The Physics of Energy, page 160
As discussed in §33.1.7, modern ultra-supercritical coal-fired power plants achieve 1st law efficiencies in the mid-40% range. Thus there is considerable room for improvement in efficiency in US coal plants. For natural gas, as also noted in §13, state-of-the-art CCGT 1st law efficiencies in excess of 60% have been achieved. So even though natural gas-fired power plants have higher efficiency than coal plants on average, there is still room for improvements in CCGT plant efficiency. Finally, as explained in §19.5, Generation III light-water reactor power plants that include reheating and regeneration are able to reach 33–37% efficiency. So although there is still room for improvement, nuclear electric power plants are operating closer to their current technical limits than either coal or combined cycle gas plants.
The total opportunities for improving energy efficiency (without changing energy sources) across the US electricity generating sector are significant. Together, coal, natural gas, and nuclear power plants account for 22.3 EJ/y of the 26.8 EJ/y of “rejected energy” in US electricity generation.8 If these power plants were improved to state-of-the-art systems with the best realizable 1st law efficiency for each primary energy source, the rejected energy would decrease from 22.3 EJ/y to 14.1 EJ/y, saving 8.2 EJ/y of primary energy per year. The associated abatement of CO2 emissions would be about 0.5 Gt(CO2)/y, which is almost 10% of total US CO2 emissions (Problem 36.15).
The opportunity for further reductions in “rejected energy” and for CO2 abatement through changing energy sources are also significant. As discussed above, in the absence of consideration of externalities such as carbon emissions, there is no clear motivation to reduce rejected energy per se if all systems being used deliver the largest fraction of available exergy possible using existing technology. The motivation for CO2 abatement, however, provides an incentive to reduce rejected energy from fossil fuel sources, however, since this has the side effect of also reducing carbon emissions. The average 1st law efficiency of coal-fired power plants is less than 3/4 of the average 1st law efficiency of US CCGT plants. Even more striking, the CO2 intensity (mass of CO2 emitted per unit of electricity produced) of coal power plants is over 2.5 times the CO2 intensity of natural gas power plants. Replacing all US coal power plants with natural gas power plants at the current average efficiency would reduce rejected energy by 9.4 EJ/y and reduce CO2 emissions by over 0.8 Gt(CO2)/y, abating nearly 15% of US yearly CO2 emissions. Upgrading natural gas power plants to CCGT plants at 60% efficiency would further reduce rejected energy by 6.4 EJ/y and further abate CO2 emissions by another 0.3 Gt/y. Of course, shifting away from fossil fuels entirely could in principle reduce electricity production related CO2 emissions nearly to zero. As emphasized in the introduction to this chapter, decisions such as these among competing technologies require economic and policy analyses that go beyond the technical aspects we have considered.
36.5.2 Automobile Efficiency and Mileage
The transportation sector was the second largest source of rejected energy in the US in 2016 (Figure 1.2). This was also the sector with the lowest 1st law efficiency (21%). This is particularly remarkable because, as discussed in §2, people and goods can in principle be transported across Earth’s surface with no losses at all; when transporting mass between two points at sea level, there is no change in potential energy and any kinetic energy transferred to the mass in transit can in principle be recuperated through regenerative braking at the end of the transport process. Most energy used in transport is lost to drag through air resistance, representing an inefficiency in the language of the preceding section.
The idea of vacuum tube trains or vactrains that eliminate air resistance by moving vehicles through evacuated tunnels or pipes has been contemplated for many years. Such transport devices could eliminate mechanical friction in motion by using magnetic levitation or other comparable mechanisms, and could use regenerative braking to recapture energy used in acceleration. Taken together, these measures could reduce the energy cost of transport tremendously. There are numerous practical obstacles to implementing such systems at large scale, particularly for proposals that involve tunneling channels for the vacuum train at great depth over large distances, so that gravitational potential energy can be used as the energy source. At this point there is no realistic plan to implement vacuum trains in any commercially viable context, but these ideas illustrate the possibility of essentially eliminating energy costs in transport and highlight the absence of any real physical limit that mandates a minimum energy cost for transport processes.
At a more immediately practical level, tremendous energy savings can be realized simply by continuing to decrease the mass and drag coefficient of standard passenger cars and light trucks. The idea of the hypercar has been championed by the American physicist Amory Lovins and others for many years, with idealized designs that could reach 130 km/L (300 mpg) by using highly streamlined aerodynamic designs, lightweight but strong composite materials, and a hybrid engine with regenerative braking. In recent years some concept cars entering production have begun to approach some of these ideals. The Volkswagen XL-1 is a two-person vehicle with a diesel-electric hybrid engine that is designed to optimize fuel economy. The XL-1 entered production in 2013, weighs roughly 800 kg, and has a drag coefficient of 0.189, roughly half that of typical commercial cars. Volkswagen quotes a fuel economy of 110 km/L (260 mpg), though that includes charging the battery roughly every 75 km; the pure diesel fuel economy is closer to 50 km/L (120 mpg).
The average fuel economy for new passenger cars in the US was 17 mpg in 1978, and reached 25 mpg (~10 km/L) in 2015. This amounts to more than a 30% reduction in fuel use and carbon emissions per mile traveled. Increasing fuel economy to 50 or 75 mpg, which seems in principle feasible within decades, would further reduce carbon emissions per mile traveled by a factor of 2 or 3, with 75 mpg giving a reduction to less than 25% of 1978 CO2 emissions per mile traveled.
While kilometers per liter or miles per gallon are often used as an approximate measure of efficiency, they are not a good measure of energy consumption or a good comparative measure across vehicles. Because a given driver tends to drive a given distance in a week or year, rather than use a given quantity of fuel, what matters on average is the amount of fuel used (L/km) or CO2 generated (kg/km) to go some fixed distance, which is inversely proportional to the mileage. In fact, outside the US automobile energy efficiency is usually quoted in units of liters per 100 km. Consider, for example, two drivers with cars that respectively get 5 km/L and 15 km/L, and suppose each drives 15 000 km in a year. The first driver uses 3000 L of gasoline and the second uses 1000 L. On average, the two drivers use 2000 L to drive 15 000 km per year. Thus L/km is an accurate measure of the yearly gasoline use of the average driver, corresponding to an average of km/L, much less than the average of km/L that would apply when each uses the same quantity of fuel.
One particular utility of using L/km rather than km/L, is to compare the relative increase in fuel economy between different vehicles. Suppose, for example, each car in the previous example made improvements leading to a savings of 500 L in its annual fuel consumption. For the inefficient car, this corresponds to an increase in mileage from 5 km/L (12 mpg) to 6 km/L (14 mpg), a relatively modest 17% increase in efficiency. For the second car, however, a similar fuel savings would require doubling its fuel economy from 15 km/L (35 mpg) to 30 km/L (70 mpg), a much more difficult challenge using current technology. The comparison is illustrated graphically in Figure 36.3. This example makes it clear that for global reduction in carbon emissions, the easiest route to immediate progress is to increase the fuel economy of those vehicles that are least fuel efficient, rather than aiming for increasingly high fuel economies for the vehicles in the fleet that are already most fuel efficient.
Figure 36.3 Amount of gasoline required to drive 15 000 km as a function of mileage. 500 L are saved by increasing mileage from 5 to 6 km/L. An equivalent savings for an automobile that gets 15 km/L would require doubling its mileage to 30 km/L.
We do not attempt to describe or analyze in detail the opportunities for improved energy savings in the full transportation sector; such a task is made quite difficult by the complex mix of modes – land, sea, and air – and scales – local, national, and intercontinental – that characterize transportation. For each transportation mode, however, there is a great potential for energy savings and carbon emission reduction. Beyond improving fuel economy, a switch from fossil fuel sources to electric cars powered by solar or wind energy would clearly provide ground transformation at minimal cost in carbon emissions. While it is unlikely that large passenger aircraft could be run from electric power alone, due to constraints on the mass of batteries, one option for a carbon-free approach to air travel would be to use biofuels. Conservation measures for transport such as pooling vehicle use through public transit, trains, carpools, etc., offer the prospect of further reductions. And at a broader level, changes in socioeconomic configurations that reduce commute distance provide opportunities for further savings and carbon emission reduction.
36.5.3 Extended Example: Home Heating
As mentioned in §36.3, home heating is the single largest contributor to home energy consumption, about 4.5 EJ of primary energy in the US [12]. Most of this energy comes in the form of natural gas and is employed with high 1st law efficiency through direct use of the thermal energy from combustion. Nonetheless, homeowners, renters, or landlords concerned about energy consumption or CO2 emissions related to residential heating can take many steps to reduce both. Some steps, such as turning down the thermostat, turning off the heat at night or lights in unoccupied rooms, represent energy conservation methods that come at zero capital cost. Other energy saving measures, such as adding insulation, upgrading windows, or reducing infiltration, provide the same level of heating performance with lower energy consumption, come at relatively low cost, and pay back the investment quickly. Some of these approaches to energy savings were described in §6.4. Still other steps, such as installing solar thermal collectors or a ground source heat pump, require significant investments. In many countries policy makers have advocated, and governments have adopted, incentives to promote one approach or another. How should these measures be compared? Ultimately choices depend on the cost of investments and the relative availability and cost of different forms of energy. The foundation of any comparison, however, lies in the basic physics that determines the amount of energy used, saved, or generated by a given behavior. In this section we compare the results of various different approaches to energy conservation and savings in the context of home heating.
Heat Losses from a Residence
To illustrate the possibilities we analyze as a simple model a “typical” family dwelling with a floor area of 100 m2, and an effective exterior wall area (including ceilings, floors, and 15 m2 of windows) of 100 m2.9 To make quantitative estimates we also need an estimate of the heat capacity of the dwelling including walls, furniture, air, etc., which is known in this context as the thermal mass. We take MJ/K, corresponding to about 2.5 t of water.
Heat must be supplied to interior spaces to make up for the heat that leaks out by conduction, convection, and radiation though walls, ceilings, floors, and windows. Air infiltration through cracks and other openings is also significant. Since all of these losses are proportional to the difference between the interior temperature T and the temperature of the environment , heat leakage can be summarized by a single parameter, the effective thermal resistance of the dwelling (see §6.2.5), which enters the equation
(36.39)
In principle, could be calculated from an assessment of the materials and construction of the dwelling; in practice this is quite complicated and , or more precisely , is instead determined empirically. In steady state, some source must provide heat at the rate (36.39) in order to keep the interior temperature constant. Some of this heat may come from normal household activities like cooking and thermal radiation from the living inhabitants, some may come from solar gain through windows, and some may be generated by a furnace or other system installed for the explicit purpose of heating the dwelling. We define to be the heating rate provided by all sources. By observing the heating rate required to maintain a temperature difference , the quantity can be determined. We take the effective thermal resistance for the entire exterior shell (including windows) of our dwelling to be (ft2℃ h/BTU in US units), so W/K.
If and are not equal, the interior temperature will change at a rate proportional to the difference and inversely proportional to the thermal mass of the dwelling,
(36.40)
This relation provides a way to empirically determine , which, like , is difficult to compute from first principles.
The yearly total amount of thermal energy required to keep the living space at a constant temperature T can be computed by setting and integrating eq. (36.39) over the period when the exterior temperature is less than T,
(36.41)
where the integral is over the period of the year (the heating season) when the integrand is positive, which is taken to have duration is the average of the exterior temperature over the heating season, and has units of -days and is known as the number of heating degree days. In many locations l the average outside temperature is recorded on each day j, allowing to be estimated as the average of the values over the days j in the heating season.
At a given location l, the number of heating degree days thus depends on the assumed interior temperature T. A standard working assumption, which we follow here, is that 20C (68 ℃) is comfortable and that appliances and occupants generate enough heat to raise the interior temperature by about 1–2C (3 ℃), making (65 ℃) a standard value.
When averaged over years, the daily outside average temperature in a given location l can be taken to be a smooth function, , and can be taken to be the average of this function over the heating season,
(36.42)
where is the length of the heating season in days and corresponds to the midpoint of the heating season.
Box 36.2 Sinusoidal Yearly Temperature Variation
To study the effects of changing the interior temperature, it is useful to have an analytic form for . As Figure 23.6(a) indicates, the insolation at temperate latitudes (e.g. 40°) varies roughly sinusoidally with a periodof 12 months, while at the equator the variation is sinusoidal with a period of 6 months (and smaller amplitude).One expects, therefore, that the temperature at a location l in the temperate latitudes, averaged over many years, would be approximately described by a sinusoidal function
where so that the cosine function goes through one oscillation in a year. Here is the average annual temperature, is the maximum (average) excursion from , and days of the year are counted starting at midwinter where is lowest. At locations closer to the equator a component with frequency should become significant. Monthly average temperature data from two US cities, Boston (latitude 42.3°) and Atlanta (latitude 33.7°), are shown in Figure 36.4, along with a sinusoidal fit. For Boston the term is negligible ( compared to the term). For Atlanta the term is about 6% of the dominant term. The fit with both and is shown in green on the Atlanta figure.
As explained in Box 36.2, in temperate latitudes the function is well approximated by
(36.43)
where days, is the average annual temperature, and is the maximum excursion of the average daily temperature from .
Substituting eq. (36.43) into eq. (36.42) gives an analytic estimate for
(36.44)
where relates the length of the heating season to the parameters that describe the yearly temperature variation at the location in question.
For example, at Boston, and =, so that days, and the sinusoidal approximation of eq. (36.44) yields -days, compared to the actual (1996–2010 average) result of 3060-days (Problem (36.16)). With these basic ingredients in hand we can evaluate different strategies to conserve or produce energy.
Energy Conservation and Savings Strategies
Turning down the thermostat Lowering the setting on the thermostat is a simple and often proposed conservation measure to save energy. How effective is it? If is lowered by one degree, from to is reduced by one degree day for every day of the heating season, so (ignoring the small resulting change in the length of the heating season)
(36.45)
In Boston one saves 260-days for a 1C thermostat set back – a very significant savings of 260/3110 = 8%. In warmer climates such as Atlanta, where , the energy savings is less, but the percentage effect is even greater. To get a feel for the numbers, for our standard dwelling as described above we find GJ for Boston (Problem 36.17). An 8% saving amounts to 3 GJ, the energy equivalent of nearly 80 L of home heating oil. We conclude that turning down the thermostat is an effective, cost free, and relatively painless way to conserve energy.
Figure 36.4 Monthly average temperature in Boston and Atlanta. The total shaded area represents the heating degree days with ; the dark shaded area corresponds to . The significance of the green line is explained in Box 36.2. Lowering the thermostat set point by one degree centigrade decreases the seasonal heating requirement by about 8% in Boston and 12% in Atlanta.
