Latent Heat

Formula

For a phase change at the transition temperature:

Q = m · L

where:

• Q = heat absorbed (or released) (J).
• m = mass undergoing phase change (kg).
• L = latent heat (J/kg) — material- and transition-specific.

Two main types:

• Latent heat of fusion (L_f) — for solid ↔ liquid transition.
• Latent heat of vaporization (L_v) — for liquid ↔ gas transition.
• Latent heat of sublimation (L_s) — direct solid ↔ gas transition (less common).

Common latent heats

Substance	Transition	L (kJ/kg)	T (°C, at 1 atm)
Water (ice ↔ liquid)	Fusion	334	0
Water (liquid ↔ steam)	Vaporization	2,260	100
Ammonia	Vaporization	1,370	-33
Ethanol	Vaporization	850	78
Mercury	Vaporization	295	357
Lead	Fusion	23	327
Aluminum	Fusion	397	660
Iron	Fusion	247	1538
Helium-4	Vaporization	20.7	-269
Nitrogen (liquid)	Vaporization	199	-196

Energy comparisons

Process	Q for 1 kg water	vs heating 1 kg water 1°C
Heat 1 kg water 1°C	4,186 J	1×
Heat 1 kg water 100°C (full liquid range)	418,600 J	100×
Melt 1 kg ice at 0°C	334,000 J	~80×
Vaporize 1 kg water at 100°C	2,260,000 J	~540×
Combine: ice 0°C → steam 100°C	3,012,600 J	~720×

Latent heat in climate

The water cycle is one of Earth's biggest energy transfer mechanisms. Solar energy evaporates water from oceans (consuming massive latent heat). Atmospheric water vapor releases this heat when it condenses (forming clouds, rain). This redistributes heat globally:

• Tropical oceans absorb solar heat → evaporate water → cools surface.
• Water vapor rises and travels (storm tracks).
• Condenses at higher altitudes or latitudes → releases heat.
• Hurricanes are massive heat engines, with 100+ exajoules (10²⁰ J) of latent heat as the energy source.

JavaScript — latent heat calculations

// Heat for phase change
function latentHeat(mass, L) {
  return mass * L;
}

// Standard water values
const L_fusion_water = 334000;       // J/kg
const L_vap_water = 2260000;         // J/kg
const c_water = 4186;                // J/(kg·K)
const c_ice = 2108;                  // J/(kg·K)
const c_steam = 2010;                // J/(kg·K)

// Total energy: ice at -10°C → steam at 110°C
function iceToSteam(mass) {
  // Heat ice from -10°C to 0°C
  const Q1 = mass * c_ice * 10;
  // Melt at 0°C
  const Q2 = mass * L_fusion_water;
  // Heat liquid 0 → 100°C
  const Q3 = mass * c_water * 100;
  // Vaporize at 100°C
  const Q4 = mass * L_vap_water;
  // Heat steam 100 → 110°C
  const Q5 = mass * c_steam * 10;
  return {
    iceWarming: Q1, melting: Q2, waterWarming: Q3, vaporizing: Q4, steamWarming: Q5,
    total: Q1 + Q2 + Q3 + Q4 + Q5
  };
}

console.log(iceToSteam(1));
// Total ~3.05 MJ; vaporization is ~75% of total

// Sweat cooling
function sweatCooling(mass_evaporated_kg) {
  return mass_evaporated_kg * L_vap_water;
}

// Marathon runner sweats 2 kg
console.log(`Marathon sweat cooling: ${(sweatCooling(2) / 1000).toFixed(0)} kJ = ${(sweatCooling(2) / 4184).toFixed(0)} kcal`);
// ~4.5 MJ ~ 1080 kcal

// Heat to melt iceberg
function iceberg(volume_m3) {
  const ice_density = 917;  // kg/m³
  const mass = volume_m3 * ice_density;
  return mass * L_fusion_water;
}

// 1 km × 1 km × 100 m iceberg
console.log(`Melt iceberg (1 km³): ${(iceberg(1e9) / 1e15).toFixed(2)} PJ`);
// ~3 × 10¹⁷ J = 300 PJ ≈ 80 TWh ≈ Sun's energy on Earth in ~3 days

// Refrigerator cycle (simplified)
function refrigCooling(mass_refrig_kg, L_v) {
  return mass_refrig_kg * L_v;
}

// 1 kg of refrigerant cycling: how much heat moved?
console.log(`R-134a (L_v ≈ 175 kJ/kg) refrig: ${refrigCooling(1, 175000)} J per cycle`);

// Hurricane energy from latent heat
function hurricaneHeat(volume_water_m3) {
  // Vaporize at sea, release latent heat in storm
  const mass = volume_water_m3 * 1000;  // 1000 kg/m³
  return mass * L_vap_water;
}

// Typical hurricane: vaporize 10¹⁰ kg of water (10 cm rain over 100,000 km²)
console.log(`Hurricane heat from 10^10 kg water: ${(hurricaneHeat(1e7) / 1e18).toFixed(1)} EJ`);
// ~22 EJ — about half of US annual energy use, in one storm

Where latent heat shows up

• Refrigeration and air conditioning. Refrigerants cycle through phases, moving large heats with small mass flow.
• Steam engines. Boiling water absorbs huge L_v; high-pressure steam carries it to turbines for work extraction.
• Climate science. Water vapor in atmosphere stores enormous latent heat; hurricane formation, climate feedback.
• Cooking. Why pots take so long to boil dry; why ice cubes cool drinks so much before melting.
• Cooling — sweating, evaporative coolers. Body uses latent heat of vaporization to cool; "swamp coolers" use water evaporation.
• Industrial — distillation, freeze-drying. Latent heat is leveraged for separation (vaporize one component), preservation (sublimation removes water without thermal damage).
• Cryogenics. Liquid nitrogen, helium for cooling — boiling point and L_v determine cooling capacity.

Common mistakes

• Mixing latent heat with specific heat. Q = m·c·ΔT for temperature change; Q = m·L for phase change. Phase change has NO temperature change.
• Forgetting which phase you're heating. Heating ice from -10°C to 0°C uses c_ice (2108). Then melt at 0°C using L_fusion. Then heat liquid water 0°C to 100°C using c_water. Different stages, different formulas.
• Wrong sign for direction. Heat ABSORBED during melting, vaporization. Heat RELEASED during freezing, condensation. Don't get the sign wrong in energy balance.
• Treating L as universal. L depends on substance AND transition. Water's L_v at 100°C (1 atm) is 2260 kJ/kg; at 25°C it's ~2440 kJ/kg (slightly higher). Tabulated values are at standard conditions.
• Forgetting that pressure affects boiling point. At higher pressure, water boils above 100°C; at lower (mountains, vacuum), below. L itself varies with P, T.
• Confusing latent heat values' magnitudes. L_vap_water (2260) is ~7× larger than L_fusion (334). They're both for water but very different.