I have been asked to give a definition of the emergy unit. I would like to do a little more and define emergy itself as well as emergy efficiency. Further, I will give some examples as they apply to special cases.
Definition (Availability). Availability (or available energy) is energy [enthalpy, H, or internal energy, U] corrected for entropy, S. Rigorous definitions of the Gibbs availability function [H T_{o}S], the Helmholtz availability function [U  T_{o}S], and entropy are given in Appendix I, Fundamentals of Thermodynamics, where the symbols and technical terms employed in this paragraph are explained. [T_{o} is the temperature o the environment, usually taken to be the temperature of the coldest body of water or the atmosphere into which the waste heat of a heat engine can be discharged. For Earth, 300 K will do. The effect of entropy on the availability function of sunlight is to reduce it by the ratio of the temperature of Earth to the temperature of the Sun a factor of about 19/20. Since the enthalpy of a proton is 4/3 times the energy, the Gibbs availability of sunlight is about 76/60 times the energy.]
Odums original definition of emergy. Odum defined emergy, measured in emjoules, to be the Gibbs availability of the sunlight, measured in joules, required to produce, by an optimal process, (1) fuels; (2) other energy sources such as wind or fresh water in mountain lakes; (3) natural resources such as grass and trees, (4) manufactured objects, (5) human resources; (6) information; and (7) any other objects of economic interest that can be associated with an identifiable quantity of sunlight. This is a sunlightbased emergy. It leads to large numbers for the emergies of primary fuels that are known only approximately; therefore, we shall modify the definition slightly to give common industrial energy products emergies that are known precisely and that are close to 1.0 in magnitude.
Definition (Standard Electricity). In this paper, singlephase, 60 Hz, 110volt alternating current delivered to the users meter is taken to be standard electricity.
Definition (Emergy Unit). My arbitrary but welldefined choice for one unit of emergy (1 MU) is 1.0 kilowatthours of standard electricity. Although electrical current carries a small amount of entropy manifest in difference currents, for all practical purposes, that is, for engineering purposes, electricity is pure work. The availability of electricity is equal to its energy; and, with this choice of emergy unit, the emergy of electrical current is numerically equal to its energy in kilowatthours. The transformity of sunlight, wind, biomass, and other energy products will be less than but close to 1.0.
Definition (Transformity). The transformity of a primary fuel is the number of kilowatthours of standard electricity one can obtain from 1 kWhr of the primary fuel by an efficient process, the tradition of reporting the availability of fuels in BTUs per pound or kilocalories per gram mole notwithstanding. Any unit of energy can be converted to kilowatthours. This is an electricitybased transformity, the units of which are emergy units per kilowatthour.
Definition (Emergy). The embodied energy or emergy of a primary fuel is the Gibbs availability of the fuel in kilowatthours multiplied by the electricitybased transformity. The emergy of anything else is the sum of all the emergy that went into producing it by an efficient process minus the emergies of any byproducts formed. The emergy of an activity is the average rate of expenditure of emergy times the time. These definitions are easily extended to include the dependence of emergy on location and time. The concept of nemergy or negative emergy can be introduced to aid in the discussion of environmental damage.
Definition (Emergy efficiency). Emergy efficiency of a manufacturing process is emergy out divided by emergy in. This efficiency is 1.0 for an optimal process because the emergy of the output is defined to be the emergy of the inputs. For a less than optimal process, the emergy efficiency is the emergy of the inputs to an optimal process over the emergy of the inputs to the process under investigation. Emergy efficiency lies between zero and one. A useful definition of emergy efficiency for the production or extraction of a fuel might be the emergy of the fuel plus the emergy of any byproducts divided by the emergy of all the inputs including the emergy supplied by nature. Clearly, the energy supplied by nature is not considered part of the energyinvested term, otherwise an EROI greater than would 1.0 could not be obtained. Thus this efficiency is necessary to completely evaluate the process under investigation.
The transformity of any fuel can be determined by using it to generate standard electricity by an efficient process. The most efficient process might be a fuel cell. Therefore, the emergy of any fuel is the Gibbs availability of the fuel multiplied by the electricitybased transformity.
Balance Equations. Sholto Maud suggested working out energy, availability, and emergy balance equations for simple extraction and conversion processes. Writing balance equations for extraction and Type 1 conversion helped me to understand what must be included in the definition of emergy and what may not be included without encountering inconsistencies. Many other people can improve their understandings by studying the balance equations discussed at http://www.dematerialism.net/MarkIIBalance.html.
Extraction. An example of extraction is the production of petroleum from the well to the refinery. Extraction is discussed in http://www.dematerialism.net/MarkIIEROI.html.
Type 1 Conversion. The first type of conversion is the production of primary energy from energy supplied by Nature for which we do not compensate Nature. This is a sustainable process provided the energy from Nature (natural energy) comes from a source that is continuously renewed by the Moon or by the Sun shining on the Earth. The input to such a process includes other types of energy, material goods, transportation, labor, taxes, etc. The output includes the principal product, one or more byproducts, waste heat, and pollution. Normally, pollution is not considered; however, the concept of nemergy (negative emergy) should be employed to account for pollution of every type even, for example, the extent to which animals are deprived of habitat by the mere existence of the energy production facility. Examples of Type 1 conversion are the production of electricity by wind power and solar power. The emergy balance equation for a Type 1 process will be discussed next:
Figure 1. Emergy Balance for Type 1 Conversion
Let us define some symbols to be used in connection with Figure 1:
Table of symbols used in this discussion 

ER 
Gibbs availability of fuel produced by process 
λ_{R} 
electricitybased transformity of fuel produced 
MR 
emergy of fuel produced by process = λ_{R} · ER 
MI 
the algebraic sum of all of the emergy inputs (except for MN) minus the byproducts 
EI 
Gibbs availability of stream MI 
μ 
ratio of EN per unit mass to ER per unit mass 
EN 
Gibbs availability of energy from Nature = μ · (ER + EI) 
λ_{N} 
the electricitybased transformity of the energy supplied by Nature 
MN 
emergy of energy from Nature = λ_{N} · EN 
β 
Energy returned over energy invested (EROI) = ER/EI = MR/MI 
EP 
the Gibbs availability of primary energy in Type 2 conversions 
λ_{P} 
the transformity of the primary energy source in Type 2 conversions 
MP 
the emergy of the primary energy supply in Type 2 conversions 
Each of the input emergies, except the emergy supplied by Nature, is to be transformed into a productequivalent emergy. Then, the emergy invested, MI, is imagined to have been produced by the same process that produced the fuel. In this way, it will be apparent immediately if the process consumes more emergy than it produces. All indirect energy expenses should be included in the MI term, in which case EROI is a good measure of the effectiveness of the process. (See http://www.dematerialism.net/MarkIIEROI.html.) [An example of an indirect cost is the prorata share of the commuting costs of the tax consultant (A) that should be charged to the worker (B) who maintains a windpower installation because the man (C) who serves B lunch had his taxes done by A.]
Then, since
_{}
_{}
and,
_{}
In the first approach, the transformity of the product is determined by the generation of standard electricity with a wellknown efficient process and the transformity of the energy from Nature, whether it be from the tides, from biomass, from wind, from sunlight itself, or from some other natural source, is determined from the emergy balance. Normally, this transformity is well established. Therefore, two separate cases obtain:
Case 1. If λ_{N}, the value we compute, is greater than λ_{N*}, the accepted value of the transformity of the natural energy, then we should report that our process is part of a more efficient route to standard electricity, and λ_{N} should be considered for a new value of the transformity of the energy supplied by Nature.
Case 2. If λ_{N} is less than λ_{N*}, then our process is less efficient than the process that established the larger value and we must report an efficiency, η, for our process because we could have generated more emergy with the same quantity of natural energy if we had used the standard process. The reader should remember that the energy from Nature is free, but the area of the solar collector or the size of the windmill is not.
_{}
In the second approach, the wellestablished value of the transformity of the energy supplied by Nature is accepted and the transformity of the product is computed from it. Call it λ_{R'}. If λ_{R'} is less than λ_{R}, the true value, we should revert to Case 1 and recalculate the transformity of the natural energy. If λ_{R'} is greater than λ_{R}, then the efficiency is λ_{R} over λ_{R'}. This is in agreement with Equation 2 above.
Let us imagine the process in the configuration illustrated by Figure 2.
Figure 2. Alternative Diagram for Type 1 Conversion
If the algebraic sum of the emergy inputs to a process minus the emergy supplied by Nature exceeds the emergy of the product, that is, if MI > MR, then the process is wasting energy resources. This is the case for some alternative energy projects that seek venture capital, government subsidies, donations, or unwary buyers. If they were not subsidized by fossil fuel, they would not work.
Type 2 Conversion. The second type of conversion is the production of secondary energy from primary energy. The production of hydrogen from methane or from electrolysis of water is an example of Type 2 conversion. Figure 2 is the same as Figure 1 except that MP, the primary energy, is substituted for MN:
Figure 3. Emergy Balance for Type 2 Conversion
In the first approach, the transformity of the product is determined by the generation of standard electricity by a wellknown efficient process and the transformity of the primary energy is computed from the emergy balance equation just as we did in the case of a Type 1 conversion, mutatis mutandis:
_{}
Case 1. If λ_{P}, the value we compute, is greater than λ_{P*}, the accepted value of the transformity of the primary energy, then we should report that our process is part of a more efficient route to standard electricity, and λ_{P} should be considered for a new value of the transformity of the primary energy.
Case 2. If λ_{P} is less than λ_{P*}, then our process is less efficient than the process that established the larger value and we must report an efficiency, η, for our process because we could have generated more emergy with the same quantity of primary energy if we had used the standard process.
_{}
In the second approach, the wellestablished value of the transformity of the primary energy is accepted and the transformity of the product is computed from it. Call it λ_{R'}. If λ_{R'} is less than λ_{R}, the true value, we should revert to Case 1 and recalculate the transformity of the natural energy. If λ_{R'} is greater than λ_{R}, then the efficiency is λ_{R} over λ_{R'}. This is in agreement with Equation 3 above. These results are worth deriving in a different way:
If a fuel the emergy of which is known is produced by the process under investigation and the sum of all of the emergy costs both direct and indirect that go into the process (computed with the true transformity λ_{P*}) minus the emergies of any useful byproducts is greater than the algebraic sum of the emergy inputs for the process that determined the known emergy of the energy product, the process under investigation is suboptimal and the efficiency, η, is
_{}_{}
and, the transformity of the product we would compute from
_{}
is higher than the true value λ_{R}. The only justification for the process is that we cannot do without the product and there is no other way to get it, which is not the case when electricity is used to produce hot water (discussed below) since hot water can be produced with less emergy by burning fuel under normal circumstances. Nevertheless, the process may be needed in extraordinary circumstances where the burning of fuel is prohibited, e. g., in a space capsule.
If the algebraic sum of the emergy inputs for the process under investigation is less than that of the older process, the transformity of the primary energy should be recalculated. It may not be expedient to discontinue production by the older process immediately because of compelling reasons not to shut down the older facilities not the least of which is the time delay before new facilities can be built. The emergy efficiency of the older process is now less than 1.0.
Type 3 Conversion. The third type of conversion is the manufacture of nonenergy goods. The manufacturing process has inputs of energy, material goods, transportation, labor, taxes, etc., and outputs that include a principal product, one or more byproducts, and waste heat. This is best illustrated with a diagram such as Figure 4.
Figure 4. Emergy Balance for Manufacturing Process
Table of symbols for Figure 4 

MI 
emergy of direct energy supplies 
MX 
emergy of inputs of material, transportation, labor, taxes, etc. 
MA 
emergy of principal product 
MB 
emergy of byproduct 
MW 
emergy of waste heat stream 
The emergy, MW, of the waste heat stream is its availability times the number of kilowatts of standard electricity that can be generated efficiently by one kilowatthour of waste heat. The emergy of the sum total of all direct energy inputs to the process is determined in the usual way. The emergy of the sum total of all nonenergy inputs must be available from past studies or must be determined during the analysis. It may include contributions from pollution etc. in which case negative emergy in the output is added to the input. Unlike the case of energy production, the transformities of the inputs cannot be influenced by the process. The emergy of the principal product and the byproduct must equal the emergy of the inputs minus the emergy of the waste heat. In the case of a principal product as the sole output, the determination is trivial. However, when one or more byproducts are present, the emergies of the byproducts and the principal project must be apportioned in a canonical manner that should be determined by the analyst on a casebycase basis.
If the emergy of a byproduct is known in some other way, it may be appropriate to use the known value. In a case where the emergies must be distributed equitably, the relation between market price, either instantaneous or averaged over time, and energy or emergy may be useful. See The Relation of Energy to Money. Thus, the emergy is apportioned according to market value. This is a singular intrusion of money into the physical realm of emergy analysis and may not be advisable. In a nonmarket economy, some combination of energy, labor, capital expenditures, product mass or heat of fusion (even) might be of use. In any case, the sum of the emergies of the products must close the emergy balance. The consumer may find it expedient to compare the emergy of any given product with the emergy of a comparable product to minimize his impact upon the environment.
Note. The EROI defined in this essay is sometimes denoted EROI1 because it is one less than the usual EROI which equals (MR + MI)/MI. The reader should realize that the terms Type 1, Type 2, and Type 3 Conversion have no currency outside of this paper.
Houston, Texas
Friday, October 27, 2006