Educational

Phase Change and Latent Heat

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by

Saim Khalid
in

In thermodynamics, phase change refers to the transition of a substance from one state of matter (solid, liquid, or gas) to another. These changes are associated with energy transfer, commonly in the form of heat, without a change in temperature. The energy required or released during a phase change is known as latent heat.

Phase changes and latent heat are fundamental concepts in physics, chemistry, and engineering, with applications ranging from refrigeration and air conditioning to industrial processing and climate science.

This post provides an in-depth explanation of phase changes, types of latent heat, formulas, practical examples, and real-world applications.

1. Introduction to Phase Change

A phase is a physically distinct form of matter. The three most common phases are:

  1. Solid – Definite shape and volume; particles vibrate about fixed positions.
  2. Liquid – Definite volume but indefinite shape; particles can move past each other.
  3. Gas – Indefinite shape and volume; particles move freely and rapidly.

Phase change occurs when energy is added or removed, causing a transition between these states:

  • Melting: Solid → Liquid
  • Freezing/Solidification: Liquid → Solid
  • Vaporization/Boiling: Liquid → Gas
  • Condensation: Gas → Liquid
  • Sublimation: Solid → Gas (without passing through liquid)
  • Deposition: Gas → Solid (without passing through liquid)

2. Concept of Latent Heat

Latent heat is the energy absorbed or released by a substance during a phase change at constant temperature.

  • The term “latent” means hidden because energy changes occur without a temperature change.
  • Symbol: LLL
  • Unit: Joule (J) in SI, calories (cal) in traditional units

Formula: Q=mLQ = m LQ=mL

Where:

  • QQQ = heat absorbed or released (J)
  • mmm = mass of the substance (kg)
  • LLL = specific latent heat (J/kg)

Key Points:

  • Temperature remains constant during the phase change.
  • Energy is used to break or form intermolecular bonds.
  • Different substances have different latent heats.

3. Types of Latent Heat

Latent heat is classified based on the type of phase change:

3.1 Latent Heat of Fusion (LfL_fLf​)

  • Energy required to convert 1 kg of solid into liquid at the same temperature.
  • Occurs during melting (solid → liquid) or released during freezing (liquid → solid).
  • Example: Melting ice at 0°C.
  • Formula:

Q=mLfQ = m L_fQ=mLf​

  • Typical values:
    • Water: Lf=334 kJ/kgL_f = 334 \text{ kJ/kg}Lf​=334 kJ/kg
    • Ice → Water: Heat absorbed = 334 kJ334 \text{ kJ}334 kJ per kg

Key Concept: Energy goes into overcoming molecular forces rather than increasing kinetic energy, so temperature remains constant.

3.2 Latent Heat of Vaporization (LvL_vLv​)

  • Energy required to convert 1 kg of liquid into vapor at the same temperature.
  • Occurs during boiling (liquid → gas) or released during condensation (gas → liquid).
  • Formula:

Q=mLvQ = m L_vQ=mLv​

  • Typical values:
    • Water: Lv=2260 kJ/kgL_v = 2260 \text{ kJ/kg}Lv​=2260 kJ/kg
    • Note: LvL_vLv​ is generally larger than LfL_fLf​ because vaporization requires breaking all intermolecular forces.

Example: Boiling water at 100°C absorbs 2260 kJ per kg without changing temperature.

3.3 Latent Heat of Sublimation (LsL_sLs​)

  • Energy required to convert solid directly into gas.
  • Occurs during sublimation (solid → gas) or deposition (gas → solid).
  • Formula:

Q=mLsQ = m L_sQ=mLs​

  • Relation:

Ls=Lf+LvL_s = L_f + L_vLs​=Lf​+Lv​

  • Example: Dry ice (solid CO₂) sublimates into gas without melting.

4. Phase Change Graphs

4.1 Heating Curve of a Substance

A heating curve shows temperature vs. heat added:

  1. Solid heating: Temperature rises → Q=mcΔTQ = mc \Delta TQ=mcΔT
  2. Melting: Temperature constant → Q=mLfQ = m L_fQ=mLf​
  3. Liquid heating: Temperature rises → Q=mcΔTQ = mc \Delta TQ=mcΔT
  4. Boiling: Temperature constant → Q=mLvQ = m L_vQ=mLv​
  5. Vapor heating: Temperature rises → Q=mcΔTQ = mc \Delta TQ=mcΔT

4.2 Cooling Curve of a Substance

  • Reverse of heating curve: Gas → liquid → solid
  • Heat is released during condensation and freezing at constant temperature.

5. Molecular Explanation

  • Solid → Liquid: Molecules overcome part of the intermolecular forces, move freely but remain close.
  • Liquid → Gas: Molecules overcome all intermolecular forces, move independently.
  • Solid → Gas: Molecules bypass liquid phase, directly overcoming forces.

Key Idea: Temperature remains constant because energy goes into potential energy (bond energy), not kinetic energy (motion).

6. Mathematical Treatment of Latent Heat

6.1 Total Heat Required

Total heat required to heat and change phase: Qtotal=Qheating+Qfusion+QvaporizationQ_{\text{total}} = Q_{\text{heating}} + Q_{\text{fusion}} + Q_{\text{vaporization}}Qtotal​=Qheating​+Qfusion​+Qvaporization​

Example: Heating 1 kg ice at -10°C to steam at 100°C:

  1. Heat ice from -10°C to 0°C: Q1=mciceΔTQ_1 = mc_{\text{ice}} \Delta TQ1​=mcice​ΔT
  2. Melt ice at 0°C: Q2=mLfQ_2 = m L_fQ2​=mLf​
  3. Heat water from 0°C to 100°C: Q3=mcwaterΔTQ_3 = mc_{\text{water}} \Delta TQ3​=mcwater​ΔT
  4. Vaporize water at 100°C: Q4=mLvQ_4 = m L_vQ4​=mLv​

Qtotal=Q1+Q2+Q3+Q4Q_{\text{total}} = Q_1 + Q_2 + Q_3 + Q_4Qtotal​=Q1​+Q2​+Q3​+Q4​

6.2 Example Calculation

  • Given: 2 kg ice at -5°C
  • Find: Heat required to convert to steam at 100°C
  • Data:
    • cice=2.1 kJ/kg\cdotpKc_{\text{ice}} = 2.1 \text{ kJ/kg·K}cice​=2.1 kJ/kg\cdotpK
    • cwater=4.18 kJ/kg\cdotpKc_{\text{water}} = 4.18 \text{ kJ/kg·K}cwater​=4.18 kJ/kg\cdotpK
    • Lf=334 kJ/kgL_f = 334 \text{ kJ/kg}Lf​=334 kJ/kg
    • Lv=2260 kJ/kgL_v = 2260 \text{ kJ/kg}Lv​=2260 kJ/kg

Steps:

  1. Heat ice to 0°C: Q1=2×2.1×5=21 kJQ_1 = 2 × 2.1 × 5 = 21 \text{ kJ}Q1​=2×2.1×5=21 kJ
  2. Melt ice: Q2=2×334=668 kJQ_2 = 2 × 334 = 668 \text{ kJ}Q2​=2×334=668 kJ
  3. Heat water to 100°C: Q3=2×4.18×100=836 kJQ_3 = 2 × 4.18 × 100 = 836 \text{ kJ}Q3​=2×4.18×100=836 kJ
  4. Vaporize water: Q4=2×2260=4520 kJQ_4 = 2 × 2260 = 4520 \text{ kJ}Q4​=2×2260=4520 kJ

Total heat: Qtotal=21+668+836+4520=6045 kJQ_{\text{total}} = 21 + 668 + 836 + 4520 = 6045 \text{ kJ}Qtotal​=21+668+836+4520=6045 kJ

7. Real-World Examples of Phase Change

  1. Ice Melting:
    • Latent heat of fusion absorbs energy → ice melts at 0°C.
    • Important in cooling drinks and refrigeration.
  2. Boiling Water:
    • Latent heat of vaporization absorbs energy → water becomes steam at 100°C.
    • Used in steam engines and power plants.
  3. Dry Ice Sublimation:
    • Solid CO₂ converts to gas → used for refrigeration and fog effects.
  4. Condensation in Clouds:
    • Water vapor releases latent heat → important in weather phenomena.
  5. Freezing of Water:
    • Latent heat released → keeps surroundings slightly warmer during ice formation.

8. Applications of Latent Heat

8.1 Refrigeration and Air Conditioning

  • Refrigerants absorb latent heat during evaporation in the cooling coil.
  • Heat is released during condensation in the condenser.

8.2 Heat Storage Systems

  • Phase Change Materials (PCMs) store thermal energy using latent heat.
  • Applications: Solar energy storage, building temperature regulation.

8.3 Industrial Processes

  • Distillation: Vaporization and condensation of liquids.
  • Metal casting: Heat removed during solidification.

8.4 Weather and Climate

  • Latent heat release during condensation drives storms and hurricanes.
  • Evaporation cools surfaces, regulating Earth’s temperature.

9. Factors Affecting Latent Heat

  1. Nature of substance: Polar molecules like water have higher latent heat due to strong hydrogen bonds.
  2. Pressure: Increasing pressure generally increases boiling point → alters latent heat.
  3. Temperature: Small changes in latent heat with temperature; often considered constant near phase change.

10. Relation with Thermodynamic Laws

  1. First Law of Thermodynamics:

ΔU=Q−W\Delta U = Q – WΔU=Q−W

  • During phase change, Q=mLQ = mLQ=mL increases internal energy (ΔU\Delta UΔU) without changing temperature.
  1. Second Law of Thermodynamics:
  • Latent heat transfer increases entropy in the surroundings.
  • Evaporation increases disorder, condensation decreases entropy locally.

11. Graphical Representation

11.1 Heating Curve

  • Temperature vs. heat added: Plateaus indicate phase change (fusion and vaporization).

11.2 Phase Diagram

  • Shows state of substance at different temperatures and pressures.
  • Key lines:
    • Fusion curve: Solid ↔ Liquid
    • Vaporization curve: Liquid ↔ Gas
    • Sublimation curve: Solid ↔ Gas
  • Critical point and triple point indicate special conditions where phases coexist.

12. Key Points Summary

  • Phase change occurs at constant temperature.
  • Latent heat is energy absorbed or released during a phase change.
  • Latent heat of fusion: Solid ↔ Liquid
  • Latent heat of vaporization: Liquid ↔ Gas
  • Latent heat of sublimation: Solid ↔ Gas
  • Energy goes into changing potential energy (intermolecular forces) rather than kinetic energy (temperature).
  • Crucial for engineering, weather, refrigeration, and industrial processes.

13. Key Formulas Recap

  1. Heat required for phase change: Q=mLQ = m LQ=mL
  2. Heat for heating/cooling without phase change: Q=mcΔTQ = mc \Delta TQ=mcΔT
  3. Latent heat of sublimation: Ls=Lf+LvL_s = L_f + L_vLs​=Lf​+Lv​

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