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What is efficiency?

Coefficient of performance (COP) - a term that can be applied, perhaps, to each system and device. Even a person has efficiency, though, probably, there is not yet an objective formula for finding it. In this article we will tell in detail what the efficiency is and how it can be calculated for different systems.

Efficiency - definition

Efficiency is an indicator that characterizes the effectiveness of a system in terms of recoil or energy conversion. Efficiency is an immeasurable value and is represented either by a numeric value in the range from 0 to 1, or as a percentage.

General formula

Efficiency is indicated by the symbol.

The general mathematical formula for finding the efficiency is written as follows:

Ƞ = A / Q, where A is the useful energy / work performed by the system, and Q is the energy consumed by this system to organize the process of obtaining a useful output.

Efficiency, unfortunately, is always less than or equal to one, because, according to the law of conservation of energy, we can not get work more than the energy spent. In addition, efficiency, in fact, extremely rarely equals one, since useful work is always accompanied by the presence of losses, for example, on the heating mechanism.

Efficiency of the heat engine

A heat engine is a device that turns heat into mechanical energy. In a heat engine, the work is determined by the difference in the amount of heat received from the heater and the amount of heat given to the cooler, and therefore the efficiency is determined by the formula:

  • Ƞ = Qn-Qx / Qn, where Qn is the amount of heat received from the heater, and Qx is the amount of heat given to the cooler.

It is believed that the highest efficiency provides engines operating on the Carnot cycle. In this case, the efficiency is determined by the formula:

  • Ƞ = T1-T2 / T1, where T1 is the temperature of the hot source, T2 is the temperature of the cold source.

Electric motor efficiency

An electric motor is a device that converts electrical energy into mechanical energy, so efficiency in this case is the device's efficiency ratio in terms of converting electrical energy into mechanical energy. The formula for finding the efficiency of an electric motor is as follows:

  • Ƞ = P2 / P1, where P1 is the summed electrical power, P2 is the net mechanical power generated by the engine.

Electric power is found as a product of the current and voltage of the system (P = UI), and mechanical power is defined as the ratio of work to unit time (P = A / t)

Transformer efficiency

A transformer is a device that converts an alternating current of one voltage into an alternating current of another voltage, while maintaining the frequency. In addition, transformers can also convert alternating current to direct current.

The efficiency of the transformer is according to the formula:

  • Ƞ = 1/1 + (P0 + PL * n2) / (P2 * n), where P0 is the idle mode loss, PL is the load loss, P2 is the active power given to the load, n is the relative degree of loading.

Efficiency or not efficiency?

It is worth noting that, in addition to efficiency, there are a number of indicators that characterize the efficiency of energy processes, and sometimes we can come across type descriptions — an efficiency of about 130%, but in this case we need to understand that the term is not completely correct, and most likely the author or the manufacturer understands by this abbreviation a slightly different characteristic.

For example, heat pumps differ in that they can give more heat than they spend. Thus, a chiller can divert more heat from a cooled object than is spent in energy equivalent for organizing a drain. The efficiency indicator of the refrigeration machine is called the coefficient of performance, denoted by the letter Ɛ and is determined by the formula: Ɛ = Qx / A, where Qx is the heat removed from the cold end,A - work spent on the process of withdrawal. However, sometimes the coefficient of performance is called the efficiency of the refrigerating machine.

It is also interesting that the efficiency of fossil fuel-fired boilers is usually calculated from the lower heat value, and it can be greater than one. Nevertheless, it is still traditionally called the efficiency. It is possible to determine the boiler efficiency by the highest calorific value, and then it will always be less than one, but in this case it will be inconvenient to compare the indicators of the boilers with the data of other installations.


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