Energy Transfer Mechanisms

This lesson covers the three mechanisms by which thermal energy is transferred: conduction, convection, and radiation. For each mechanism, the molecular explanation is given alongside practical applications. This topic connects thermal physics to real-world energy efficiency, including the concept of U-values for building insulation.

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Conduction

Key Definition: Conduction is the transfer of thermal energy through a material by the vibration of particles and (in metals) by the movement of free electrons, without bulk movement of the material itself.

Molecular Explanation

In a solid:

1. Molecules at the hot end vibrate with greater amplitude (they have more kinetic energy).
2. These molecules collide with their cooler neighbours, transferring kinetic energy.
3. Energy is passed along from molecule to molecule through the solid.
4. There is no net movement of molecules — only energy is transferred.

In metals, conduction is much faster because:

• Free (delocalised) electrons can move rapidly through the lattice.
• When electrons gain kinetic energy at the hot end, they can travel quickly to cooler regions and transfer energy through collisions with the lattice ions.
• Electron conduction is typically 100–1000 times more effective than lattice vibration conduction.

Thermal Conductivity

The rate of energy transfer by conduction is given by:

P = kA(θ₁ − θ₂) / L

where:

• P = rate of energy transfer (W)
• k = thermal conductivity of the material (W m⁻¹ K⁻¹)
• A = cross-sectional area (m²)
• (θ₁ − θ₂) = temperature difference across the material (K)
• L = thickness of the material (m)

Thermal Conductivity Values

Material	Thermal Conductivity (W m⁻¹ K⁻¹)	Classification
Copper	400	Excellent conductor
Aluminium	237	Good conductor
Steel	50	Moderate conductor
Glass	1.0	Poor conductor
Brick	0.6	Poor conductor
Wood	0.15	Insulator
Fibreglass	0.04	Good insulator
Air (still)	0.025	Excellent insulator
Expanded polystyrene	0.03	Excellent insulator

Note that still (trapped) air is one of the best insulators, which is why many insulation materials work by trapping pockets of air.

Worked Example — Rate of Conduction

Question: A copper rod of length 0.50 m and cross-sectional area 2.0 × 10⁻⁴ m² has one end maintained at 100 °C and the other at 20 °C. Calculate the rate of energy transfer through the rod. (k_copper = 400 W m⁻¹ K⁻¹)

Solution:

P = kAΔθ/L = 400 × 2.0 × 10⁻⁴ × (100 − 20) / 0.50

P = 400 × 2.0 × 10⁻⁴ × 80 / 0.50

P = 6.4 / 0.50

P = 12.8 W

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Convection

Key Definition: Convection is the transfer of thermal energy by the bulk movement of a fluid (liquid or gas) due to differences in density.

Molecular Explanation

1. A region of fluid is heated (e.g. near a heat source at the bottom).
2. The heated fluid expands, becoming less dense than the surrounding cooler fluid.
3. The less dense warm fluid rises (buoyancy force exceeds weight).
4. Cooler, denser fluid moves in to replace it.
5. This sets up a convection current — a continuous circulation of fluid.
6. Energy is carried from hot regions to cold regions by the moving fluid.

Key Points

• Convection cannot occur in solids because the particles are fixed in position and cannot flow.
• Convection is most effective when there is a large temperature difference and the fluid can move freely.
• Convection can be natural (driven by density differences) or forced (driven by a fan or pump).
• Preventing convection is an important insulation strategy — trapping air in small pockets (e.g. in a duvet or cavity wall insulation) prevents convection currents from forming.

Examples of Convection

• Domestic heating: A radiator heats the air near it; the warm air rises and circulates around the room. Despite their name, radiators primarily transfer energy by convection, not radiation.
• Sea breezes: During the day, land heats up faster than sea. Hot air rises over the land, and cooler sea air flows in to replace it — creating an onshore breeze.
• Convection in the Earth's mantle: Convection currents in the semi-liquid mantle drive plate tectonics.

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Radiation

Key Definition: Thermal radiation is the transfer of energy by electromagnetic waves (primarily infrared), which can travel through a vacuum.

Key Properties

• All objects emit and absorb thermal radiation.
• The rate of emission depends on temperature, surface area, and the nature of the surface.
• Radiation does not require a medium — it can travel through a vacuum (this is how the Sun's energy reaches the Earth).
• Hotter objects emit radiation at higher intensity and at shorter wavelengths (Wien's displacement law).

Stefan-Boltzmann Law

The total power radiated by an object is given by:

P = σAT⁴

where:

• P = power radiated (W)
• σ = Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
• A = surface area of the object (m²)
• T = absolute temperature of the surface (K)

For a non-ideal (grey body) emitter:

P = εσAT⁴

where ε is the emissivity (0 ≤ ε ≤ 1). A perfect black body has ε = 1.

Wien's Displacement Law