Describe, in terms of particles, why thermal conduction is bad in gases and most liquids

2.3.1 Conduction

Learning Objective

Describe, in terms of particles, why thermal conduction is good in solids but poor in liquids and gases, and explain the special roles of lattice vibrations (phonons) and free electrons in metals.

Key Points to Remember

• Conduction = transfer of kinetic energy from hotter particles to neighbouring cooler particles.
• The rate of conduction depends on:
  • Particle spacing – the average distance between neighbouring particles.
  • Inter‑molecular (or inter‑atomic) forces – how strongly particles are held together.
  • Mobile charge carriers – free electrons in metals that can carry energy rapidly.
• In short: the closer the particles and the stronger the connection between them, the faster the energy can be passed on.

Particle‑Level Explanation

Solids – good conductors (lattice vibrations + free electrons)

• Particles form a regular, closely‑packed lattice; separations are only a few Å.
• Strong metallic, covalent or ionic bonds keep particles in fixed positions, so collisions are continuous.
• Energy propagates as lattice vibrations (phonons). In metals a sea of free electrons moves through the lattice, transporting kinetic energy many times faster than phonons alone.

Liquids – generally poor conductors

• Particles remain close (similar spacing to solids) but are not locked into a fixed lattice; they can slide past one another.
• Inter‑molecular forces are moderate (e.g., hydrogen bonding in water). Collisions occur, but each collision transfers only part of the kinetic energy before the molecules separate again.
• Consequently the overall rate of energy transfer is much lower than in a solid, though still higher than in a gas because the particles are nearer together.

Gases – very poor conductors

• Average separation of molecules is many times their own diameter; most of the volume is empty space.
• Inter‑molecular forces are negligible, so molecules travel in straight‑line paths until they collide.
• Collisions are infrequent and each transfers only a small fraction of kinetic energy, giving a slow “random‑walk” of heat.

Why Conduction Is Poor in Gases and Most Liquids

1. Large average separation of particles (especially gases) – fewer collisions per unit time → slower energy transfer.
2. Weak or moderate intermolecular forces – less efficient transfer of kinetic energy during each encounter.
3. Random, high‑speed motion – energy spreads by a random walk rather than a coordinated vibration chain.
4. Note: Liquids conduct better than gases because their particles are much closer, even though the transfer is still far less efficient than in a solid.

Mathematical Formulation (Reference)

Fourier’s law for one‑dimensional steady‑state conduction:

$$ Q = -k\,A\,\frac{dT}{dx} $$

• $Q$ – heat transferred per unit time (W)
• $k$ – thermal conductivity (W m⁻¹ K⁻¹)
• $A$ – cross‑sectional area (m²)
• $\frac{dT}{dx}$ – temperature gradient (K m⁻¹)

Because $k$ is orders of magnitude smaller for gases and most liquids than for solids, the same temperature gradient produces far less heat flow.

Typical Thermal Conductivity Values

Practical Activity – Demonstrating Good vs. Bad Conductors

1. Materials: two rods of equal length & cross‑section (copper and wooden or plastic), a small candle or hot‑water bath, two identical thermometers or infrared sensors, a hollow tube, a pump (to evacuate air) or a can of a known gas.
2. Procedure:
   1. Place the heat source at one end of each rod.
   2. Secure a thermometer at the opposite end of each rod.
   3. Start a timer and record the temperature every 30 s for 5 min.
   4. Plot the temperature‑rise curves to compare the rate of heat transfer.
   5. Optional extension: fill the hollow tube with air, repeat the experiment, then evacuate the tube (or fill it with a gas of known $k$) and repeat. The evacuated tube shows an even slower rise, illustrating the very low conductivity of gases.
3. Safety Checklist:
   • Handle the candle or hot water with heat‑proof gloves.
   • Do not touch the hot ends of the rods directly.
   • Secure thermometers to avoid breakage.
   • If using a vacuum pump, ensure the tube is rated for reduced pressure and wear eye protection.
4. Link to AO2: Students should present the temperature‑rise graphs, label the axes, and comment on why the metal rod conducts heat faster than the wooden/plastic rod and why the evacuated tube conducts the slowest.

Everyday Applications

• Thermos flasks – a vacuum removes gas, virtually eliminating conduction.
• Insulating foams – trap tiny pockets of air; the gas’s low $k$ reduces heat loss.
• Heat sinks – made of metals to exploit high $k$ and rapid electron‑mediated conduction.
• Coolants – water conducts better than air but far worse than metals, making it suitable for moderate‑speed heat removal.