Water Phase Lab - 2D Phase Diagram, Boiling Point and Heating Curve

Controls

Live readouts

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Numerical check

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Performance graph

How to use

Left: the pressure-temperature phase diagram of water with the three real boundary curves (melting, vaporisation, sublimation), the triple point and the critical point. The white circle is the state you choose (temperature slider and pressure slider); the readout names its phase and the boiling, melting and sublimation temperatures at that pressure. The red dot rides along the chosen isobar as a heater adds energy.

Right: the matching heating curve for the chosen mass at the same pressure, starting from ice at 200 K. The flat steps are latent heat: melting needs 334 kJ per kg, boiling about 2257 kJ per kg at 1 atm - roughly 7 times more.

Try: lower the pressure to about 3 (1 kPa) and watch the boiling point drop to about 7 C; go below 611 Pa (log 2.79) and liquid water disappears - ice sublimes straight to vapour; raise it above log 7.34 (22 MPa) and there is no boiling step at all (supercritical); at high pressure ice melts below 0 C because the melting curve slopes backwards.

The science

Phase boundaries are the real International Association for the Properties of Water and Steam (IAPWS) correlations. Vaporisation (Wagner-Pruss): ln(p/p_c) = (T_c/T)(a₁τ + a₂τ^1.5 + a₃τ³ + a₄τ^3.5 + a₅τ⁴ + a₆τ^7.5), τ = 1 − T/T_c with T_c = 647.096 K, p_c = 22.064 MPa.

Sublimation: ln(p/p_t) = θ⁻¹ Σ aᵢ θ^{bᵢ}, θ = T/T_t; melting of ice Ih: p/p_t = 1 + 1.19539·10⁶ (1 − θ³) + 8.08183·10⁴ (1 − θ^25.75) + 3.33827·10³ (1 − θ^103.75) with triple point T_t = 273.16 K, p_t = 611.657 Pa (melting formula valid to 209.9 MPa).

Slopes obey the Clapeyron equation dp/dT = h / (T Δv); for boiling with an ideal vapour this becomes Clausius-Clapeyron d ln p / dT = h_fg / (R_v T²). Ice is less dense than liquid water (Δv < 0), so the melting curve slopes backwards: about −13.5 MPa per kelvin.

Heating curve: sensible heat Q = m c ΔT (c_ice = 2090, c_liquid = 4186, c_vapour = 2010 J/kg/K, held constant) plus latent heat m h_f = 334 kJ/kg and h_fg from the Watson relation h_fg(T) = 2257 kJ/kg · [(1 − T/T_c)/(1 − 373.15/T_c)]^0.38.

Honest simplifications: constant specific heats (real values change with temperature and pressure), Watson scaling instead of full IAPWS-95 enthalpies, ice Ih only (the high-pressure ice forms III to XV are not drawn), no superheating or supercooling, no heat loss from the vessel, pure water.

Keyboard, touch and accessibility

Space pauses or resumes the simulation.
R resets it to its initial state.
C re-runs the numerical check.
All sliders are native range inputs and work with arrow keys, Home and End; on touch devices drag on the canvas where the sim supports pointer input.
Rendering is capped at a device pixel ratio of 2 so phones stay smooth; the frame-time graph above shows the cost of the current settings (green line is 16.7 ms, i.e. 60 frames per second).

What is checked and why you can trust it

Every time the page loads, and whenever you press Re-run check, the simulation evaluates its own mathematics against an independent reference, such as a closed-form formula, a finite-difference derivative or an exhaustive count. Each line above reports PASS or FAIL together with the measured numbers, so you can see by how much it agrees. Results are also published on window.__msChecks for automated testing. The check never uses the same code path as the animation it validates, otherwise it would only confirm itself.

How to read a failure: a FAIL line means the measured discrepancy exceeded the stated tolerance for the current slider values. Try Reset, then move the sliders back toward their defaults; if a check still fails at the defaults it is a bug worth reporting. Tolerances are chosen from the numerical method itself, never tuned to make a test pass: round-off level (1e-9) for exact algebra, about 1e-3 for finite differences and Monte Carlo estimates with a few hundred thousand samples, and a documented margin for stochastic learning runs.

Reproducibility: the particle and pen simulations use the browser random generator for initial positions, so exact pixels differ between visits, but the checks depend only on mathematics and not on those positions. Fixed wave tables (curl noise) and fixed grammars (L-system) are deterministic.

This is an educational model. It shows the mechanism clearly, but it is deliberately simplified; the science panel lists what was left out.