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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. [citation needed] A steam power plant used to generate electricity may have 30-40% efficiency. [citation needed]
The terms "wall-plug efficiency" or "energy conversion efficiency" are therefore used to denote the overall efficiency of the energy-conversion device, deducting the losses from each stage, although this may exclude external components needed to operate some devices, such as coolant pumps. [12] [13]
Another is overpotential, the difference between the theoretical and actual electrode voltages needed to drive the reaction at the desired rate. 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 ...
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%.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
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:
Efficiency is the often measurable ability to avoid making mistakes or wasting materials, energy, efforts, money, and time while performing a task. In a more general sense, it is the ability to do things well, successfully, and without waste.
The above efficiency formulas are based on simple idealized mathematical models of engines, with no friction and working fluids that obey simple thermodynamic rules called the ideal gas law. Real engines have many departures from ideal behavior that waste energy, reducing actual efficiencies below the theoretical values given above.