Efficiency

The efficiency, e, of a system is defined as the work output divided by the energy input. From the definition of power, you can also see that the efficiency is also equal to the ratio of output to input power:

\[ \rm \mathbf{\varepsilon = \frac{W_{out}}{E_{in}} = \frac{P_{out}}{P_{in}}} \]

Example:

A machine with efficiency 50% has a power input of 1000 W.

Question:

How much work is done by the machine in 60 s?

Answer:

e = 50% = 0.50
P_out = e P_in = 0.50 $\cdot$ 1000 W = 500 W
W_out = P_outt = 500 W $\cdot$ 60 s = 3.0 $\cdot$ 10⁴ J