Steam & Condensation: Why Vapour Turns Back Into Water

Boiling versus evaporating: two different transitions

Water turns to vapour in two distinct ways. Evaporation happens at any temperature, from the surface only, whenever some fast-moving molecules have enough kinetic energy to escape the liquid's intermolecular bonds — it is why a puddle dries at room temperature. Boiling happens throughout the liquid's volume, and only once the saturation vapour pressure of the liquid equals the surrounding atmospheric pressure, so vapour bubbles can form and grow anywhere, not just escape from the surface. That single condition — saturation pressure meets ambient pressure — is why water boils at 100°C at sea level and at a lower temperature on a mountain, where the air pressure is lower.

Clausius–Clapeyron: why saturation pressure rises so fast with temperature

The curve that separates liquid water from water vapour on a pressure–temperature diagram is described by the Clausius–Clapeyron relation, which follows from equating the Gibbs free energy of both phases at equilibrium:

dP/dT = L / (T * dV)                      // exact form
P(T) = P0 * exp( -L/R * (1/T - 1/T0) )      // integrated, ideal-gas approximation

Here L is the latent heat of vaporisation and R the specific gas constant. The exponential means saturation pressure is extremely sensitive to temperature — a common working approximation, the Magnus formula, captures the same curve for the range meteorologists care about: e_s(T) ≈ 6.1094 · exp(17.625T / (T + 243.04)) in hectopascals, with T in Celsius. Roughly speaking the air's capacity to hold water vapour before it saturates grows by about 7% per degree Celsius near room temperature — the physical basis of the Clausius–Clapeyron scaling that shows up throughout climate science when discussing how a warmer atmosphere holds more moisture.

Condensation: crossing the saturation line

Condensation is the same equilibrium approached from the other side. Once the partial pressure of water vapour in a parcel of air exceeds the local saturation pressure — which happens either because the air is cooled (saturation pressure drops as it cools) or because more vapour is added — the excess water has nowhere to go as gas and nucleates into liquid droplets, usually around microscopic aerosol particles (dust, salt, pollution) that act as condensation nuclei. Without any nuclei, pure water vapour can become substantially supersaturated before droplets form spontaneously — the same supersaturation principle used deliberately in a cloud chamber to make particle tracks visible.

Dew point and the adiabatic lapse rate

The dew point is the temperature to which a parcel of air must be cooled, at constant pressure and moisture content, for it to become saturated — the Magnus formula run in reverse. As a moist air parcel rises, it expands and cools at the dry adiabatic lapse rate of roughly 9.8°C per kilometre, because no heat is exchanged with the surroundings and the cooling comes purely from the parcel doing work as it expands. The altitude at which the parcel's temperature crosses its own dew point is the cloud base — the flat, sharp bottom you see on cumulus clouds, because every rising parcel in similar surrounding air crosses that threshold at almost exactly the same height. Above the cloud base the released latent heat of condensation partially offsets further cooling, so a saturated parcel instead cools at the slower moist adiabatic lapse rate, roughly 5°C per kilometre near the surface.

T_dp ~= T - (100 - RH) / 5             // quick estimate, deg C, RH in %
cloud_base_m ~= 125 * (T - T_dp)       // Espy's rule, metres

What the simulation models

The particle system on this page represents individual water-vapour molecules as points carrying kinetic energy. As they rise they lose energy at a rate set by the lapse rate; once a particle's local vapour pressure exceeds the Clausius–Clapeyron saturation curve for its temperature, it is converted into a slower-moving droplet particle, and droplets that collect enough neighbours are rendered as visible cloud. It is a simplified, particle-based stand-in for the continuum physics above — the goal is to make the invisible threshold of saturation, and the reason clouds have a flat base, something you can watch happen rather than only calculate.

Frequently asked questions

Try it live

Everything above runs in your browser — open Steam & Condensation and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.