AcademyMatter at Thermal Scale
Questions

Academy

Phases of Matter

Level 1 - Physics topic page in Matter at Thermal Scale.

Principle

Phase diagrams show which phase of matter is stable for a given pressure and temperature.

Phase boundaries mark conditions where two phases can coexist in equilibrium.

Notation

\(p\)
pressure
\(\mathrm{Pa}\)
\(T\)
absolute temperature
\(\mathrm{K}\)
\(L\)
latent heat per unit mass
\(\mathrm{J\,kg^{-1}}\)
\(T_t,p_t\)
triple-point temperature and pressure
\(\mathrm{K,\;Pa}\)
\(T_c,p_c\)
critical temperature and pressure
\(\mathrm{K,\;Pa}\)
\(\Delta s\)
specific entropy change across a transition
\(\mathrm{J\,kg^{-1}\,K^{-1}}\)
\(\Delta v\)
specific volume change across a transition
\(\mathrm{m^{3}\,kg^{-1}}\)

Method

Derivation 1: Read a phase diagram

A point in the \(p\)-\(T\) plane usually lies inside one phase region. A point on a boundary represents phase equilibrium.

Single phase
\[(p,T)\ \text{inside a region}\Rightarrow\text{one stable phase}\]
Phase boundary
\[(p,T)\ \text{on a boundary}\Rightarrow\text{two phases coexist}\]
Triple point
\[(p_t,T_t)\Rightarrow\text{solid, liquid, and gas coexist}\]
Critical point
\[(p_c,T_c)\Rightarrow\text{liquid-gas distinction ends}\]

Derivation 2: Connect boundary slope to transition properties

Along a phase boundary, both phases remain in equilibrium as pressure and temperature change together. The Clapeyron relation links the boundary slope to latent heat and volume change.

Entropy jump
\[\Delta s=\frac{L}{T}\]
Boundary slope
\[\frac{dp}{dT}=\frac{\Delta s}{\Delta v}\]
Clapeyron form
\[\frac{dp}{dT}=\frac{L}{T\Delta v}\]

If pressure is below the triple-point pressure, a liquid phase cannot exist for that substance; heating a solid then leads to sublimation rather than melting followed by boiling.

Rules

These are the compact phase-diagram relations.

Phase boundary
\[\text{two phases coexist on a boundary}\]
Triple point
\[\text{solid}+\text{liquid}+\text{gas coexist}\]
Critical point
\[T>T_c\Rightarrow\text{no sharp liquid-gas boundary}\]
Clapeyron relation
\[\frac{dp}{dT}=\frac{L}{T\Delta v}\]

Examples

Question
A substance is below its triple-point pressure. What phase change occurs when its solid is heated at that pressure?
Answer
The liquid phase is not stable below the triple-point pressure, so the solid changes directly to gas by sublimation.

Checks

  • A phase boundary is not a region; it is a coexistence line.
  • The triple point is a unique pressure-temperature condition.
  • Above the critical point, liquid and gas are not separated by a sharp phase transition.
  • Sublimation occurs when solid changes directly to gas.

Previous

Molecular Speeds

Next

Thermodynamic Systems