Latent Heat and Phase Changes

Latent heat is the thermal energy absorbed or released when a substance changes state at constant temperature, and the energy required is Q = mL, where L is the specific latent heat of fusion (melting) or vaporization (boiling) in J/kg. In brief: for water, L_f = 334 kJ/kg (ice to water) and L_v = 2,260 kJ/kg (water to steam). During a phase change the energy goes into breaking or forming bonds between particles, increasing their potential energy rather than their kinetic energy, so the temperature stays constant.

Ice keeps a drink cold far better than the same mass of cold water, and a burn from steam is worse than one from boiling water. Both are due to latent heat. This guide explains what happens during melting, boiling and condensing, gives the formulas, compares the latent heats in a table, works through a calculation of the total energy to turn ice into steam, and corrects common mistakes.

What happens during a phase change?

When a solid is heated to its melting point, the temperature stops rising even though the heater continues to supply energy. The energy is used to overcome the forces between the particles, so that they can move past each other as a liquid. The same occurs at the boiling point, where much more energy is needed to separate the particles completely. The reverse changes release energy: when water vapor condenses or water freezes, the same energy is given to the surroundings. That is why steam is dangerous (it releases 2,260 kJ/kg on condensing on the skin, plus the energy lost as it cools), and why oranges are sprayed with water before a frost: freezing releases energy that protects the fruit.

How is latent heat calculated?

Q = mL

• Specific latent heat of fusion (L_f): energy to change 1 kg of solid to liquid at its melting point, with no change in temperature.
• Specific latent heat of vaporization (L_v): energy to change 1 kg of liquid to gas at its boiling point. It is larger than L_f, because the particles must be completely separated against the attractive forces, and the gas must push back the atmosphere as it expands.

For a full process, add the energy for each stage: heating a phase uses Q = mcΔT, and a phase change uses Q = mL.

Latent heats compared

Worked example: from ice to steam

How much energy is needed to turn 0.100 kg of ice at −10 °C into steam at 110 °C at normal pressure? Use c(ice) = 2,100, c(water) = 4,180, c(steam) = 2,010 J/(kg·K), L_f = 334,000 J/kg, L_v = 2,260,000 J/kg.

1. Warm the ice from −10 °C to 0 °C: Q₁ = 0.100 × 2,100 × 10 = 2,100 J.
2. Melt the ice: Q₂ = 0.100 × 334,000 = 33,400 J.
3. Warm the water from 0 °C to 100 °C: Q₃ = 0.100 × 4,180 × 100 = 41,800 J.
4. Boil the water: Q₄ = 0.100 × 2,260,000 = 226,000 J.
5. Warm the steam from 100 °C to 110 °C: Q₅ = 0.100 × 2,010 × 10 = 2,010 J.
6. Total: 2,100 + 33,400 + 41,800 + 226,000 + 2,010 = 305,310 J ≈ 305 kJ.

Boiling takes about 74 percent of the total energy (226,000 ÷ 305,310). As another example, a 0.050 kg ice cube at 0 °C added to 0.250 kg of water at 20 °C: melting uses 0.050 × 334,000 = 16,700 J. The water can give up 0.250 × 4,180 × 20 = 20,900 J in cooling to 0 °C, so all the ice melts, and the rest of the energy (4,200 J) warms 0.300 kg of water by 4,200 ÷ (0.300 × 4,180) = 3.3 °C. The final temperature is 3.3 °C.

How was latent heat discovered?

Joseph Black discovered latent heat around 1761, when he noticed that melting ice stays at 0 °C although it continues to absorb heat. His ideas were important for James Watt, who used them to improve the steam engine. Black also introduced the term “latent” (hidden) because the heat could not be detected with a thermometer.

Where does latent heat matter?

Refrigerators and air conditioners use the evaporation of a refrigerant to absorb heat. Sweating cools the body, because evaporating sweat takes latent heat from the skin. Steam is used in heating and in sterilization (autoclaves), and in meteorology, condensation of water vapor releases latent heat that powers thunderstorms and hurricanes.

Which mistakes are common?

Mistake 1: Using Q = mcΔT during melting or boiling

The temperature does not change, so ΔT = 0. Use Q = mL.

Mistake 2: Thinking that no energy is supplied when the temperature is constant

Energy is being supplied, but it changes the potential energy of the particles.

Mistake 3: Confusing L_f and L_v

Use fusion for melting and freezing, and vaporization for boiling and condensing.

Mistake 4: Forgetting the stages

For a multi-stage process, add the energy of each stage, including heating each phase.