D
Definitions of Energy Efficiency

The term energy efficiency is used in several ways. The definition perhaps most often used is based simply on how much of a given task or product (be it the heating of a building for a specified time, the miles driven by a car, or the tons of iron smelted) is achieved per unit of energy expended for that task or product. For example, the number of tons of iron, t, that can be recovered from ore per Btu of energy, E, used in the smelting process, t/E, is one possible measure of energy efficiency.

Another definition is based on the total energy, Etot, required to provide a product. According to this definition, the energy efficiency for making a ton of iron would be the tons of iron, t, per Btu of total energy required, including mining, transportation, smelting, and any other input, t/Etot.

Both of the measures of energy efficiency defined above would be termed first-law efficiency (derived from the first law of thermodynamics), being based simply on actual energy use and not taking into account such things as the excess entropy due to the irreversibility of real processes. Hence, in many situations, one may use a second-law efficiency (derived from the second law of thermodynamics), which, instead of energy, uses the free energy, usually the Gibbs free energy, G, where G = H – TS. H is the enthalpy, and H = E + pV, where p is pressure and V is the volume of the system—in this case the volume of the iron produced. T is the temperature and S is the entropy. Because most processes are carried out at constant pressure, enthalpy H is the most appropriate measure, and one uses H rather than energy E. If one wishes to use the second-law efficiency, one simply replaces E, the energy used, with G, the free energy, in the expressions for the first-law efficiency.



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OCR for page 315
D Definitions of Energy Efficiency T he term energy efficiency is used in several ways. The definition perhaps most often used is based simply on how much of a given task or product (be it the heating of a building for a specified time, the miles driven by a car, or the tons of iron smelted) is achieved per unit of energy expended for that task or product. For example, the number of tons of iron, t, that can be recovered from ore per Btu of energy, E, used in the smelting process, t/E, is one possible measure of energy efficiency. Another definition is based on the total energy, Etot, required to provide a product. According to this definition, the energy efficiency for making a ton of iron would be the tons of iron, t, per Btu of total energy required, including min- ing, transportation, smelting, and any other input, t/Etot. Both of the measures of energy efficiency defined above would be termed first-law efficiency (derived from the first law of thermodynamics), being based simply on actual energy use and not taking into account such things as the excess entropy due to the irreversibility of real processes. Hence, in many situations, one may use a second-law efficiency (derived from the second law of thermodynam- ics), which, instead of energy, uses the free energy, usually the Gibbs free energy, G, where G = H – TS. H is the enthalpy, and H = E + pV, where p is pressure and V is the volume of the system—in this case the volume of the iron produced. T is the temperature and S is the entropy. Because most processes are carried out at constant pressure, enthalpy H is the most appropriate measure, and one uses H rather than energy E. If one wishes to use the second-law efficiency, one simply replaces E, the energy used, with G, the free energy, in the expressions for the first-law efficiency. 

OCR for page 315
 Real Prospects for Energy Efficiency in the United States Additionally, one other kind of definition of energy efficiency is sometimes used, based on how much the actual process deviates from the thermodynamic limit. According to this definition, a perfect process would have a value of infin- ity for either its first-law or second-law efficiency; that is, the efficiency would be the tons of iron produced per amount of energy or free energy beyond the thermodynamic limit. Hence, for a perfect process, the denominators in these measures would be zero. No real process achieves the thermodynamic limit, of course, and so no real process has an infinite efficiency according to this last kind of definition. It is also possible to use a more realistic counterpart of the (preceding) defini- tion based on the comparison with the thermodynamic limit—namely, a compari- son based on the most efficient possible process subject to a chosen time or rate constraint. This approach enables the user to compare, for example, the relative advantages and disadvantages (in energy efficiency terms) of higher-capacity but slow processes and lower-capacity but faster processes. In practice, one very rarely encounters an explicitly stated definition of energy efficiency. Most commonly, people tend to use the very first definition, the amount of a task or product (the heating of a building for a specified time, the miles driven by a car, the tons of ore smelted, and so on) per direct unit of energy required for that task. When a different definition is being used, the user generally specifies which definition is being used. In this report, because the data have been taken from a very wide variety of sources, virtually none of which specified a defi- nition, the panel assumed that the first and simplest definition was intended. This is not to imply that if the panel itself were to derive the efficiencies from primary data that it would use that same definition. The pragmatic course was taken here to allow the analysis to be carried out.