Molecular speeds at 4 temperatures

At its defaults it draws molecular speeds at 4 temperatures. The distribution of molecular speeds in a gas, with each curve enclosing the same area. Raising the temperature moves the peak right and lowers it: the same molecules, spread over a wider range of speeds.

speed-distribution is one function in lib/figures/thermal.js — cycles, distributions and the statistics underneath them. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

The distribution of molecular speeds in a gas, with each curve enclosing the same area. Raising the temperature moves the peak right and lowers it: the same molecules, spread over a wider range of speeds.

Molecules with speeds drawn from the Maxwell–Boltzmann distribution and directions drawn uniformly in the plane of the figure. Those moving toward the wall will bounce off it, reversing the component perpendicular to it and delivering twice that momentum each — and pressure is nothing but the rate at which that momentum arrives. Because the directions here lie in a plane rather than in space, the perpendicular component carries half the energy rather than the third it carries in a real gas.

Molecules with speeds drawn from the Maxwell–Boltzmann distribution and directions drawn uniformly in the plane of the figure. Those moving toward the wall will bounce off it, reversing the component perpendicular to it and delivering twice that momentum each — and pressure is nothing but the rate at which that momentum arrives. Because the directions here lie in a plane rather than in space, the perpendicular component carries half the energy rather than the third it carries in a real gas.

Molecules with speeds drawn from the Maxwell–Boltzmann distribution and directions drawn uniformly in the plane of the figure. Those moving toward the wall will bounce off it, reversing the component perpendicular to it and delivering twice that momentum each — and pressure is nothing but the rate at which that momentum arrives. Because the directions here lie in a plane rather than in space, the perpendicular component carries half the energy rather than the third it carries in a real gas.

Molecules with speeds drawn from the Maxwell–Boltzmann distribution and directions drawn uniformly in the plane of the figure. Those moving toward the wall will bounce off it, reversing the component perpendicular to it and delivering twice that momentum each — and pressure is nothing but the rate at which that momentum arrives. Because the directions here lie in a plane rather than in space, the perpendicular component carries half the energy rather than the third it carries in a real gas.

The distribution of molecular speeds inside a container at 300 K and in the beam that escapes through a small hole in it, each normalised to its own peak. They are not the same distribution. A molecule's chance of reaching the hole in a given time is proportional to how fast it is going, so the beam carries one more factor of speed than the gas does — v³ rather than v² times the Boltzmann factor — and the beam is therefore faster and hotter than what it came from. The mean speed inside is 476 m/s and in the beam 561 m/s, a ratio of 1.1781 against the exact 3π/8; and the mean kinetic energy is 1.500 kT inside against 2.000 kT in the beam, which are exactly 3/2 and 2. That difference is not a subtlety. A molecular beam made by effusion has a temperature, in the sense of a mean energy, a third higher than its source; a gas slowly leaking from a container leaves the remainder cooler than it would be if a fair sample had gone; and every calculation of a rate through an aperture that uses the bulk distribution is wrong by this factor.

physicscheck asserts something about speed-distribution that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.