Charge your phone and the charger goes warm. Pedal a bike and the chain gets hot. Switch on an old-style light bulb and it heats the room almost as much as it lights it. In every one of these cases you paid for a chunk of energy — but only some of it did the job you actually wanted. The rest leaked away, mostly as heat, doing nothing useful at all.
Efficiency is the number that tells you how good a device is at spending its energy on the right thing. It compares the useful energy a device transfers out with the total energy it was supplied:
A device that is 0.7 (or 70%) efficient turns 70 J of every 100 J it is given into the energy you want, and wastes the other 30 J. The bigger the fraction, the less you waste — but, as you'll see, that fraction can never quite reach 1.
Efficiency is a ratio of two energies, so it has no units — the joules on the top and bottom cancel. It always comes out as a number between 0 and 1, which we very often multiply by 100 to state as a percentage.
Because energy is conserved — never created, never destroyed — the total supplied is always the useful part plus the wasted part:
So if you know any two of these three numbers you can always find the third, and from there the efficiency.
Example 1 — find the efficiency. An electric motor is supplied
The other
Example 2 — find the useful output. A kettle is
That is the energy that actually heats the water; the remaining
Example 3 — an old filament bulb. A filament light bulb is supplied
Nineteen parts heat for every one part light — a filament bulb is really a little heater that happens to glow. This is exactly why they have been replaced by LEDs.
Example 4 — using power. A pump has an input power of
A Sankey diagram is a picture of where a device's energy goes. It starts as a single wide arrow on the left — the total energy supplied — and then splits: the useful transfer carries straight on, while the wasted transfers peel off (usually downward, and usually labelled as thermal energy to the surroundings).
The clever part is that the width of every arrow is drawn in proportion to the amount of energy it carries. So the widths of the branches always add up to the width of the arrow going in — you can literally see conservation of energy. A very efficient device has a fat useful branch and thin wasted ones; a wasteful device is the other way round. The bar below is a stripped-down Sankey: one input, split into a useful part and a wasted part.
Here is a fixed
Since the wasted energy nearly always escapes as unwanted heat, raising efficiency almost always means cutting down that wasted heat. A few everyday examples:
You can shave friction, add insulation and switch to LEDs, but the efficiency stubbornly stays a whisker below 1 (well below it, for anything with moving parts or a hot flame). Some energy is always spread out into the surroundings as thermal energy — friction between surfaces, warm exhaust gases, resistance heating up wires, sound waves rattling away. A machine that turned all of its input into useful work, wasting nothing, would be a perpetual-motion machine — and centuries of inventors have shown you cannot build one. The best real power stations reach around 60%; a big electric motor can top 90%; but 100% is a line you can approach and never cross.
The one apparent exception is a device whose useful job is heating: an electric heater turns essentially all of its electricity into thermal energy in the room, so it is close to 100% efficient — but only because here the "wasted" heat is exactly what you wanted.