Illustrated Physics
physics, drawn
Concept

Enthalpy — where it appears

The energy of a system plus its pressure times its volume, the heat taken up in a change at constant pressure. In a moving fluid it is also the inertia per unit volume, which for a gas hotter than its rest energy is mostly heat.

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

Throttling a gas, and the curve that says which way it goes. Curves of constant enthalpy for a van der Waals gas, in temperature and pressure both measured against the critical values. A gas pushed slowly through a plug or a valve keeps its enthalpy, so it moves along one of these curves — from right to left, since the pressure falls. Where a curve slopes upward to the right the gas cools as it expands; where it slopes downward it warms. An ideal gas would give horizontal lines and no change at all, because its enthalpy depends on the temperature alone; every curve here is bent, and the bending is the attraction between molecules and the room they take up, fighting. The dashed line through the tops of the curves is the inversion curve, and the maxima were found on the drawn points rather than put there — they lie on the closed form to 0.65 per cent. Which side of it a gas starts on decides the sign of the effect, and that is the whole of why air can be liquefied by throttling at room temperature and hydrogen cannot: hydrogen has to be pre-cooled below its own inversion temperature first, which is why Dewar needed liquid air before he could get liquid hydrogen, and why Onnes needed liquid hydrogen before he could get helium.

The gas that cools by being let go

Push a gas through a plug and its temperature changes, although no work is done on anything and no heat goes anywhere. Which way it changes depends on where it starts: inside a dome in the pressure–temperature plane it cools, outside it warms, and hydrogen at room temperature is outside — which is why liquid hydrogen needed liquid air first.

thermodynamics · Phase change What the heat shares out, and what it does not. Two averages per particle in the Maxwell–Jüttner gas, in units of kT, against kT/mc² on a logarithmic scale: the momentum times the velocity, p·v, whose average over the three directions gives the pressure, and the kinetic energy. The first is 3 at every temperature, computed here by averaging over the distribution and equal to 3 to four decimal places across the whole figure — so the pressure is exactly nkT, the ideal gas law, from a gas colder than a star to one hotter than the early universe. The kinetic energy is not shared out the same way. It is 1.506 kT when the gas is cold, Boltzmann's 3/2, and rises to 3.00 kT when it is ultra-relativistic, because for a fast particle the energy is p·c and p·v, which is what equipartition hands out, is the whole of it rather than twice it.

The gas law relativity leaves exact

Heat a gas until its particles move at nearly the speed of light and almost everything Maxwell and Boltzmann said about it changes. The speeds pile up just below c instead of spreading out. The energy per particle climbs from three halves of kT to three. The heat capacity doubles, and the ratio of heat capacities falls from five-thirds to four-thirds. One law survives untouched: the pressure is still exactly nkT, at a thousand degrees or a hundred thousand million. The reason it survives is the reason the others change. What heat hands out equally to every way of moving is not energy but momentum times velocity, and for slow particles those happen to differ only by a factor of two.

relativity · Relativistic thermodynamics

Named alongside it

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

Adiabatic indexEquation of stateEquipartitionFree expansionHeat capacityThe ideal gas lawIntermolecular forcesInversion temperatureJoule thomsonLiquefactionMaxwell juttner distributionReal gas

All concepts