Phase Diagrams: Triple Points, Critical Points & the States of Matter

Reading a P-T diagram

A phase diagram maps which state of matter — solid, liquid or gas — is stable at a given pressure and temperature. Draw pressure on the vertical axis and temperature on the horizontal one and the plane splits into three regions separated by three curves. The sublimation curve separates solid from gas, the melting curve separates solid from liquid, and the vaporisation curve separates liquid from gas. Cross a curve and the substance changes state; every point on a curve is a pair of pressure and temperature at which two phases coexist in equilibrium.

The three curves meet at exactly one point, the triple point: the unique pressure and temperature at which solid, liquid and gas all coexist simultaneously. For water this is 0.01°C at 611.657 Pa (about 0.006 atm) — so precise that it used to define the kelvin itself. Below the triple-point pressure, liquid water cannot exist at all: ice warmed at low pressure sublimates straight to vapour, which is why freeze-dried food and dry ice (solid CO2, triple point at 5.1 atm) skip the liquid phase at normal atmospheric pressure.

The critical point and the vanishing boundary

Follow the vaporisation curve upward and it does not continue forever — it terminates at the critical point (374°C, 22.1 MPa for water). Beyond that pressure and temperature, the distinction between liquid and gas disappears: there is no latent heat of vaporisation left to release, and the substance becomes a single supercritical fluid with a density between typical liquid and gas values. Supercritical CO2 (above 31.1°C, 7.4 MPa) is used industrially to extract caffeine from coffee beans and essential oils from plants because it diffuses like a gas but dissolves like a liquid, and simply venting the pressure leaves no residue.

water:     triple point   0.01 °C,  0.006 atm
           critical point  374 °C,  218  atm
CO2:       triple point  -56.6 °C,  5.11 atm
           critical point  31.1 °C,  72.8 atm

Why the melting curve for water leans backward

Almost every substance's melting curve has a positive slope — squeezing a solid harder makes it melt at a higher temperature, because the solid is denser than the liquid and pressure favours the smaller volume. Water is the famous exception: ice is about 9% less dense than liquid water, so its melting curve slopes slightly backward. Pressing on ice near 0°C nudges it toward the denser liquid phase and can melt it at a lower temperature — part of the (much debated) explanation for why a skate glides, alongside frictional heating.

The slope is quantified by the Clausius-Clapeyron equation, which relates the gradient of any coexistence curve to the entropy and volume change of the transition:

dP/dT = ΔS / ΔV  =  L / (T · ΔV)

L  = latent heat of the transition (J/mol)
T  = coexistence temperature (K)
ΔV = molar volume change, V_phase2 - V_phase1

Because ΔV is negative for water's melting transition (liquid is denser than solid) while L is positive, dP/dT comes out negative — one clean derivation of that backward-leaning line from thermodynamics alone.

Metastable states: superheating and supercooling

The curves show where phases are in equilibrium, not where transitions are forced to happen. In a very clean container, water can be cooled below 0°C without freezing (supercooling) or heated above 100°C without boiling (superheating), because nucleating a new phase needs a seed — a bubble, a dust particle, a scratch on the glass — and pure, still liquids can lack one. This is also why a supercooled cloud droplet flash-freezes the instant an aircraft wing, or a shaken bottle, gives it a nucleation site.

Frequently asked questions

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