Availability, Exergy, the Second Law and all that.......

Mark Simpson and James Kay

© COPYRIGHT 1989

The absurdity of cutting butter with a chainsaw is immediately obvious to anyone. When doing any job we match the size and power of the tool used to do the job to the size and power of the task we wish to perform.

Unfortunately, such common-sense seldom applies to energy policy. Little attempt is ever made to match the quality of the energy source to that required by the job. This is because energy analysts continue to advocate policies with no reference to the science of energy - thermodynamics.

An examination of thermodynamic principles reveals that the current focus on energy conservation, as a strategy, is at best incomplete and at worst wholly incorrect. As it is converted from one form to another, energy is neither lost nor destroyed. It does, however, "lose a certain quality which can be described as its ability to do work." [1] Since it is the ability of energy to do work which gives energy its value to society, we should strive to conserve available work, not energy.

The amount of available work and the amount of energy in a particular fuel source are often unequal quantities. Because conventional energy analysis fails to recognize this distinction, wasteful policies are often implemented in which the amount of work that can be extracted from an energy source is very large relative to the amount of work required to do the job. We end up cutting butter with a chainsaw.

As we shall examine in more detail later, using electricity for resistance heating of homes and buildings is a case where the energy source is disproportionate to the task. Most of the electricity used for space heating is wasted because it could have been used to perform far more work than the small amount of work required to keep us warm.

A new measure of efficiency based on the second law of thermodynamics has been developed that incorporates the concept of available work. Using a second law energy efficiency, Dr. M.H. Ross at the University of Michigan and Dr. R.H. Williams at Princeton University have estimated that in many sectors of the economy, notably residential space heating and industrial process steam production, that fuel consumption could be cut by half or more. [2]

Because of the enormous potential for fuel savings that a second law efficiency analysis makes evident, it is important that analysts, educators, and students understand the principles of this approach to energy analysis. This article intends to outline these principles and how they differ from a conventional approach so that we can begin to realize the true potential for conservation of energy resources.

Conventional energy analysis applies the first law of thermodynamics to evaluate energy options. The first law of thermodynamics is the law of the conservation of energy. According to the first law, energy is neither created nor destroyed in any normal physical or chemical process, but merely changed from one form to another. Because the total amount of energy remains constant, the energy lost by a system during any process equals the energy gained by the system's surroundings.

Consider Niagara Falls as an example. The water at the top of the falls has gravitational potential energy by virtue of its height above the gorge. This energy is transformed into kinetic energy as the water drops over the falls. The kinetic energy of the falling water can be used to produce work, and indeed is used very successfully to generate electricity.

But what about the water at the bottom of the falls. It is tempting to believe that the original gravitational potential energy that the water possessed at the top of the falls has been lost. "Has the first law been violated? No, the water at the bottom of the falls is one eighth of a Celsius degree warmer than the water at the top of the Falls." [3] This heat energy is caused by the friction of the water molecules crashing against one another and against the rocks. The roar of the falls indicates that some of the original gravitational potential energy has also been transformed into sound energy.

The total amount of sound and heat energy at the bottom of the falls is exactly equal to the total amount of gravitational potential energy at the top of the falls. The essential difference between the two forms of energy is that we can harness the high quality concentrated gravitational potential energy at the top of the falls to perform work -- we can run an electric generator for example -- whereas the low quality heat and sound energy at the bottom is too dispersed to be of any use.

A traditional first law analysis does not account for these differences in energy qualities. A first law efficiency only compares the total amount of energy put into a system to the total amount gotten out of the system. The problem with such an approach is that because it does not indicate how much work could have been extracted from the energy source, it is impossible to determine if the capacity of the energy source to perform useful work has been wasted.

This inadequacy in a first law analysis becomes evident when attempting to recover heat that is lost up the chimney in a typical combustion furnace. A first law analysis indicates that 60 percent of the fuel's energy goes into the heated air while 40 percent of the fuel's energy is lost up the chimney with the combustion gases. A second law analysis, however, would indicate that only 25 percent, not 40 percent, of the fuel's capacity to perform useful work is lost up the chimney. Remember, we value energy because of its ability to perform work. A second law approach shows that the major inefficiencies are in the combustion and heat transfer processes -- where 30 and 35 percent of the fuel's capacity to perform work is comsumed, respectively. A first law analysis would encourage an energy analyst to focus attention on the chimney, the wrong place. [4]

THE SECOND LAW OF THERMODYNAMICS:

An approach to energy efficiency based on the second law of thermodynamics clearly indicates whether or not the capacity of an energy source to perform useful work has been achieved.

As already mentioned, energy varies in its quality or capacity to do useful work. Water at the top of a high cliff is a high quality energy source because it can be used to perform work. We can use the falling water to turn a turbine and produce electricity. But the high quality concentrated energy in the falling water is turned into low quality dispersed heat energy as it reaches the bottom of the cliff. This process of energy degradation is one way of stating the second law of thermodynamics. The second law is the law of energy degradation. During any chemical or physical process the quality or capacity of the energy to perform work is irretrievably lost.

The degradation of energy quality is permanent and irreversible. Consider, for example, the impossibility of concentrating all of the dispersed additional heat of one eighth of a degree Celsius in the water at the bottom of the falls to drive a pump to raise the water back to the top of the cliff.

The irreversible reduction in energy quality described by the second law of thermodynamics fits with our common-sense notion that something is lost when we burn fuel. We don't lose quantity - it is conserved as the first law tells us - but the second law tells us that what we lose is energy quality, or the capacity to perform useful work.

AVAILABILITY:

The second law of thermodynamics clearly indicates that we should not necessarily strive to conserve energy, rather we should attempt to conserve the capacity of the energy source to perform work. To do this requires the concept of availability.

Availability is a measure of the maximum capacity of an energy system to perform useful work as it proceeds to a specified final state in equilibrium with its surroundings. [5] The available work that can be extracted from an energy source depends on the state of the source's surroundings. The greater the difference between the energy source and its surroundings, the greater the capacity to extract work from the system. While the energy of a system is also proportional to the difference between an energy source and its surroundings, energy and availability are not the same thing. A simple example illustrates the difference between energy and availability.

Source: Michael J. Moran, Availability Analysis: A Guide to Efficient Energy Use (New Jersey: Prentice-Hall, Inc., 1982), p.2.

Consider a large enclosure consisting of a small container of fuel surrounded by a great deal of air, as shown in figure 1. If we burn the fuel, the air temperature inside the enclosure will rise, and we will be left with a slightly warm mixture of combustion products and air. "Though the total quantity of energy in the enclosure is unchanged, the initial fuel-air combination has greater potential [exergy or availability to perform useful work] than the final warm mixture." [6] The initial situation is intrinsically more useful. The fuel can be used in some device to generate electricity, to heat water, or to run an engine. While energy is conserved, burning the fuel irreversibly destroys its availability or capacity to perform useful work.

As you may have noticed, several terms are commonly used to refer to the capacity of an energy source to perform work. "Exergy" is often used in Europe, while "Availability" is more common in the United States. In Canada the two terms are used interchangeably. "Capacity" and "Potential" are also used, although less frequently.

SECOND LAW EFFICIENCY:

A second law efficiency accounts not only for energy quantity but also for energy quality. The method of calculating second law efficiencies "reminds us that energy in itself has no value unless it can be used to produce work by flowing from one place to another; that every human activity such as heating a home requires work; that the value of energy is measured by the work it can do; and that the efficiency with which energy is used ought to be measured by how closely the amount of available work used to accomplish the task corresponds to the minimum amount of energy the task requires." [7]

A second law efficiency is the ratio of the minimum amount of available work required to do a particular job to the amount of available work actually used to do the job. [8] Contrast this with a first law efficiency which is the ratio of energy out to energy in.

Electric baseboard heaters provide a good example to illustrate the distinction between a first and second law efficiency measure. The availability or capacity of electricity to perform useful work is great. As electricity is used in a baseboard heater, the availability is lost and cannot be used to produce any more work. The energy in the electricity, however, is almost completely transformed into heat energy to heat the home.

Analysts often quote efficiency figures of 90 percent or greater for electric baseboard heaters. From a first law perspective they are correct: over 90 percent of the energy in the electricity is converted to heat energy. But this efficiency calculation says nothing about the available work that is wasted in this energy conversion. Ross and Williams have calculated the second law efficiency of electric baseboard heaters to be 2.5 percent, considerably less than the 90 percent quoted by most analysts using a first law efficiency. [9] Table 1 indicates similar discrepancies in other sectors of the economy between the two efficiency measures.

TABLE 1: COMPARISON OF FIRST AND SECOND LAW EFFICIENCIES

Source: American Institute of Physics, Efficient Use of Energy (New York: American Institute of Physics, 1975), pp.49-50.

While 90 percent of the energy in the electricity may be converted to heat energy, very little of the availability or capacity of the electricity to perform work is used. Heating a home is a task that requires very little work. The air temperature has to be heated to only 20 degrees Celsius. But the electricity in the baseboard heater has the capacity to do far more work than just heat the house. For instance, if the electricity were used to drive a heat pump, much less electricity would be used to heat the home. The electricity saved by using the heat pump would then be available to perform some other task requiring high quality energy (i.e. running a micro-computer).

A heat pump is a device that moves energy from one place to another. For instance, a fluid in the device could be pumped through underground pipes in the backyard of a house. The fluid absorbs the heat in the ground and is then pumped back into the house where the fluid gives up its acquired heat to the air in the house. A heat pump can also work in reverse in the summertime to remove heat from the house and release it to the outside air. Heat pumps use far less electricity to perform the same heating job as baseboard heaters because the electricity is not used for heating, it is used to run the heat pump's motor. The motor pumps the energy in the ground into the house (or vice versa in the summer). The motor itself requires very little energy to move very large amounts of energy. However, the motor requires high quality energy (i.e. electricity). By using a heat pump to heat the capacity, or availability, of the electricity to perform useful work is used much more fully relative to resistance heating.

(It is impossible for anything to be more than 100 percent efficient, otherwise it would be creating energy out of thin air, yet all first law analyses quote heat pumps and air conditioners as having efficiencies greater than 200 percent! (see Table 1) Such efficiency calculations include the heat that the device is moving, such as the heat in the ground in the heat pump example, as part of the output energy, but not as part of the input energy. Since the device's output energy far exceeds the electrical input energy an effeciency greater than 100% is arrived at.).

For more detailed discussion and examples on a second law approach to energy analysis, refer to the bibliography at the end of this article.

As the electric baseboard heater example illustrates, when determining second law efficiencies it is essential to know what task the energy source is being used to perform. Not only is it necessary to know whether lighting, heating, or motor power is required, it is also necessary to know the conditions of the task. For example, when providing heat to the interior of a house, the insulation level, air tightness, and the temperature at which heat is to be delivered must be specified in order to determine how much work is required to do the job.

While these details pose problems of gathering information, they are also absolutely necessary for any energy conservation measure. "Only an explicit analysis of the end-use process can show the implications of, and potential for, changes in both the demand for energy services and the technology and efficiency with which they are provided." [11] Consider the example of reducing demand for residential space heating. Methods could include setback thermostats, increased insulation levels, and caulking and weatherstripping. "In order to assess the potential fuel savings from such measures, it would be necessary to have data on the sizes, insulation levels, infiltration rates, heating fuels, heating device efficiencies and local climatic conditions of the homes in question." [12]

Only the amount of energy entering and leaving a particular device is required by a first law analysis. A second law analysis, however, because it requires such detailed information, serves to promote and complement all forms of energy conservation.

A second law analysis also points out where certain fuels are being used inappropriately, such as the case where electricity is used in resistance heaters for space heating. A second law approach to energy analysis indicates that,

Because a second law approach illustrates the enormous waste of using electricity for space heating, we must re-evaluate the need for large, centralized electrical generating facilities. Low quality energy tasks such as space heating can be provided more efficiently and cheaply by other means. In some office buildings, Ontario Hydro headquarters for example, heating is provided by capturing the "waste" heat emitted by office equipment such as computers, photocopiers, people and lights. Ducting collects this excess heat and redistributes it to cooler areas of the building or stores it for later use. Thus, the high capacity or availability of electricity to perform work is not wasted on a task (heating) that requires very little work and the overall need for electricity is reduced. We avoid cutting butter with a chainsaw.

Numerous other examples exist where the energy source can be matched thermodynamically to the task. As previously mentioned, ground source heat pumps are an excellent way to make use of the low quality heat in the ground to provide for the low quality energy demand of space heating and of not wasting our capacity to perform other tasks that require a high quality energy source.

Clearly, maximizing the second law efficiency will lead to different strategies than maximizing first law efficiencies. For example if Ontario needs more space heating capacity, a second law strategy would consist of identifying appropriate low quality energy sources in the locale of the structures to be heated and ways of tapping the sources. This is in contrast to a first law strategy which would consist of using highly "efficient" electrical heaters, and thus building more nuclear power plants. Inevitably, the maximization of the second law efficiency would have a significant impact on policy choices. [14]

BIBLIOGRAPHY

Brzustowski, T.A. and P.J. Golem. "Second Law Analysis of Energy Processes Part 1: Exergy - An Introduction" in Transactions of the Canadian Society of Mechanical Engineers (CSME). 1978.

Commoner, Barry. The Poverty of Power. New York: Alfred A. Knopf Inc., 1976.

Gardner, Thomas Douglas. Evaluating the Potential for Improved Energy Efficiency with Application to the Simulated Economic Resource Framework (SERF). Waterloo: By the Author, Graduate Thesis, 1987.

Georgescu-Roegen, Nicholas. "The Steady State and Ecological Salvation: A Thermodynamic Analysis" in Bioscience, April 1977, pp. 266-270.

Moran, Michael J. Availability Analysis: A Guide to Efficient Energy Use. New Jersey: Prentice-Hall Inc., 1982.

Reynolds, William C. and Henry C. Perkins. Engineering Thermodynamics. New York: McGraw-Hill, 1977.

Rifkin, Jeremy and Ted Howard. Entropy: A New World View. New York: Viking, 1980.

Ross, Marc H. and Robert H. Williams. "The Potential for Fuel Conservation" in Technology Review, February 1977, pp. 49-57.

Ross, Marc H. and Robert H. Williams. "Energy Efficiency: Our Most Underrated Energy Resource" in Bulletin of the Atomic Scientists, November 1976, pp. 30-38.

Torrie, Ralph. Half Life: Nuclear Power and Future Society. A Report to the Royal Commission on Electric Power Planning, Ottawa: Ontario Coalition for Nuclear Responsibility, 1981.

1. Ralph Torrie, Half Life: Nuclear Power and Future Society (Ottawa: Ontario Coalition for Nuclear Responsibility, 1981), p.176.

2. Marc H. Ross and Robert H. Williams, "Energy Efficiency: Our Most Underrated Energy Resource" in Bulletin of the Atomic Scientists, November 1976, p.132.

3. Torrie, p.174.

4. Thomas Douglas Gardner, Evaluating the Potential for Improved Energy Efficiency with Application to the Simulated Economic Resource Framework (SERF) (Waterloo: By the Author, 1987), pp.29-30.

5. American Institute of Physics, Efficient Use of Energy (New York: American Institute of Physics, 1975), p.28.

6. Michael J. Moran, Availability Analysis: A Guide to Efficient Energy Use (New Jersey: Prentice-Hall Inc., 1982), pp.2-3.

7. Torrie, pp.178-179

8. American Institute of Physics, p.29.

9. Ross and Williams, p.31.

10. Torrie, p.178.

11. Gardner, p.7

12. Gardner, p.8

13. Torrie, p.180.

14. American Institute of Physics, p.28.

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