Phase Changes

The four phases

Phase	Particle behavior	Density	Examples
Solid	Strong bonds, fixed positions, vibrate	High	Ice, iron, rock
Liquid	Bonds present but mobile	High	Water, oil, mercury
Gas	Mostly free, weak interactions	Low	Steam, air, helium
Plasma	Ionized atoms, electrons	Variable	Lightning, sun, neon signs

The six phase transitions

From → To	Name	Heat	Example
Solid → Liquid	Melting (fusion)	Absorbed (L_f)	Ice → water
Liquid → Solid	Freezing (solidification)	Released	Water → ice
Liquid → Gas	Vaporization (boiling, evaporation)	Absorbed (L_v)	Water → steam
Gas → Liquid	Condensation	Released	Steam → water
Solid → Gas	Sublimation	Absorbed (L_s)	Dry ice → CO₂ vapor
Gas → Solid	Deposition	Released	Frost, snow

Phase diagrams

A phase diagram plots pressure (P) on y-axis vs temperature (T) on x-axis, with regions for each phase. Boundaries are the conditions where transitions occur.

For water:

• Solid (ice) region — left of melting curve, high P or low T.
• Liquid water — center.
• Vapor (gas) — right of vaporization curve, low P or high T.
• Triple point — 273.16 K, 611.7 Pa. All three phases coexist.
• Critical point — 647.1 K (374°C), 22.06 MPa. Above this, no liquid-gas distinction.
• Anomaly — water's solid-liquid line slopes negatively (higher P melts ice at lower T).

Real-world phase change phenomena

Phenomenon	Explanation
Pressure cooker	High P → boiling at >100°C → faster cooking
Mountain altitude — water boils <100°C	Lower P → lower boiling point. Hard to brew coffee on Everest.
Ice melts under pressure	Anomalous; why ice skating works (?? - actually mostly friction)
Frost on cold morning	Deposition (water vapor → ice on cold surfaces)
Dew on grass	Condensation (water vapor → liquid on cold grass)
Sublimation of dry ice	Below CO₂ triple point at 1 atm; goes directly solid → gas
Boiling water cools surroundings	Steam carries away latent heat
Frozen pipes burst	Water expands ~9% when freezing
Cloud formation	Water vapor condenses on aerosols as air rises and cools
Geysers	Superheated water → flash to steam → eruption

Clausius-Clapeyron equation

How phase transition temperature varies with pressure:

dP/dT = L / (T·ΔV)

For vaporization at 1 atm, ΔV ≈ V_gas (gas dominates). Using ideal gas (V = RT/P):

dP/dT ≈ L·P / (R·T²)

Integrated form gives boiling point vs pressure curve. Predicts boiling point on Mt. Everest (~70°C at ~30% sea-level pressure), pressure-cooker boiling (~120°C at ~2 atm).

JavaScript — phase change calculations

// Total heat for ice → liquid → steam
function iceToSteam(mass) {
  const c_ice = 2108;
  const c_water = 4186;
  const c_steam = 2010;
  const L_fusion = 334000;
  const L_vap = 2260000;
  
  // -10°C ice → 0°C ice → 0°C water → 100°C water → 100°C steam → 110°C steam
  const Q_ice_warming = mass * c_ice * 10;        // -10 → 0°C
  const Q_melting = mass * L_fusion;              // melt at 0°C
  const Q_water_warming = mass * c_water * 100;   // 0 → 100°C
  const Q_vaporizing = mass * L_vap;              // boil at 100°C
  const Q_steam_warming = mass * c_steam * 10;    // 100 → 110°C
  
  return {
    Q_ice_warming, Q_melting, Q_water_warming, Q_vaporizing, Q_steam_warming,
    total: Q_ice_warming + Q_melting + Q_water_warming + Q_vaporizing + Q_steam_warming
  };
}

console.log(iceToSteam(1));
// Total ~3.06 MJ; vaporization step is ~74%

// Boiling point at altitude (rough Clausius-Clapeyron)
function boilingPoint(altitude_m) {
  const T_0 = 373.15;  // 100°C
  const P_0 = 101325;
  const M = 0.018;     // water molar mass kg/mol
  const R = 8.314;
  const L = 2.26e6 * M;  // latent heat per mole
  // P ≈ P_0 · exp(-altitude / scale_height); scale_height ~ 8 km
  const P = P_0 * Math.exp(-altitude_m / 8000);
  // ln(P/P_0) = -L/R · (1/T - 1/T_0) → 1/T = 1/T_0 - R·ln(P/P_0)/L
  const T = 1 / (1/T_0 - R * Math.log(P/P_0) / L);
  return T - 273.15;  // Celsius
}

console.log(`Boiling at sea level: ${boilingPoint(0).toFixed(1)}°C`);
console.log(`Boiling at Denver (1.6 km): ${boilingPoint(1600).toFixed(1)}°C`);  // ~94
console.log(`Boiling at Mt Everest (8.85 km): ${boilingPoint(8850).toFixed(1)}°C`);  // ~71

// Pressure cooker effect
function pressureCookerBoiling(P_atm) {
  const T_0 = 373.15;
  const M = 0.018;
  const R = 8.314;
  const L = 2.26e6 * M;
  const P = P_atm * 101325;
  const T = 1 / (1/T_0 - R * Math.log(P / 101325) / L);
  return T - 273.15;
}

console.log(`Pressure cooker (2 atm): ${pressureCookerBoiling(2).toFixed(1)}°C`);  // ~120

// Freezing point depression (e.g., salting roads)
function freezingPointDepression(molality, K_f = 1.86) {
  // ΔT = K_f · m (van't Hoff for non-volatile solute)
  return -K_f * molality;
}

console.log(`5% salt water: ΔT_freeze = ${freezingPointDepression(0.85 * 2).toFixed(1)}°C`);
// Salt dissociates, factor 2; ~1.7 m → -3.2°C (freezes at -3.2°C)

Where phase changes show up

• Cooking and food. Boiling, frying, freezing, freeze-drying. Pressure cooker exploits raised boiling point.
• Weather and climate. Cloud formation, rain/snow, hurricanes (driven by latent heat release), permafrost melt.
• Refrigeration. Refrigerant cycles between liquid and gas to move heat efficiently.
• Industrial. Distillation, crystallization, freeze-drying, glass making (annealing).
• Geology. Magma cooling and crystallization, ice ages, rock formation.
• Astrophysics. Star formation (gas clouds collapse and ignite), planetary atmospheres (volatile boiling and condensation).
• Medicine. Sterilization (steam at high P), cryogenic preservation, freeze-drying medications.

Common mistakes

• Forgetting T doesn't change during phase transitions. Adding heat to boiling water keeps T at 100°C; it just makes more steam. Once water is gone, T rises again.
• Ignoring pressure dependence. Boiling, melting, etc. all depend on pressure. "Boiling point of water" is meaningful only at specified pressure.
• Mixing up sublimation and evaporation. Evaporation — liquid → gas (slow, surface only). Vaporization includes boiling (rapid, throughout liquid). Sublimation — solid → gas (no liquid stage).
• Using wrong specific heat or latent heat. Each phase has its own c (ice 2108, water 4186, steam 2010). Each transition has its own L. Don't mix.
• Treating all matter the same. Each substance has its own phase diagram, transition T, latent heats. Water's behavior (anomalous expansion, high L_v) is unusual.
• Forgetting the triple and critical points. Above critical T and P, no liquid-gas distinction. Below triple point, no liquid phase at any P. These edges have important physics.