron. 3He and 4He are helium atoms with nuclei consisting of two protons and one neutron (3He) or two protons and two neutrons (4He).
Gravity is a long-range force proportional to the masses of the interacting bodies. Physicists have long searched to see if there might be a long-range force that is proportional to baryon number. Think about the composition of atoms and propose a “thought experiment” that could detect such a
Physicists searching to see if the proton decays have looked for the reaction. Which of the conservation laws explored in this chapter does this decay violate?
Jet engines use a variant of the Brayton cycle in which the gases are only expanded in the turbine to a pressure sufficient to drive the compressor and the plane’s mechanical and electrical systems; the resulting gases are expelled from the engine at high velocity. Research jet engines and
Explain in words what is going on in the Rankine reheat cycle of Figure 13.16(a) and, referring to the figure, explain the statements made at the end of the discussion in the text about the efficiency, power output, and turbine conditions for this cycle. T. 800 700 5) P+ 600 Preheat 500 400 T_
The efficiency of the idealized Carnot-like Rankine cycle of Figure 13.12(b) is higher than for fixed but lower than the Carnot limit for 3 T 800 700 z 600 P+ Tvap (p) 500 P- 400 300 4. 2 4 6. 8 (b) entropy [kJ/kg K] temperature [KI 00
Describe in words how you would compute the coefficient of performance for an ideal vapor-compression cycle working between temperatures T+ and T- . Assume that you have data on the thermodynamic properties of the refrigerant both at saturation and in the super heated vapor phase. Remember
A vapor-compression cycle is specified by a closed, counterclockwise loop in the ST-plane. Show that if the loop is executed reversibly then the area of the loop is equal to the net work performed on the fluid in a cycle. Explain why the area of the ideal VC cycle {1234} in Figure 13.5(b) is not
There are several other paradigms for simple refrigerators. Research and describe a gas phase Stirling refrigeration cycle or a gas phase Brayton refrigeration cycle. What does the corresponding thermodynamic cycle look like in the ST plane? What are the applications of the cycle you study?
The saturation domes for R-134a and isopentane shown in Figures 13.4 and 13.18? are quite asymmetric, with steep (R-134a) or even re curving (isopentane) saturation curves. Water, on the other hand, has a relatively symmetric saturation dome (Figure 12.9) Explain why this feature makes R-134a
Discuss the distinction between an adiabatic and an isentropic process. For example, how can it be that a compressor that works very quickly, allowing negligible heat transfer, can nevertheless increase the entropy of a gas?
Why is water not a suitable fluid for a vapor-compression kitchen refrigerator? What about for an air conditioner intended to operate between 24 °C and 40 °C?
Use steam table data to estimate accurately the pressure at which water would boil at room temperature (20◦C). Similarly estimate the temperature at which water boils on top of Mt. Everest, where the air pressure is approximately 1/3 atm?
Under calm, clear conditions during the summer in a temperate climate similar to Boston’s, meteorologists can predict the minimum night time temperature quite accurately by making measurements of the relative humidity during the day. Explain why estimates made the same way are much less accurate
Since the volume parameterizes the points on the phase transition line between liquid and vapor (see Figure 12.7 one could use the density instead of the quality as the thermodynamic variable to characterize the mixed phase. Why do you suppose this is not done? 40 700 K 650 K 600 K 10 550 K Y 4
A heat pipe is a device that uses heat conductivity and the large latent heat of phase change to transfer heat very efficiently between two solid bodies. Research the subject. What is the role of gravity? Why is the heat pipe evacuated before a carefully measured amount of fluid is added. How can
Research what a pressure cooker is and describe the physical principles that make it work.
An insulated cylinder closed by a piston is initially filled with one liter of ice at –20 °C. The piston is pulled out, doubling the volume and initially creating a vacuum above the ice. Describe qualitatively what happens as the system comes into equilibrium at –20 °C. Now the system is
What is the role of gravity in boiling heat transfer? Do you think boiling heat transfer would work well on an Earth-orbiting satellite?
A dual cycle attempts to model an SI engine more realistically. It models the combustion process in two steps. First some heat is added at constant volume, then the rest is added at constant pressure. Draw the dual cycle in the pV- and ST-planes. How are the Otto and Diesel cycles related to the
Why would a diesel engine be hard to start in cold weather?
What is the rationale for modeling combustion as a constant pressure process in the Diesel cycle when it was modeled as constant volume in the Otto cycle?
Would you advocate incorporating an Atkinson-like step (isobaric compression after the completion of the power stroke) in a diesel engine? Explain.
Research and summarize the advantages and disadvantages of two stroke engines for personal motor vehicles. What do you see as their future?
An ideal gas is heated to a temperature Tin and allowed to expand a small amount against an external ambient pressure, where the external gas has temperature Tout. We found that the fraction of thermal energy dU used to do useful work dW precisely realized the Carnot efficiency. Show that the
Since it is not used up in a Carnot cycle, the gas used as a working fluid could be chosen to optimize the properties of the engine. What advantages would helium (a monatomic gas) have over air in a Carnot engine?
The Ericsson engine, invented by Swedish-American inventor John Ericsson in 1833, is based on a cycle that esembles a Stirling cycle except that the isometric steps are replaced by isobaric steps. It uses a re generator in the same way as a Stirling engine. Sketch the Ericsson cycle in the
An inventor comes to you with a proposal for a new high-tech material containing tiny Stirling engines which exploit the energy difference between the human body and the outside environment. He claims that a complete bodysuit made of his material will generate 15 W of power in steady state when
In an engine cycle like the one shown in Figure? heat is added over a range of temperatures. Explain why even if it were run reversibly, its efficiency would be less than the Carnot limit defined by the high- and low-temperature set points and shown in the figure ( ?C = T4-T2)/T4. Is this in

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The Physics of Energy 1st edition Robert L. Jaffe, Washington Taylor - Solutions

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