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The efficiency

Efficiency describes the ratio of output power (useful power) to input power (energy supplied) in a system and is a measure of the efficiency with which a system converts energy. Using the example of an electric motor, Figure 1 shows how its power balance is composed.

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Figure 1: Efficiency of an electric motor. Shows the ratio of output power to input power. Efficiency describes the efficiency of the motor in converting energy.

The electric motor is supplied with electrical energy at the input, which it absorbs as input power \(P_\mathrm {zu}\). The desired output power \(P_\mathrm {ab}\) in this case is of a rotary nature. The waste heat generated by the motor, as well as the noise and friction it causes, together result in the power loss \(P_\mathrm {v}\).

1 Calculation of efficiency

Efficiency is typically expressed as a percentage. An efficiency of 100means that all of the energy supplied is effectively converted into useful energy. However, this is not achievable in practice due to losses, usually in the form of heat, friction or sound. Mathematically, efficiency \(\eta \) (eta) is defined as follows:

\begin {equation} \eta = \frac {P_\mathrm {{out}}}{P_\mathrm {{in}}} \cdot 100 \% \end {equation}

In reality, efficiency will never be 100To keep losses to a minimum, it is important to be aware of the mechanisms that cause them and to reduce them wherever possible. The following section explains the principle of loss mechanisms using a light bulb as an example.

2 Loss mechanisms of a light source

A prime example of the relevance of efficiency is the classic incandescent light bulb. It produces light by passing electricity through a wire, which heats up so much that it begins to glow. Less than 5 per cent of the energy used is converted into light. More than 95% of the energy is converted into heat. Due to their poor efficiency, incandescent light bulbs have been gradually banned in the EU since 2009. Figure 2 shows a classic incandescent light bulb on the left and an energy-saving light bulb on the right.

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Figure 2: Energy conversion in incandescent bulbs and energy-saving bulbs. Whereas an incandescent bulb converts most of the electrical energy it consumes into heat and only a small portion into light, an energy-saving bulb converts a significantly higher proportion of the electrical energy into light.

High efficiency is desirable in many applications, as it means that less energy is converted into forms of energy that are generally undesirable, and instead remains available to the system as useful energy. In practice, however, many factors such as material properties, design and operating conditions are crucial for maximising efficiency. Efficiency plays a crucial role in environmental and energy technology, as it is directly related to energy consumption and environmental impact. More efficient systems can help to reduce energy demand and greenhouse gas emissions.

  

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Figure 3: Example circuit Efficiency

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Figure 4: Simple circuit. shows a simple electrical circuit consisting of a battery, a switch and a light bulb. Closing the switch completes the circuit, causing the light bulb to glow by converting electrical energy into light and heat.

Calculation of efficiency

A heat engine extracts energy of \( Q_\text {zu} = 5000 \,\mathrm {J} \) from a heat source and performs mechanical work of \( W = 1200 \,\mathrm {J} \) in the process..

Wanted: Efficiency \( \eta \)

Formula: \[ \eta = \frac {\text {Useful work}}{\text {Supply of thermal energy}} \cdot 100\% = \frac {W}{Q_\text {zu}} \cdot 100\% \]

Insert: \[ \eta = \frac {1200\,\text {J}}{5000\,\text {J}} \cdot 100\% = 24\% \]

The efficiency is \( \eta = 24\% \).

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