Latent Heat & Phase-Change Energy Balances

Separate sensible heating from latent heat so your enthalpy balance doesn't double-count energy during melting/boiling.

Material & Energy BalancesChemical Engineering Year 1Free preview

⏱️ About 16 min

Why does water keep absorbing heat at 100°C without getting hotter — and how do you account for that cleanly in an energy balance?

💡

The big idea: During a phase change at constant T and P, enthalpy changes by latent heat (no sensible heat term during the transition).

🎯 By the end, you'll be able to

Define latent heat of fusion and vaporization and distinguish them from sensible heat
Write the enthalpy change across a phase change at constant temperature and pressure
Compute total heat for a multi-step heating process that includes a phase change
Avoid the common pitfall of adding CpΔT during the phase-change plateau

📎 Helpful to know first

Open-System Energy Balances

Latent Heat vs Sensible Heat

Sensible heat changes temperature: you supply heat and the temperature rises (or falls). In contrast, latent heat changes phase at (approximately) constant temperature and pressure.

Two standard latent heats for water (standard reference values):

Latent heat of fusion at 0°C: λ_fus = 334 kJ/kg
Latent heat of vaporization at 100°C: λ_vap = 2257 kJ/kg

During melting/boiling at the phase-change temperature, heat flows in but the temperature stays essentially constant until the phase change completes.

\[ \Delta H_{\text{phase change}} = m\,\lambda \;=\; n\,\Delta \bar{H}_{\text{phase change}} \]

At constant T and P through the phase-change plateau, the enthalpy change is latent heat (no CpΔT term during the transition).

Energy Balance Pattern for “Heat → Phase Change → Heat”

A very common heating path is:

Heat within one phase (sensible): Q = m C_p (T₂ − T₁)
Change phase at constant T (latent): Q = m λ
Heat within the new phase (sensible): Q = m C_p (T₃ − T₂)

For water as liquid, a standard reference value is C_p,liq ≈ 4.18 kJ/(kg·K).

⚠️ Pitfall: Don't add sensible heat during the phase change

During a phase change at constant T (e.g., boiling at 100°C at 1 atm), the temperature is not changing, so a term like m C_pΔT across the boiling plateau is zero. All the heat during the plateau is latent heat: mλ.

📝 Worked example: At 1 atm, 1.00 kg of liquid water at 25°C is heated to saturated steam at 100°C. Use C_p,liq = 4.18 kJ/(kg·K) and λ_vap(100°C) = 2257 kJ/kg. Compute the total heat required.

Step 1 (sensible heating of liquid, 25°C → 100°C):
Q₁ = m C_p,liq (T₂ − T₁) = (1.00 kg)(4.18 kJ/(kg·K))(100 − 25) K
Q₁ = (1.00)(4.18)(75) kJ = 313.5 kJ
Step 2 (vaporization at 100°C, constant T and P):
Q₂ = m λ_vap = (1.00 kg)(2257 kJ/kg) = 2257 kJ
Total heat required:
Q_total = Q₁ + Q₂ = 313.5 kJ + 2257 kJ = 2570.5 kJ

✓ Q_total = 2570.5 kJ (313.5 kJ sensible + 2257 kJ latent)

✏️ Practice: At 1 atm, how much heat is required to boil 0.500 kg of water at 100°C into saturated steam at 100°C? Use λ_vap(100°C) = 2257 kJ/kg.

Solution

This is a pure phase change at constant temperature, so only latent heat is needed:
Q = m λ_vap = (0.500 kg)(2257 kJ/kg) = 1128.5 kJ

Check your understanding

1. At 1 atm, liquid water boils at 100°C. While it is boiling (liquid + vapor present), the best statement is:

During boiling at constant pressure, heat input goes into the phase change (latent heat), so T stays near 100°C while H increases.

2. For a phase change at constant T and P, the enthalpy change is:

Across the phase-change plateau, ΔH = mλ (latent heat).

✅ Key takeaways

Sensible heat changes temperature: Q = m C_p ΔT
Latent heat changes phase at constant T and P: ΔH = mλ (no CpΔT during the plateau)
Total heating through a phase change is the sum of sensible + latent (+ sensible, if applicable)
Common mistake: double-counting by applying C_p across a phase-change plateau

➡️ Phase changes change enthalpy without changing temperature. Chemical reactions can do something even more dramatic: they can release or absorb large amounts of enthalpy even at a fixed temperature. Next we compute heats of reaction from standard formation data.

Want to test yourself on this? Try the Chemical Aptitude test →