A.3.13—Efficiency

Useful fraction

Efficiency is the ratio of useful output to total input:

$$\eta=\frac{E_{useful}}{E_{input}}=\frac{P_{useful}}{P_{input}}$$

Choose matching quantities

Use energy ratios for the same process and time interval, or power ratios when input and output are rates. Efficiency is dimensionless and is often reported as a percentage.

Worked example from local Question Bank row 29709

Solar intensity is $240\,\mathrm{W\,m^{-2}}$ over $2.50\times10^4\,\mathrm{m^2}$, so input power is

$$P_{in}=(240)(2.50\times10^4)=6.0\times10^6\,\mathrm{W}=6.0\,\mathrm{MW}$$

For a useful output of $1.6\,\mathrm{MW}$,

$$\eta=\frac{1.6}{6.0}=0.27=27\%$$

The remaining input is transferred through non-useful pathways.

Common trap

Do not invert the ratio or use the total output, including unwanted transfers, as the useful output.