Phase Transitions and Modern Thermal Applications

1. Introduction

Matter exists in different physical states, commonly called phases. The three familiar states are solid, liquid and gas. Under particular conditions, matter may also exist as plasma and in specialised quantum states such as Bose-Einstein condensates.

A phase transition is a physical change in which a substance changes from one state or phase to another due to variations in temperature, pressure or other thermodynamic conditions.

Phase transitions are important in meteorology, materials science, energy storage, engineering, medicine, food preservation and modern industrial technology.

2. States of Matter

2.1 Solid

A solid has a definite shape and volume. Its particles are closely packed and generally vibrate around relatively fixed positions.

Solids may be crystalline or amorphous.

2.2 Liquid

A liquid has a definite volume but takes the shape of its container. Its particles remain relatively close together but can move past one another.

2.3 Gas

A gas has neither a fixed shape nor a fixed volume. Its particles move freely and occupy the available space.

2.4 Plasma

Plasma is an ionised state of matter containing free electrons and positive ions. It is electrically conductive and responds to electric and magnetic fields.

Examples include stars, lightning, auroras and fluorescent discharge tubes.

2.5 Bose-Einstein Condensate

A Bose-Einstein condensate is a special state of matter formed when certain bosonic particles are cooled to temperatures extremely close to absolute zero.

At these temperatures, a large number of particles occupy the same lowest quantum state and display collective quantum behaviour.

3. Phase Transitions

A phase transition occurs when a substance changes from one physical phase to another.

The principal phase transitions include:

4. Melting and Freezing

4.1 Melting

Melting is the transition from solid to liquid due to the absorption of thermal energy.

At the melting point, a pure crystalline substance changes phase at approximately constant pressure and temperature while latent heat is absorbed.

4.2 Freezing

Freezing is the transition from liquid to solid due to the removal of thermal energy.

During freezing, latent heat is released to the surroundings.

4.3 Melting Point

The melting point is the temperature at which a solid and liquid phase coexist in equilibrium at a specified pressure.

The melting point may vary with pressure. For many substances, increasing pressure raises the melting point, but water is an important exception near ordinary conditions.

5. Vaporisation and Condensation

5.1 Vaporisation

Vaporisation is the conversion of a liquid into a gas. It occurs through evaporation or boiling.

Evaporation: A surface phenomenon in which molecules escape from the liquid into the gaseous state. It can occur below the boiling point.

Boiling: A bulk process in which vapour bubbles form throughout the liquid when its vapour pressure equals the external pressure.

5.2 Factors Affecting Evaporation

Evaporation increases with:

• Higher temperature.
• Larger exposed surface area.
• Greater air movement.
• Lower surrounding humidity.
• Lower external pressure, under comparable conditions.

5.3 Condensation

Condensation is the conversion of vapour into liquid when energy is removed or when conditions bring the vapour to saturation.

Examples include dew formation, cloud formation and water droplets on a cold glass.

6. Sublimation and Deposition

6.1 Sublimation

Sublimation is the direct transition from solid to gas without passing through the liquid state.

Examples include:

• Dry ice (solid carbon dioxide).
• Naphthalene under suitable conditions.
• Iodine crystals under heating.

6.2 Deposition

Deposition is the direct transition from gas to solid.

Examples include frost formation and the formation of ice crystals from water vapour.

7. Latent Heat and Phase Changes

Latent heat is the energy absorbed or released during a phase transition without a corresponding change in temperature of a pure substance at constant pressure while the phase change is occurring.

The amount of heat involved is:

[
Q=mL
]

Where:

• (Q) = heat transferred in joules.
• (m) = mass in kilograms.
• (L) = specific latent heat in J kg(^{-1}).

7.1 Specific Latent Heat of Fusion

The energy required per unit mass to convert a solid into liquid at its melting point without changing temperature.

7.2 Specific Latent Heat of Vaporisation

The energy required per unit mass to convert a liquid into vapour at its boiling point without changing temperature.

The latent heat of vaporisation is generally greater than the latent heat of fusion for a given substance.

8. Heating and Cooling Curves

A heating curve shows how the temperature of a substance changes as heat is supplied.

Its main stages are:

1. Heating of the solid.
2. Melting at approximately constant temperature.
3. Heating of the liquid.
4. Boiling at approximately constant temperature.
5. Heating of the gas.

During the flat portions of the curve, energy is used for the phase transition rather than increasing the average temperature.

A cooling curve follows the reverse sequence, with heat released during condensation and freezing.

9. Phase Diagrams

A phase diagram represents the stable physical phases of a substance under different temperature and pressure conditions.

9.1 Triple Point

The triple point is the unique combination of temperature and pressure at which solid, liquid and gas phases coexist in thermodynamic equilibrium.

For water, the triple-point temperature is approximately 273.16 K, and its pressure is approximately 611.7 Pa.

9.2 Critical Point

The critical point is the temperature and pressure at which the distinction between liquid and gas phases disappears.

Above the critical temperature and critical pressure, a substance may exist as a supercritical fluid.

9.3 Critical Temperature

The critical temperature is the highest temperature at which a gas can be liquefied by pressure alone.

9.4 Supercritical Fluids

Supercritical fluids exhibit properties intermediate between those of liquids and gases.

Supercritical carbon dioxide is used in extraction processes, including decaffeination and specialised industrial separation.

10. First-Order and Second-Order Phase Transitions

10.1 First-Order Phase Transition

A first-order phase transition involves a discontinuous change in a first derivative of the thermodynamic potential and is generally associated with latent heat.

Melting and boiling are common examples.

10.2 Second-Order or Continuous Phase Transition

A continuous phase transition does not involve latent heat in the same way as a first-order transition. Instead, certain thermodynamic response properties change sharply or become singular near the transition.

Examples include certain magnetic ordering transitions and superconducting transitions under appropriate classifications.

11. Thermal Expansion and Phase Behaviour

Temperature changes can cause matter to expand or contract. During phase transitions, changes in molecular arrangement may produce much larger volume changes.

Water exhibits an unusual density behaviour: it reaches maximum density at approximately 4°C at atmospheric pressure. Ice is less dense than liquid water, so it floats.

This behaviour has major environmental consequences because floating ice can insulate water beneath it and support aquatic life during winter.

12. Modern Thermal Applications

12.1 Phase-Change Materials

Phase-change materials (PCMs) absorb or release substantial thermal energy during a phase transition.

They are used in:

• Building temperature regulation.
• Thermal energy storage.
• Solar energy systems.
• Temperature-controlled packaging.
• Electronic equipment cooling.
• Clothing and protective materials.

A PCM may absorb heat while melting and release stored heat when it solidifies.

12.2 Thermal Energy Storage

Thermal energy storage systems store energy for later use.

Common approaches include:

Sensible heat storage: Energy is stored by raising the temperature of a material.

Latent heat storage: Energy is stored through a phase transition.

Thermochemical storage: Energy is stored through reversible chemical reactions or sorption processes.

12.3 Cryogenics

Cryogenics is the science and technology of producing and studying very low temperatures.

Applications include:

• Liquid nitrogen storage.
• Medical preservation.
• Cryogenic cooling of superconducting magnets.
• Aerospace systems.
• Scientific research.
• Industrial gas separation.

Liquid nitrogen has a normal boiling point of approximately 77 K, or -196°C.

12.4 Superconductivity

Superconductivity is a phenomenon in which certain materials exhibit zero electrical resistance below a critical temperature, together with characteristic magnetic behaviour.

Superconducting materials are used in MRI machines, particle accelerators and advanced scientific equipment.

12.5 Thermal Management of Electronics

Modern electronic systems generate heat during operation. Excessive temperature can reduce performance and damage components.

Thermal management techniques include:

• Heat sinks.
• Cooling fans.
• Liquid cooling.
• Heat pipes.
• Vapour chambers.
• Phase-change materials.

12.6 Heat Pipes

A heat pipe is a passive heat-transfer device that uses evaporation and condensation of a working fluid to transport thermal energy efficiently.

It is used in computers, electronics, spacecraft and industrial equipment.

12.7 Freeze-Drying

Freeze-drying, also known as lyophilisation, removes water from a frozen product mainly through sublimation under reduced pressure.

It is used for pharmaceuticals, biological materials and selected food products.

12.8 Thermal Processing of Food

Thermal processes such as pasteurisation, sterilisation, freezing and drying are used to improve food safety and shelf life.

Each process involves controlled heat transfer and phase behaviour.

13. Environmental and Industrial Applications

Phase transitions are central to:

• Cloud formation and precipitation.
• Snow and ice formation.
• Refrigeration and air conditioning.
• Steam power generation.
• Desalination.
• Metal casting.
• Glass manufacturing.
• Petroleum refining.
• Pharmaceutical production.
• Energy storage.

14. Worked Numerical Examples

Example 1: Heat Required to Melt Ice

Calculate the heat required to melt 2 kg of ice at 0°C. The specific latent heat of fusion of ice is (334,000\ J,kg^{-1}).

Formula:

[
Q=mL_f
]

Solution:

[
Q=2\times334000
]

[
Q=668000\ J
]

Answer: 668 kJ of heat is required.

Example 2: Heat Required for Vaporisation

Calculate the energy required to vaporise 0.5 kg of water at its boiling point. Take the specific latent heat of vaporisation as (2.26\times10^6\ J,kg^{-1}).

[
Q=mL_v
]

[
Q=0.5\times2.26\times10^6
]

[
Q=1.13\times10^6\ J
]

Answer: The required energy is 1.13 MJ.

Example 3: Total Heat for Heating and Melting Ice

Calculate the heat required to convert 1 kg of ice at -10°C into water at 0°C.

Take:

• Specific heat capacity of ice = (2100\ J,kg^{-1}K^{-1}).
• Latent heat of fusion = (334000\ J,kg^{-1}).

Step 1: Heat ice to its melting point.

[
Q_1=mc\Delta T
]

[
Q_1=1\times2100\times10=21000\ J
]

Step 2: Melt the ice.

[
Q_2=mL_f=1\times334000=334000\ J
]

Step 3: Calculate total heat.

[
Q_{\text{total}}=Q_1+Q_2
]

[
Q_{\text{total}}=21000+334000=355000\ J
]

Answer: 355 kJ is required.

15. Common Examination Distinctions

36 Key Takeaways for Exams

1. Matter commonly exists as solid, liquid and gas.
2. Plasma is an ionised state of matter.
3. A Bose-Einstein condensate is formed at extremely low temperatures.
4. A phase transition is a change from one physical phase to another.
5. Melting converts a solid into a liquid.
6. Freezing converts a liquid into a solid.
7. Vaporisation converts a liquid into a gas.
8. Condensation converts a gas into a liquid.
9. Evaporation occurs at the liquid surface.
10. Boiling is a bulk process involving vapour bubble formation.
11. Sublimation is the direct conversion of solid into gas.
12. Deposition is the direct conversion of gas into solid.
13. Latent heat is transferred during a phase change without a corresponding temperature change under the usual equilibrium conditions.
14. Specific latent heat is energy required per unit mass for a phase transition.
15. The latent heat equation is (Q=mL).
16. Latent heat of vaporisation is generally greater than latent heat of fusion.
17. Heating curves show temperature changes and phase transitions.
18. Triple point is the condition where three phases coexist in equilibrium.
19. The triple point of water is approximately 273.16 K.
20. The critical point marks the end of the liquid-gas phase boundary.
21. Above the critical point, a substance can exist as a supercritical fluid.
22. First-order phase transitions involve latent heat.
23. Continuous phase transitions are commonly classified as second-order transitions.
24. Water has maximum density near 4°C at atmospheric pressure.
25. Ice is less dense than liquid water.
26. Phase-change materials store and release latent heat.
27. Thermal energy storage helps balance energy supply and demand.
28. Cryogenics deals with very low temperatures.
29. Liquid nitrogen boils at approximately 77 K at normal pressure.
30. Superconductivity occurs below a material’s critical temperature.
31. Heat pipes transfer heat through evaporation and condensation.
32. Freeze-drying removes frozen water mainly through sublimation.
33. Pasteurisation and sterilisation are thermal food-processing techniques.
34. Phase transitions are important in refrigeration and power generation.
35. Thermal management protects electronic components from overheating.
36. Phase-transition science is essential in modern energy, materials and industrial technologies.