Phase Changes — Melting, Boiling and the Energy Hidden in Latent Heat

The six transitions

Matter comes in three familiar phases — solid, liquid, gas — and it switches between them more dramatically than most students expect. There are six possible transitions, each with its own name:

• Melting (fusion): solid → liquid (ice to water)
• Freezing (solidification): liquid → solid (water to ice)
• Vaporization: liquid → gas — by evaporation (surface, any temperature) or boiling (throughout, at the boiling point)
• Condensation: gas → liquid (dew on morning grass)
• Sublimation: solid → gas directly (dry ice vanishing into vapor)
• Deposition: gas → solid directly (frost crystals on a window)

Each transition moves energy in or out — and the thermometer, surprisingly, ignores it all.

Why the temperature stops climbing

Heat a block of ice and the temperature climbs steadily — until it hits 0 °C. Then the thermometer stalls. Heat keeps pouring in, the ice keeps melting, but the temperature refuses to move until the last crystal is gone. Only then does the water start warming again.

The same stall happens at 100 °C while water boils. The reason: temperature measures average molecular kinetic energy, but during a phase change the incoming energy goes into potential energy — pulling molecules out of their bonded arrangement. Bonds break first; thermometers wait.

Latent heat: the hidden energy

The energy of rearrangement is latent heat ($L$): the energy per kilogram needed to change phase at constant temperature.

$$Q = mL$$

For water at normal pressure, the two key values are:

• Latent heat of fusion $L_f = 334\ \mathrm{kJ/kg}$ — melting ice (or freezing water).
• Latent heat of vaporization $L_v = 2260\ \mathrm{kJ/kg}$ — boiling water (or condensing steam).

Vaporization costs nearly seven times fusion: tearing molecules completely free of the liquid takes far more energy than merely loosening them into a liquid. Condensing steam releases the same 2260 kJ/kg — which is why steam burns are devastating.

Reading a heating curve

Plot temperature against steadily added heat for water starting as ice, and you get the classic heating curve: a rising slope (warming ice), a flat plateau at 0 °C (melting), a rising slope (warming water), a long flat plateau at 100 °C (boiling), then a rising slope (heating steam).

The slopes are governed by specific heats ($Q = mc\Delta T$) — sensible heat, energy you can sense on a thermometer. The plateaus are governed by latent heats ($Q = mL$) — latent heat, hidden from the thermometer. Confusing the two formulas is the most common error in calorimetry problems.

Worked example: melting two kilograms of ice

How much energy melts $2.0\ \mathrm{kg}$ of ice already at 0 °C?

$$Q = mL_f = 2.0 \times 334{,}000 = 668{,}000\ \mathrm{J}$$

About 668 kJ — roughly the energy of a 100 W light bulb burning for nearly two hours — and the temperature never leaves 0 °C. If the ice had started at −10 °C, you would first warm it with $Q = mc\Delta T$ (ice's specific heat is about 2100 J/(kg·K)), then apply the latent formula: sensible heat first, latent heat second.

Sublimation and deposition in the wild

Dry ice is solid carbon dioxide, and at normal pressure it never melts — it sublimates directly to gas at −78.5 °C, which is why it vanishes without a puddle and why it is so useful for shipping frozen goods.

Nature runs the same transitions constantly: snow can sublimate straight into dry winter air, frost deposits from vapor onto cold surfaces, and freeze-drying preserves food and vaccines by freezing them, then sublimating the ice away under low pressure — leaving the structure intact with the water gone.

Everyday phase-change engineering

Your body is a phase-change engineer: sweat evaporates, and each gram carries away roughly 2.4 kJ of latent heat — enormously effective cooling for a few grams of water.

Refrigerators exploit the cycle in reverse: a working fluid evaporates inside the fridge (absorbing heat) and condenses in the coils behind it (dumping heat into the room). Every phase change is an energy transaction, and technology has learned to spend that currency both ways.

Variables and units

Common mistakes

Real-world applications

• Sweating cools you because each gram of evaporated sweat carries away roughly 2.4 kJ of heat.

• Refrigerators pump heat by repeatedly evaporating and condensing a working fluid.

• Freeze-drying preserves food and medicines by sublimating ice directly to vapor.