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### DDefinitions 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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