Questions and Answers of The Physics Energy

Estimate the relative range in highway miles of a passenger vehicle with comparable size and drag coefficient to the Camry described in §2, assuming it is operating using (a) A 40 L gasoline tank
Consider the advantages and potential limitations of a purely electric vehicle with a 200 MJ battery energy storage system. For what fraction of your vehicle use would this be practical?
A silver cell is an alkaline dry cell in which the manganese/carbon cathode is replaced by silver-oxide (Ag2O), so the net reaction is Zn + Ag2O → ZnO + 2Ag. Investigate the properties of silver
Investigate and discuss pumped heat electricity storage and/or pumped cryogenic electricity storage [289]. Consider the effects that reduce the efficiency of these systems below the Carnot limit.
Discuss the merits of different storage types for (a) storage of off peak electrical power on large-scale energy grids, (b) automobiles without combustion engines,(c) on board power systems
For each of the energy storage parameters described in §37.1, identify an application for which this parameter is critical. For each such application, discuss some good options for energy storage or
Check the claimed rating and actual energy production of the solar photo voltaic system described in§36.5.3.
A frequent traveler, who lives alone in Washington DC (T̅ ≅ 13.2 ◦C, ΔT ≅ 12 ◦C), is away from home every other week throughout the year. Normally she keeps her
Perform a numerical estimate of the savings in heating energy for the residence modeled in §36.5.3 in Boston when the thermostat is turned off for eight hours, assuming that the outdoor temperature
In ?5.2.2 we described a simple system in which a piston is used to extract energy from a hot gas with efficiency(5.20) Show that the energy extracted precisely corresponds to the energy of the
Systems that are colder than their environment have positive energy. Suppose a quantity of monatomic gas originally at ambient temperature and pressure (T0, p0) is adiabatically and reversibly
What is the energy of sunlight (in units of W/m2 at normal incidence)? Discuss how energy is destroyed when sunlight is converted to electricity by photo voltaic cells, by solar thermal electric
Consider and discuss the relative benefits in the contexts of efficiency, energy savings, and decarbonization, as well as the practical and economic challenges, for switching from coal power to
Assume that in a given scenario with no significant increase in nuclear power usage and gradually increasing reliance on renewables over the next century, atmospheric CO2 levels reach a maximum of
Investigate vacuum tube trains as an efficient, low-carbon transportation option. To what extent could they use gravity to accelerate/decelerate? Where would such train lines make sense Would they be
Consider the power/power density ratio 105 m2 for the “zero dimensional” hydro resource in the figure in Box 36.3, compared to the “1D” waves resource (107m2) and the “2D” solar resource
Consider a system 1 where a container is divided into two parts by an impermeable membrane. The two equal-size parts contain nitrogen and oxygen gases at the same pressure and temperature. The
Estimate the thermodynamic limit on the 1st law efficiency of a device that turns heat radiation from a wood fire into electricity.
Since the conversion of laser light to electricity can be so efficient, why not use low-temperature heat to power a laser and then convert the laser light to electricity at high efficiency?
Using the methods developed in Box 35.4.2, find a lower limit on the energy per kilogram of carbon for removing carbon directly from ambient air. Compute the energy cost of removing all 10 Gt/year of
Fertilizing phytoplankton in the deep ocean was mentioned briefly as a proposed way to sequester large amounts of CO2. Explore this proposal. What do its advocates claim? What criticisms have been
Data are available on the location of coastlines on several continents during the Pliocene era when temperatures were at levels projected to be reached over the next century. Locate data on a region
In §35.3.3 we remarked that the fact that ice floats in seawater has far-reaching consequences for climate and life on Earth. Discuss what Earth’s surface might look like if ice did not float.
The radio-isotope beryllium-10 (10Be) is often employed in studies of paleoclimates. How is 10Be formed? With which aspects of paleoclimate is correlated? How is used, for example, to extract climate
The particles of black soot in Figure 34.15 seem to drill down into the surrounding ice. Can you think of a geometrical condition that might give a good first-order estimate of how far down they go?
Hydrogen and helium are the two most common elements in the universe. What are their concentrations in Earth's atmosphere? Why are they so rare?
The term inversion describes a weather event in which the lapse rate near the ground is negative – the temperature actually increases with height. Explain why inversions are often associated with
Estimate the relative carbon output of heating a home using(a) natural gas, (b) electrical heating powered by electricity from coal-fired power plants.How much do your assumptions about what
Investigate the production of helium. How was it formed? Why is it found in natural gas? How much of it is recovered? Discuss conservation of the world’s helium resources.
Explain why petroleum is currently the primary source of fuel for land and air transport, while coal is the primary fuel for electric power plants.
Determine the current relative costs of crude oil, gasoline, coal, and natural gas on a per unit of energy basis.
Assume that enthalpy is a linear function h(s, T) = as + bT. Consider a single-flash cycle, assuming that the saturated liquid and vapor curves between T? and T+?form an isosceles
Both nuclear and geothermal power plants use saturated steam in Rankine cycles. What are the fundamental differences between the thermodynamics of these two energy sources?
Find out how the Kalina cycle works and discuss its application to geothermal power. To what kind of resources is it best suited?
Use Newton?s law to compute the gravitational acceleration g(r) as a function of radius r within a sphere of total mass M that is uniformly distributed through the volume. Compute g(r) in a simple
Derive the statements made about the power density of 1 m and 10 m deep ocean swells in §31.2.4.
Explain the following statement made in the discussion of tidal barrage power: “In realistic tidal basins, the surface area of the basin is larger at high tide than at low, so more energy can be
Suppose a spherically symmetric body with some angular momentum L begins to contract under its internal gravitational attraction. Assume that the object’s angular momentum is conserved during its
Using the results of §31.3.2 discuss the eventual fate of the Earth– Moon system: Is the length of the month increasing or decreasing as a result of tidal forces? How about the length of the day?
In contrast to traditional hydropower plants where water is stored behind large dams, run of the river (ROR) hydro-plants use flowing water with little or no water storage (pondage). Investigate and
Consider how the circumstances of a hydro turbine differ from those of a wind turbine, and explain why the Betz limit does not apply for hydropower.
Compute the pressure at a depth Z below the surface in a reservoir behind a hydroelectric dam. Compute the work done by a volume of water ?V as it passes from this pressure on one side of a turbine
Since the pressure is symmetric with respect to reflection across the yz-plane, the cylinder shown in Figure 29.15(b), which is immersed in the uniform flow of an ideal, incompressible fluid,
Consider the flow of air across an airplane wing considered in the ground-based reference frame where the air is stationary far from the airplane (no wind). Is Bernoulli’s equation relevant here?
There are many flawed “elementary explanations” of lift. One (mentioned in §29.4) is based on the idea that air takes an equal time to pass above and below an airfoil. What is the argument? What
What is the Magnus effect and what does it have to do with the phenomenon of lift?
Aspirator pumps are used in many applications, ranging from emptying fish tanks to providing vacuum for industrial processes. How do they work?
Derive the formula for Mn in eq. (28.12) Mn[f (v, k, λ)] du υ" fov, k, λ) Γ(1+m/k)
Show that Γ(n) = (n − 1)! for integer n.
Investigate the history of the Cape Wind project in the state of Massachusetts and discuss the arguments made in favor of and against this project.
The Bahrain World Trade Center is a prominent example of building-integrated wind power. What are the parameters of this installation? What are its pros and cons? What is your opinion of
What is the most promising site for wind power within a 100 kilometer radius of your location? Can you identify the meteorological origin of its favorable position? If you can find data, make an
When an iceberg is driven across the ocean?s surface by a steady wind, it is subject to the combination of forces described in Box 27.2 plus a drag force proportional to ?bv, where b is a constant.
If an OTEC system could achieve 1/2 of Carnot efficiency, at approximately what rate could energy be extracted sustainably from ocean surface waters in the tropics? What area of ocean would need to
Estimate the centrifugal forces acting on a 60 kg person standing at the equator due to(a) Earth’s rotation about its axis,(b) Earth’s yearly revolution about the Sun, and(c) The Sun’s
Discuss and research in more detail the open- and closed-cycle OTEC systems discussed in §27.6. Example questions: Why is such low pressure required for the open-cycle system? Why can the open
It is often said that the Coriolis force determines the direction that water circulates as it goes down a drain. Do you think this is possible? Perhaps an experiment is in order?
Use the Coriolis force to explain the direction of winds circulating around storms (low-pressure areas) and fair weather systems (high pressure areas) in the Northern and Southern Hemispheres.
Assuming that one half of the energy in solar radiation absorbed at the oceans’ surface is lost to latent heat flux (evaporation), give an order-of-magnitude estimate of the rate at which water
The Coriolis force determines the directions of the trade winds, mid latitude Westerlies, and Polar Easterlies as described in the text. What about the strength of these winds? How, for example,
The absorption coefficient of water for light of wavelength 450 nm is roughly κ450 ≅ 0.0001 cm−1 while for light of wavelength 750 nm it is roughly κ750 ≅ 0.03 cm−1. Estimate the depth
Investigate the raceway pond and photo bioreactor approaches to microalgal biomass production. Discuss the relative advantages and challenges of these approaches, and the typical realized rate of
Estimates suggest that 80% of the nitrogen in fertilizer is lost to the environment and does not benefit crops. Investigate the negative side effects of nitrogen fertilizer runoff. If this lost
Show that the right-hand side of (25.25) Cannot exceed Egap and goes to this value only in the limit T ? 0. E2 ETKBTO-1 E2 eE /kBT -1 dE Egap kBT In Voc < e SE dE JE gap
Compute the momentum of an electron with kinetic energy 2 eV and compare to the momenta of a photon with the same energy. Explain why such a photon cannot excite an electron in silicon without
Derive the Fermi?Dirac distribution (25.8) Start by considering a single electron state of energy E that is either occupied (n = 1) or not occupied (n = 0) by an electron. Now, consider coupling
The absorption coefficient of silicon has a strong dependence on photon energy, as shown in Figure 25.16 For simplicity, consider an idealized material, material S, similar to crystalline silicon,
An actual solar cell has internal resistances that affect the behavior of the circuit. These can be modeled as a single shunt resistance Rp in parallel with the diode, and another resistance Rs in
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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)
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
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

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