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A premium efficiency electric motor: more than 90% (see Main Article: Premium efficiency). A large power transformer used in the electrical grid may have efficiency of more than 99%. Early 19th century transformers were much less efficient, wasting up to a third of the energy passing through them.
In mechanical engineering, mechanical efficiency is a dimensionless ratio that measures the efficiency of a mechanism or machine in transforming the power input to the device to power output. A machine is a mechanical linkage in which force is applied at one point, and the force does work moving a load at another point.
Even a rechargeable battery with 100% faradaic efficiency requires charging at a higher voltage than it produces during discharge, so its overall energy efficiency is the product of voltage efficiency and faradaic efficiency.
Shockley and Queisser include a graph showing the overall efficiency as a function of band gap for various values of f. For a value of 1, the graph shows a maximum efficiency of just over 40%, getting close to the ultimate efficiency (by their calculation) of 44%.
Energy conversion efficiency depends on the usefulness of the output. All or part of the heat produced from burning a fuel may become rejected waste heat if, for example, work is the desired output from a thermodynamic cycle.
A total of 64 experiments were performed in which the actual Faraday efficiency was measured. The results were analyzed twice; once with the popular assumption that the Faraday efficiency is 100%, and, again, taking into account the measured Faraday efficiency in each experiment. The average Faraday efficiency measured in these experiments was 78%.
Suppose { P θ | θ ∈ Θ } is a parametric model and X = (X 1, …, X n) are the data sampled from this model. Let T = T(X) be an estimator for the parameter θ. If this estimator is unbiased (that is, E[ T ] = θ), then the Cramér–Rao inequality states the variance of this estimator is bounded from below:
Faraday discovered that when the same amount of electric current is passed through different electrolytes connected in series, the masses of the substances deposited or liberated at the electrodes are directly proportional to their respective chemical equivalent/equivalent weight (E). [3]