What is Efficiency?

Efficiency is the ratio of the useful work performed by a machine or in a process to the total energy expended or heat taken in. A flowchart for the energy levels associated with any system that converts energy from one form to another is provided in [Fig. 1].
Fig. 1: Flowchart for the energy levels.
Note that the output energy level must always be less than the applied energy due to losses and storage within the system. The best one can hope for is that $W_{out}$ and $W_{in}$ are relatively close in magnitude. Conservation of energy requires that
$$ \text{input = output + lost or stored}$$
Dividing both sides of the relationship by time $t$ gives
$$ {W_{in} \over t} = {W_{out} \over t} + {W_{lost} \over t}$$
$$ \bbox[5px,border:1px solid red] {\color{blue}{ P_{in} = P_{out} + P_{lost}}}$$
The efficiency ($\eta$) of the system is then determined by the following equation:
$$ \text{Efficiency} = {\text{power output} \over \text{power input}}$$
$$ \bbox[5px,border:1px solid red] {\color{blue}{\eta = {P_o \over P_i}}}$$
where $\eta$ (the lowercase Greek letter eta) is a decimal number. Expressed as a percentage,
$$ \bbox[5px,border:1px solid red] {\color{blue}{\eta \% = {P_o \over P_i} \times 100\%}} $$
In terms of the input and output energy, the efficiency in percent is given by
$$ \bbox[5px,border:1px solid red] {\color{blue}{\eta \% = {W_o \over W_i} \times 100\%}} $$
The maximum possible efficiency is 100%, which occurs when $P_o = P_i$, or when the power lost or stored in the system is zero. Obviously, the greater the internal losses of the system in generating the necessary output power or energy, the lower is the net efficiency.

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