The Physics of Energy, page 156
Sulfate aerosols Another approach that has been advocated is the large-scale release of sulfate aerosols into the atmosphere, leading to both a direct albedo effect and to nucleation of clouds giving a secondary albedo effect, as discussed in §34.4.3. At some level, this mechanism is already in use, because coal plant emissions of sulfur dioxide are currently producing a net negative radiative forcing, offsetting some of the positive radiative forcing arising from increasing CO levels. Since the atmospheric lifetime of sulfates is much shorter than CO, sulfates would have to be injected into the atmosphere continuously in order to prevent return to greenhouse conditions.
Cloud seeding Another simple type of geoengineering that has been suggested would be to seed low-lying clouds by injecting other kinds of particulate matter into the low atmosphere. For example, injecting ocean salt into the air above the ocean could increase cloud cover and increase albedo. If done at a sufficiently large scale to counteract substantial radiative forcing on the order of several W/m, this could lead to unexpected changes in precipitation and circulation patterns.
35.4.4 Adaptation
In the absence of finding technically, economically, and politically acceptable mechanisms for implementing options 1, 2, or 3, humankind will have to adapt to changing climate and weather patterns beginning in the near future and continuing over the next several hundred to thousand year time frame. While very fast on the geological time scale, significant changes in seasonal weather and sea levels will only occur over decades, relatively long on the time scale of the human attention span. These changes will necessitate substantial migration of human populations from areas affected by changes such as desertification or sea level rise, and/or projects to provide irrigation, dikes, and the like. Natural ecosystems will not have time to adapt through evolution, and in many places already are constrained by human land use. Climate change will add to the strong external stresses already imposed on many terrestrial and ocean ecosystems by human activity.
Discussion/Investigation Questions
35.1 The radio-isotope beryllium-10 () is often employed in studies of paleoclimates. How is formed? With which aspects of paleoclimate is correlated? How is used, for example, to extract climate information from ice cores?
35.2 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.
35.3 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 of interest to you and consider some of the implications.
35.4 Fertilizing phytoplankton in the deep ocean was mentioned briefly as a proposed way to sequester large amounts of CO. Explore this proposal. What do its advocates claim? What criticisms have been voiced? What is your opinion of the present state of affairs?
Problems
35.1 Compute the insolation at 65° latitude on the summer solstice for tilt of 22.05° and compare to the value at 24.5°.
35.2 Variation in sunspot activity leads to variation in the solar constant by roughly 1–2 W/m with a roughly 11 year cycle. Assuming an albedo of , estimate the radiative forcing arising from an increase in the solar constant by 2 W/m. Using the IPCC mean result for feedback, what increase in surface temperature would this cause?
35.3 Since the formation of the solar system 4.6 billion years ago, the net solar luminosity has increased roughly 40% from its initial value. Assuming that luminosity has increased at a constant rate, estimate the solar constant 100 million years ago, during the Cretaceous period. Assuming current climate conditions and an albedo of , what radiative forcing would be needed to keep Earth in its current state (as of say 1950) if the Sun had the luminosity of the Cretaceous period? What level of atmospheric CO would achieve this radiative forcing?
35.4 In another billion years solar luminosity will increase by roughly another 10%. Estimate the resulting radiative forcing and change in terrestrial surface temperature.
35.5 Compute the time to melt 3000 m thickness of ice if there is an extra 5% of 200 W/m average daily insolation for four months out of the year beyond the insolation that would give an ablation rate matching the accumulation rate from fresh snowfall.
35.6 Compute the time for the oceanic mixed layer (350 M km 200 m) to warm by 3.2 K, using 50% of the energy coming from a change in radiative forcing of 3.7 W/m. Advanced version: assume that radiative forcing is proportional to as the surface warms and describe the time-history of the surface water by writing and solving a differential equation.
35.7 Reproduce the graphs in Example 35.1 by performing the numerical calculations on a computer. Find a way of improving the assumptions and redo the calculation.
35.8 Assume that 1% of a net radiative forcing of 3.7 W/m worldwide goes to melting ice over land. Estimate the rate of sea level rise from this melting.
35.9 (a) Assume that the rate of carbon emission at 10 Gt/year increases at a constant rate to a maximum of 20 Gt/year in 2050, and then decreases at the same rate. Assume that ocean and land biomass together absorb excess CO at a constant rate of Gt/year. In what year will atmospheric CO levels peak? What will be the level of atmospheric CO in that year? (b) Repeat the analysis under the more optimistic assumption that ocean and land biomass together absorb 2.5% of the excess in atmospheric carbon above 600 Gt each year, assuming for simplicity that atmospheric carbon is 800 Gt in 2010.
35.10 Estimate the contribution to global sea level rise over a century if Greenland’s glaciers continue to melt at a rate of 290 Gt/y.
35.11 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 current carbon emissions and compare to total electric production worldwide.
35.12 A concern with plans for capture of CO directly from ambient air (DAC), is the sheer volume of material that must be processed. One design requires fans to blow air at 2 m/s through 2.8 m thickness of absorber and other materials and aims to absorb 50% of the CO from the airstream. Assume a rectangular installation of length , height 100 m (and thickness 2.8 m). How large must be in order for this DAC plant to remove the CO produced by a 1 GW coal-fired power plant operating at 30% efficiency? How large a population (in the US or in your country) could have its carbon footprint eliminated by this DAC plant assuming the plant to be powered by a non-carbon source? Use the results of Problem35.11 to redo this estimate if the coal power plant itself powers the DAC facility.
* * *
1 See Appendix D.2 for a timeline that identifies the geological eras mentioned throughout this chapter.
2 More generally, the orbital time scale refers to time periods on the order of tens or hundreds of thousands of years that are relevant for periodic changes in orbital geometry.
3 It is generally assumed that this fluctuation range in luminosity over the solar cycle, which has been empirically measured only in the last few decades, has held over longer periods of time.
4 Some arguments have also been put forth that human activity may have played some part in cooling during the Little Ice Age through changes in forestation.
5 Some explanations for such a hiatus even in the presence of forcing from anthropogenic CO include decreased solar activity, negative radiative forcing from sulfates in increased coal emissions, and cooling from ocean oscillations. Whether there was in fact a true hiatus has been questioned by a careful reanalysis of sea and land surface temperature records [262].
6 Also known as the BLAG hypothesis after its originators, American geologists R. A. Brenner, A. C. Lasaga, and R. M. Garrels.
CHAPTER 36
Energy Efficiency, Conservation, and Changing Energy Sources
Energy conservation and energy efficiency can decrease the total quantity of energy used by humanity, reducing pressure on finite resources and minimizing undesirable side effects of energy use such as climate change, pollution, and habitat destruction.The finite nature of fossil fuels and other non-renewable resources motivates conservation and efficiency and will eventually necessitate a shift to renewable energy resources. The impact of carbon emissions on global climate also motivates conservation and efficiency as well as a more rapid change to renewable resources. In this chapter we consider these issues, integrating material from the preceding parts of the book.
Although they are conceptually quite different, energy efficiency and conservation are often discussed together and sometimes conflated. Here we use energy efficiency to refer to the relative amount of useful output, such as mechanical work, that can be obtained by a device or system from a given input, such as thermal energy. The quest for greater energy efficiency is primarily a scientific and engineering challenge. Energy conservation, on the other hand, involves choosing among systems or altering behavior with the goal of using less energy. Energy conservation involves economic, social, and policy choices that can be informed by, but not solely determined by technical considerations. A simple physics analysis can determine how much energy can be saved by turning down a home thermostat (§36.5.3), but it cannot predict the willingness of a family to set the thermostat to 18°C and don sweaters rather than T-shirts indoors in midwinter.
The first parts of this chapter are devoted to a quantitative reconsideration of the notion of efficiency. So far in this book we have introduced several measures of effectiveness for devices that transform or transfer energy, such as the efficiency of a heat engine or a photodiode. These are known as 1st law efficiencies: the amount of a desired output such as work or thermal energy divided by the energy input. In §36.1 we briefly summarize the 1st law efficiencies and other related concepts introduced throughout the book along with the fundamental physical limits that constrain them.
Reader’s Guide
This chapter explores the related concepts of efficiency and conservation and the long-term prospects for changing energy sources. The concepts of 1st and 2nd law efficiencies are introduced and applied to transformations of energy from one form to another. Exergy or available work is introduced as a measure of the useful work that can be extracted from a given energy resource,and exergy is related to 2nd law efficiency. A few case studies are presented to illustrate the use of physics to provide input to energy conservation analyses. Finally, an overview is given of large-scale and high-density energy resources that may in the future replace fossil fuels as primary energy sources.
Prerequisites: §5 (Thermal energy), §8 (Entropy and temperature), §10 (Heat engines), §9 (Energy in matter), §13 (Power cycles).
The concept of exergy arises in §37 (Energy storage).
When the 1st law efficiency of a device is quoted, it gives no indication of how well the device performs compared to the best performance allowed by the laws of thermodynamics. This information is provided by the 2nd law efficiency, which is introduced in§36.2. There we define and tabulate 2nd law efficiencies for many of the most commonly encountered processes. To illustrate 2nd law efficiencies we consider the practical example of the most efficient way to provide space heating in §36.3.
The notion of 2nd law efficiency leads naturally to the question of how to quantify the maximum amount of useful energy that can be provided by a given device or system located in a particular environment. This maximum energy is known as the availablework or exergy of a device or system relative to the environment. Exergy is a very useful concept, which enjoys widespread use in engineering fields and in industrial ecology, the study of the flow of materials and energy through industrial systems. Both exergy and 2nd law efficiency were mentioned briefly in §32.4.2 in connection with the performance of geothermal power plants. In §36.4 we examine exergy more closely, show how it can be used to evaluate the utility of various energy sources, and return to the question first raised in §1 (Introduction) about the meaning of the phrase “energy consumption” in light of the fact that energy is conserved. We point out that exergy is a quantitative measure of the value of energy, and that the transition from “useful” to “useless” energy can be understood as the destruction of exergy.
No special physics concepts are required to evaluate proposals for energy conservation, which we consider in §36.5. Instead, the role of physics in energy conservation is usually to provide technical input to decisions where economic and policy considerations are of fundamental importance. In keeping with the scope of this book, we do not attempt to treat the economics of energy conservation here. Instead we present several examples to illustrate how the principles developed in this book provide the scientific input necessary to evaluate the potential for energy conservation and to enable informed economic choices among competing technologies. The American Physical Society has produced two excellent reports on energy efficiency where further information on efficiency and conservation can be found [275, 276].
We conclude this chapter with some global perspective on energy resources that is relevant when considering the prospects for changing energy sources over the long term, or in the shorter term motivated by decarbonization of energy systems. In §36.6, we summarize the extent of available resources that have potential for large-scale power production or that may be particularly economically favorable due to high energy density. Finally, we examine the potential of these resources for replacing fossil fuels in the long run.
36.1First Law Efficiency
Many measures of performance have been introduced throughout this book to indicate how effectively a device or system transforms energy from one form to another. The ratio of the desired energy output or transfer, which is often work or thermal energy, divided by the energy input, which may come in any form, defines the 1st law efficiency of the device or system,
(36.1)
Some transformations are by their nature quite efficient. For example, electrical energy can be transformed into mechanical energy by a motor with losses of only a few percent. Others are necessarily very wasteful, notably the transformation of heat into work, which becomes very inefficient when the heat source is only slightly warmer than the ambient environment.
There are obvious issues with eq. (36.1) as a definition of efficiency. In particular, although it is natural to think of “efficiency” as a quantity that is less than one, η can be much greater than one in the case of heat pumps and other heat extraction devices, where η coincides with what we earlier called the coefficient of performance (CoP, §10.6.1). This and other issues can be resolved by introducing the concept of 2nd law efficiency, which we do in the following section.
In this section we briefly review 1st law efficiencies and some related ideas for various energy transformation processes and collect the limits on these efficiencies. Although many of these ideal limits are rarely approached (and even then only in laboratory devices), they are the benchmarks to which practical devices should be compared. The 1st law efficiencies reviewed in this chapter are summarized in Table 36.1. We also discuss several other types of energy limits in this context that are not precisely 1st law limits, namely the Betz limit on energy extraction from wind by a system modeled as an actuator disk, and the limit on how much computation can be performed with a given amount of energy.
36.1.1 Transformations Involving Mechanical and Electrical Energy
Transformation from one form of mechanical energy to another, for example from the gravitational potential energy of water stored behind a dam to the rotational motion of a turbine, or from the reciprocating motion of pistons in an automobile to the rotation of the wheels, can in principle be carried out with very little waste. Losses are mainly due to friction between moving parts or to resistive drag by a fluid, typically air or water. Friction and air/water resistance convert entropy-free mechanical energy into the random vibrations of solids or the random motion of a fluid and therefore increase the entropy of the system.
For convenience, we refer here to all macroscopic forms of mechanical energy as “work,” and define the 1st law efficiency for transformation between one form of mechanical energy and another as
(36.2)
To the extent that frictional losses can be eliminated, mechanical energy can be transformed from one form to another with nearly perfect efficiency,
(36.3)
The transformation of the kinetic energy in a flowing fluid into useful mechanical energy requires further consideration. As discussed in §28 and §30, the Betz limit requires that a device such as a horizontal-axis wind turbine (HAWT) that can be modeled as an actuator disk of area A, operating in a plane perpendicular to a steady, unidirectional fluid flow, can harvest no more than 16/27 or 59% of the power that passes across an area in the flowing fluid far from the device. The rest of the energy remains in the flowing fluid, however, and can, in principle, be captured by devices placed further downstream. Although it is therefore not an absolute efficiency limit like Carnot’s limit on heat engines, Betz’s limit plays an important role in judging the effectiveness of wind and tidal stream turbines.
