Energy Stores & Transfers

Definition

• The efficiency of a system is the fraction of the energy supplied to it that comes out in the useful form
• Stated as an equation:

efficiency = (useful energy output / total energy input) × 100 %

• Efficiency is a pure ratio and has no units; it may be given as a decimal between 0 and 1 or as a percentage between 0 and 100 %
• A high-efficiency system wastes very little; a low-efficiency system spreads most of its input into the surroundings

Useful and wasted always add to the input

• Because energy is conserved:

total energy input = useful energy output + wasted energy

• This lets you find any one of the three when the other two are known

Example — a battery-powered drill draws 320 J of electrical energy from its battery during one 4-second burst. Heating in the motor windings and the noise of the cutting account for 80 J of waste during the same burst. Calculate the efficiency of the drill.

• Useful energy output = total input − wasted = 320 − 80 = 240 J
• Efficiency = (240 / 320) × 100 % = 75 %

Sankey diagrams

• A Sankey diagram is a visual way to show an energy transfer:
  • The width of each arrow is drawn in proportion to the amount of energy it represents
  • The left-hand stub is the total input
  • The straight horizontal arrow on the right shows the useful output
  • The arrows that branch downwards show the wasted outputs (often labelled with the loss mechanism, such as heating, sound, or friction)
• A modern LED bulb has a Sankey diagram with a wide horizontal arrow (light output) and only a thin branch (heat waste); an old filament bulb has the opposite shape, with most of the input wasted as heat

Example — a small electric winch is rated to lift loads. A measurement shows that 400 J of electrical energy supplied to the winch produces 90 J of useful gravitational-potential-store energy in the lifted load. Find the wasted energy and the efficiency.

• Wasted = total input − useful = 400 − 90 = 310 J
• Efficiency = (90 / 400) × 100 % = 22.5 %