Illustrated Physics
physics, drawn
Concept

Steady state — where it appears

A condition in which nothing measured changes in time, although energy or matter may be flowing through, as heat flows steadily through a wall. Whether a system reaches one, and whether it is stable, is a separate question from whether it exists.

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

Everything in the chain decaying at the parent's rate. The activity of each member of ²³⁸U → ²³⁴Th → ²³⁴Pa, relative to the parent's, against time in days. The parent's half-life is far the longest, so its activity is effectively constant over the range drawn while each daughter rises to meet it. Once they have, every member of the chain is decaying at exactly the same rate — secular equilibrium, checked here to one per cent off the integrated solution — because each is being made as fast as it is disappearing. The amounts are not equal at all: the abundance of each member sits in the ratio of its half-life to the parent's, which for radium in uranium is one part in three million and is why radium had to be extracted from tonnes of ore.

The chain that runs at its slowest member's rate

Put decays in series and something happens that no single decay does. The population settles where every member is being made exactly as fast as it disappears, so every activity in the chain is equal — while the amounts differ by twelve orders of magnitude, in the ratio of the half-lives. A gram of uranium contains a third of a microgram of radium and two hundred million million million atoms fewer of radon, and both numbers are read off a list of half-lives.

quantum · Decay The fold beyond which no heap is steady. The centre's steady temperature rise, in units of RTₐ²/E, against the Frank-Kamenetskii parameter δ, for a slab, a long cylinder and a sphere, found by integrating the steady heat equation outward from the centre: each shape has two steady states for every δ below a critical value — a cool, stable one and a hot, unstable one — and none above it. The fold is at δ = 0.878, 2.000, 3.322 for the slab, cylinder and sphere: a sphere tolerates nearly four times a slab's δ at the same half-width, because its surface is larger in proportion to its volume and heat from its centre has more ways out. A real heap, which is neither, has a critical δ between, and fixing it for a given shape is the first step in calculating the size at which a store becomes unsafe.

The heap that sets itself alight

A haystack, a coal stockpile, a bin of oily rags or a silo of damp grain can catch fire with no spark at all. A slow reaction inside makes a little heat; the heap holds it in; the warmer middle reacts faster and makes more. Whether that ends in a warm heap or a burning one is decided by a single number built from the heap's size, the air's temperature and the reaction's speed — and past one value of it there is no steady temperature at all. The critical size shrinks steeply as the weather warms, and the heap gives almost no warning before it goes.

thermodynamics · Diffusion

Named alongside it

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

AbundanceActivation energyActivityArrhenius lawBifurcationConservation lawsDecayDecay chainEquilibriumExponential decayHalf-lifeHeat conduction

All concepts