Illustrated Physics
physics, drawn
Concept

Power — where it appears

The rate at which work is done or energy delivered, measured in watts; for a force acting on something moving it is the force times the speed. A machine's power caps the force it can apply at a given speed, not the force it can apply at rest.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The ceiling, the estimate, and three power stations. Two efficiencies against the ratio of the cold reservoir's temperature to the hot one. The upper curve is Carnot's 1 − Tc/Th, which is a ceiling on the work per unit of heat and is reached only by an engine that runs infinitely slowly, because a reversible heat flow needs a vanishing temperature difference to drive it and therefore infinite time. The lower curve is 1 − √(Tc/Th), the efficiency of an engine with finite thermal contact run for the most power rather than the most work. Three measured plants are marked: West Thurrock, coal runs at 36 per cent against a ceiling of 64 and a finite-time estimate of 40; CANDU, nuclear runs at 30 per cent against a ceiling of 48 and a finite-time estimate of 28; Larderello, geothermal runs at 16 per cent against a ceiling of 33 and a finite-time estimate of 18. Every one of them is closer to the lower curve — within 4.4 points at worst, against 16.5 at best from the ceiling. The second law is not what limits a working power station. What limits it is that somebody wants the electricity this year.

The engine that has to finish

Carnot's ceiling is exact and it is reached only by an engine that takes for ever, because a reversible heat flow needs a vanishing temperature difference to drive it. Ask instead for the most power rather than the most work per joule of heat, and the answer is a different function of the same two temperatures — and three measured power stations sit on it rather than on the ceiling.

thermodynamics · Heat engines Grip, then power, then air. The force a 1500 kg car can put through its driven wheels against road speed, with 100 kW at the wheels and a tyre friction coefficient of 0.9. The grip allows 13.2 kN at any speed; the engine allows its power divided by the speed, a hyperbola; the car gets whichever is smaller, drawn solid. The two are equal at 7.6 m/s, 27 km/h: below it the car is limited by friction and extra power would change nothing, above it by power and better tyres would change nothing. The rising curve is the resistance, rolling plus air, which grows as the square of the speed; it meets the drive at 61.2 m/s, 220 km/h, the top speed, solved for and checked there.

The speed at which grip hands over to power

A car's specification lists its power, and power does not limit how hard a car can push. It limits how hard it can push at a given speed, and at low speed that limit is higher than anything the tyres can transmit. So every car leaves the line as a friction problem and becomes a power problem a second later, at a crossover speed that decides which upgrade would make it faster — and at the top of its speed range a third limit, the cube of the speed, takes over from both.

mechanics · Energy

Named alongside it

The objects these essays reach for when they reach for this one.

The Carnot cycleDragEfficiencyEndoreversibleEnergyEntropyFrictionGear ratioHeat enginesIrreversibilityKinetic energyOptimisation

All concepts