💡 Key Insight: During a phase change, temperature remains constant even as energy is added/removed!

Latent Heat

Latent heat is energy required to change phase without changing temperature.

Heat of Fusion (L_f)

Energy to melt (or freeze) 1 kg of substance:

$Q = mL_f$

For water: $L_f = 334,000$ J/kg = 334 kJ/kg

Heat of Vaporization (L_v)

Energy to vaporize (or condense) 1 kg of substance:

$Q = mL_v$

For water: $L_v = 2,260,000$ J/kg = 2260 kJ/kg

Note: $L_v > L_f$ because you must completely overcome intermolecular forces for vaporization.

Heating Curve for Water

When heating ice from -20°C to steam at 120°C:

Stage 1: Ice warms (-20°C → 0°C) $Q_1 = m c_{ice} \Delta T = m(2090)(20)$

Stage 2: Ice melts at 0°C (phase change) $Q_2 = m L_f = m(334,000)$ Temperature stays at 0°C!

Stage 3: Water warms (0°C → 100°C) $Q_3 = m c_{water} \Delta T = m(4186)(100)$

Stage 4: Water boils at 100°C (phase change) $Q_4 = m L_v = m(2,260,000)$ Temperature stays at 100°C!

Stage 5: Steam warms (100°C → 120°C) $Q_5 = m c_{steam} \Delta T = m(2010)(20)$

Total energy: $Q_{total} = Q_1 + Q_2 + Q_3 + Q_4 + Q_5$

Why Temperature Stays Constant

During phase changes:

• Energy goes into breaking molecular bonds
• Does NOT increase kinetic energy (temperature)
• Potential energy increases, kinetic energy constant
• Both phases coexist at transition temperature

Example: Ice-water mixture stays at 0°C until all ice melts.

Evaporation vs. Boiling

Evaporation

• Occurs at surface
• Happens at any temperature
• Faster molecules escape
• Causes cooling (loses high-energy molecules)

Boiling

• Occurs throughout liquid
• Happens at specific temperature (boiling point)
• Vapor pressure equals atmospheric pressure
• Bubbles form inside liquid

Important Values for Water

Pressure Dependence

• Higher pressure → higher boiling point

  • Pressure cooker: cooks faster at higher T
  • Mountain top: water boils below 100°C

• Lower pressure → lower boiling point

  • Vacuum chamber: water boils at room temp

Melting point is less affected by pressure (except for water/ice).

Problem-Solving Strategy

1. Identify all stages of heating/cooling
2. Separate into segments:
   • Temperature changes: $Q = mc\Delta T$
   • Phase changes: $Q = mL$
3. Add all energy contributions: $Q_{total} = \sum Q_i$
4. Watch for mixed-phase problems (some melts, some doesn't)
5. Check if enough energy for complete phase change

Common Mistakes

❌ Forgetting temperature is constant during phase change ❌ Using wrong specific heat (ice vs. water vs. steam) ❌ Adding ΔT during phase change (it's zero!) ❌ Confusing L_f and L_v ❌ Not checking if phase change is complete

Find: Energy required $Q$

Solution:

Since ice is already at melting point, only need energy for phase change:

$Q = mL_f = (2.0)(334,000) = 668,000 \text{ J} = 668 \text{ kJ}$

Answer: 668 kJ is required to melt the ice

Note: Temperature stays at 0°C during melting!