Heating Curve & Phase Change Essentials

Phase changes and latent heat

• Phase changes: solid ↔ liquid ↔ gas; includes solid→liquid (melting), liquid→gas (vaporization), and reverse processes (freezing, condensation)
• During a phase change, temperature does not change; the absorbed/released heat goes into rearranging particles, not warming/cooling
• Latent heats:
  • Fusion (solid ⇄ liquid): $Q = m L_f$
  • Vaporization (liquid ⇄ gas): $Q = m L_v$
• For heating/cooling within a single phase: $Q = m c \, \Delta T$ (c is specific heat)
• Common water values:
  • $L_f \approx 334\ \, \mathrm{J\, g^{-1}}$
  • $L_v \approx 2260\ \, \mathrm{J\, g^{-1}}$
  • $c_w \approx 4.18\ \, \mathrm{J\, g^{-1} \ ^\circ C^{-1}}$

Heating and cooling curves

• Axes: X = input heat, Y = temperature
• Single-phase regions: temperature rises/falls (slopes)
• Phase-change plateaus: constant temperature while phase change occurs
  • Melting at 0°C for water (solid → liquid)
  • Boiling at 100°C for water (liquid → gas)
• During melting/boiling, the added heat goes into changing phase, not increasing temperature
• Two-phase regions exist during partial melting or partial vaporization (mixtures of phases)
• The cooling curve is the reverse of the heating curve (same plateaus, different direction)

Water heating curve: key sequence (ice to steam)

• Start: solid ice at a low temperature (e.g., −40°C)
• Heat to 0°C: solid ice warms until melting point
• Melting plateau at 0°C: solid → liquid; heat input goes into fusion
• Liquid water heats from 0°C to 100°C
• Boiling plateau at 100°C: liquid → steam; heat input goes into vaporization
• Steam heats above 100°C or, upon cooling, steam condenses back through the same plateaus
• States at points:
  • Below 0°C: solid
  • During 0°C plateau: solid–liquid mixture
  • Between plateaus: liquid
  • At 100°C plateau: liquid–gas mixture
  • Above 100°C: gas

Practical burn comparison: 100°C steam vs 100°C water

• Both at 100°C, but steam can transfer more heat to skin due to latent heat release during condensation
• Heat transfer per mass (conceptual):
  • Hot water burn: $Q<em>{ ext{water}} = m c</em>w (100 - 37)$
  • Steam burn: $Q<em>{ ext{steam}} = m L</em>v + m c_w (100 - 37)$
• Since $L<em>v \gg c</em>w \times (100-37)$, steam releases more energy when it condenses and cools on skin
• Latent heat is the key factor in the greater severity of steam burns

Other examples and problem types

• Ethanol: apply the same approach with ethanol’s $L<em>v$ and its own $c$ and $L</em>f$
• General problem approach:
  • Identify phase-change steps
  • Assign the appropriate heat equation to each step
  • Sum the heats of all steps

Exam-type problem: steam to ice at 0°C (three steps)

• Given: 175 g steam at 100°C condenses, then cools to 0°C, then freezes to 0°C ice
• Steps (identify and write equations): 1) Condense steam: $Q<em>1 = m L</em>v$
  • 100°C steam → 100°C water
    2) Cool water: $Q<em>2 = m c</em>w (100 - 0)$
  • 100°C water → 0°C water
    3) Freeze at 0°C: $Q<em>3 = m L</em>f$
  • 0°C water → 0°C ice
• Total heat lost: $Q = Q<em>1 + Q</em>2 + Q_3$
• Numerical values (approx):
  • $L_v \approx 2260\ \, \mathrm{J\, g^{-1}}$
  • $c_w \approx 4.18\ \, \mathrm{J\, g^{-1} \, ^{\circ}C^{-1}}$
  • $L_f \approx 334\ \, \mathrm{J\, g^{-1}}$
  • Mass: $m = 175\ \mathrm{g}$
• Example total (rounded): approximately $5.27\times 10^5\ \mathrm{J} \approx 527\ \mathrm{kJ}$
• Key exam skill: decompose into steps, apply the correct equation to each, and sum

Quick recall tips

• Latent heat governs heat during phase changes; temperature stays constant during these steps
• Use $Q = m L<em>f$ for fusion, $Q = m L</em>v$ for vaporization, and $Q = m c \, \Delta T$ for heating/cooling within one phase
• On a heating/cooling curve, read the substance’s state at any point by the plateau presence and phase regions
• For burns, steam is more dangerous than hot water because of the additional heat from condensation (latent heat)
• In problems, list steps (e.g., H1, H2, H3) and apply the corresponding equations to each step