Experiment
Heat a crystal built from three hundred atoms and watch it melt, then evaporate. On the phase diagram you will find the triple point of water. You will also measure how much energy boiling absorbs and see why on Everest water boils at just 70 °C.
Solid — crystal
Atoms vibrate around fixed positions.
Temperature in units of ε/k (for argon, 1 unit ≈ 120 K). ↑ ↓
Shrinks the container and raises the pressure. ← →
Simplified model: 300 atoms in 2-D, Lennard-Jones potential, reduced units. In 2-D the liquid range is narrow (about 0.40–0.50), and the numbers are not the temperatures of real argon.
Water: curves from the IAPWS equations. Boundaries between the high-pressure forms of ice are simplified.
Drag the marker or use ↑ ↓ (temperature) and ← → (pressure); hold Shift to go faster.
The water in the pot is at 20 °C.
Pressure from the International Standard Atmosphere (ISA) model; the real value changes with the weather by a few percent.
The drawing is schematic: 1 kg of steam at 100 °C takes up about 1.7 m³. We assume a constant pressure of 1 atm, no heat losses, and that all the steam stays in the vessel.
Two atoms attract each other weakly from afar and repel strongly when too close. This is described by the Lennard-Jones potential:
Temperature is a measure of the average energy of motion. In two dimensions the average kinetic energy of an atom is ⟨Ek⟩ = kT. When kT is much smaller than ε, the atoms sit in a lattice like balls in a honeycomb — each has six neighbors. When the vibrations become comparable to the depth of the well, the lattice falls apart (liquid), and at an even higher temperature the atoms fly off (gas).
At every time step the program computes the forces and moves the atoms using the velocity Verlet algorithm:
The thermostat gently rescales the velocities toward the set temperature. Without the thermostat the sum of kinetic and potential energy stays constant. In an open container the fastest atoms escape, so the rest cool down. That is why a puddle dries up and sweat cools us.
During melting and boiling the temperature stands still, even though the heater keeps running. The energy then goes into breaking bonds, not into speeding up the molecules.
For 1 kg of ice going from −20 °C to steam at 100 °C: 42 + 334 + 419 + 2,257 = 3,052 kJ. Boiling alone takes as much as 74% of this energy.
A phase diagram shows which phase is stable at a given temperature and pressure. Along the lines two phases coexist. At the triple point (for water 0.01 °C and 611.657 Pa) all three coexist. Beyond the critical point (373.95 °C, 22.06 MPa) the difference between liquid and vapor disappears. The slope of each line is given by the Clausius–Clapeyron equation:
Ice is less dense than water (Δv < 0), so water's melting line tilts to the left: pressure lowers the melting point, but only by about 0.0075 °C per atmosphere. In engineering, vapor pressure is also described by the empirical Antoine equation, log10 p = A − B/(C + T). This page uses the exact IAPWS equations for water.
Water boils when its vapor pressure equals the surrounding pressure. The higher you go, the thinner the air:
On Rysy (2,499 m), the highest peak in Poland, you get about 747 hPa and boiling at about 92 °C. On Everest (8,849 m) it is about 314 hPa and boiling at about 70 °C. Pasta takes longer to cook there. A pressure cooker works the other way: about 1 bar of overpressure raises the boiling point to about 120 °C.
The atom simulation is two-dimensional and has only 300 particles. The CO₂ and nitrogen curves are approximate equations from the literature. The heating curve assumes a constant specific heat and zero losses. Supercooled water actually has a slightly higher specific heat than 4.19 kJ/(kg·K).
A gas so hot that electrons break away from the atoms. It glows in the Sun, in lightning and in neon signs. Most ordinary matter in the Universe (stars, interstellar gas) is in fact in the plasma state.
Above the critical point there is no longer a boundary between liquid and gas. The fluid seeps into crevices like a gas but dissolves substances like a liquid. Supercritical CO₂ (above 31 °C and 7.4 MPa) is used to remove caffeine from coffee.
Very pure water in a smooth container can stay liquid even a dozen or more degrees below 0 °C, because there is no seed for a crystal. A jolt or a speck of ice triggers instant freezing. Try it in mode 3.
At atmospheric pressure dry ice does not melt — it turns straight into vapor (−78.5 °C). The reverse process, vapor turning directly into a crystal, is deposition: that is how frost forms. In freeze-drying, frozen food is dried in a vacuum by sublimating the ice.
Cooled to a fraction of a microkelvin, thousands of atoms behave like a single “superwave.” The first such condensate was made in 1995 by Eric Cornell and Carl Wieman (rubidium atoms), and a few months later by Wolfgang Ketterle (sodium atoms). In 2001 all three received the Nobel Prize.