Thermal and electrical properties

Why it matters

Mechanical properties decide whether a part breaks; thermal and electrical properties decide whether it works at all. A heat sink must move heat; a building's insulation must stop it. Wires must conduct, and the insulation around them must not. Parts that heat up must expand without cracking or jamming. This lesson compares how the four classes of materials conduct heat and electricity and how much they expand, and links each behaviour back to bonding and structure.

Thermal conductivity

Heat flows through a solid by two routes: free electrons (in metals) and lattice vibrations, called phonons (in everything). Fourier's law gives the heat flow rate through a slab:

q = k · A · ΔT / L        (watts)

where k is the thermal conductivity in W/(m·K), A the area, ΔT the temperature difference across it and L its thickness.

Typical room-temperature values (approximate):

Metals conduct best because free electrons carry heat. Alloying scatters electrons, which is why stainless steel conducts about a quarter as well as plain carbon steel. Polymers and glasses have disordered structures that scatter phonons, so they conduct poorly. Foams and fibre insulation work by trapping still air.

Worked example. A 1 m² single pane of glass, 4 mm thick, has 20 °C on the inside surface and 0 °C on the outside surface. q = 1 × 1 × 20 / 0.004 = 5,000 W. In reality the air films on each side add much more resistance than the glass itself, so actual losses are far lower, but the calculation shows why thin glass alone is a poor insulator and why double glazing traps a layer of gas.

Thermal expansion

Most materials expand when heated:

ΔL = α · L · ΔT

with α the coefficient of linear thermal expansion (per K, often quoted in 10⁻⁶/K). Approximate values: aluminium 23, copper 17, steel 12, soda-lime glass 9, borosilicate glass 3.3, alumina about 8, polyethylene 100–200, Invar (an iron-nickel alloy) about 1.5.

Worked example. A 2.0 m aluminium rail warms by 40 K: ΔL = 23 × 10⁻⁶ × 2.0 × 40 = 1.84 mm. A steel rail of the same length would grow only 0.96 mm. When two materials with different α are joined (a metal frame around glass, a polymer part screwed to steel), the mismatch causes stress as the temperature changes. Borosilicate glass resists cracking when heated quickly partly because its expansion is so low.

Weak bonds mean large α: polymers expand roughly ten times as much as metals. Strong bonds in ceramics mean small α, but ceramics are also brittle, so thermal shock (a sudden temperature change across the part) can still crack them.

Electrical conductivity

Electrical resistivity ρe (Ω·m) and conductivity σe = 1/ρe span more than twenty orders of magnitude, more than almost any other physical property:

Band theory explains the spread. In metals, the highest occupied electron energy band is only partly filled, so electrons move freely: conductors. In insulators the filled valence band is separated from the empty conduction band by a wide gap (several eV), so almost no electrons can cross. Semiconductors have a small gap (about 1.1 eV for silicon), so some electrons are thermally excited across it, and adding tiny amounts of dopant (phosphorus or boron in silicon) controls the conductivity precisely.

Temperature affects them in opposite ways: a metal's resistance rises with temperature (vibrating atoms scatter electrons), while a semiconductor's resistance falls (more electrons are excited across the gap).

Copper is the standard conductor for wiring. Aluminium conducts about 60 % as well by volume but is much lighter, so overhead power lines use aluminium conductors, often with a steel core for strength.

Linking the two

In metals the same free electrons carry heat and charge, so good electrical conductors are usually good thermal conductors (the Wiedemann-Franz relationship). Diamond is a notable exception: an electrical insulator that conducts heat superbly through its very stiff lattice.

Common mistakes

• Confusing conductivity with resistivity, which are reciprocals.
• Ignoring units. k in W/(m·K) and thickness in metres, not millimetres.
• Assuming a strong material conducts well. Stainless steel is strong but a modest conductor of heat and electricity.

Recap

• Metals conduct heat and electricity through free electrons; polymers and glasses insulate.
• ΔL = α·L·ΔT; polymers expand most, ceramics least.
• Band gaps separate conductors, semiconductors and insulators.
• Metal resistance rises with temperature; semiconductor resistance falls.