Physics · Lesson 14

Heat transfer, kinetic theory & vapours

JAMBWAECNECO

What the syllabus asks

JAMB: heat transfer, kinetic theory, vapours, humidity

WAEC: heat transfer: conduction, convection, radiation; thermal conductivity and its applications; land and sea breezes; good and bad absorbers/emitters, Leslie cube; vacuum flask; greenhouse effect; kinetic theory of matter and of gases (assumptions, explanation of pressure, temperature, evaporation); vapours: evaporation and boiling, saturated and unsaturated vapour, saturated vapour pressure,…

NECO: heat transfer: conduction, convection, radiation; thermal conductivity and its applications; land and sea breezes; good and bad absorbers/emitters, Leslie cube; vacuum flask; greenhouse effect; kinetic theory of matter and of gases (assumptions, explanation of pressure, temperature, evaporation); vapours: evaporation and boiling, saturated and unsaturated vapour, saturated vapour pressure,…

What you will learn

Describe conduction, convection and radiation and explain each in terms of particles or waves.
Use Q/t = kAΔθ/L for conduction through a slab.
Explain everyday applications: cooking pots, land and sea breezes, vacuum flask, greenhouse, roofs.
State the assumptions of the kinetic theory and use it to explain pressure, temperature and evaporation.
Distinguish evaporation from boiling and saturated from unsaturated vapours.
Explain the effect of pressure on boiling point.
Define dew point and relative humidity and calculate relative humidity.

Key points

Conduction: energy passed between particles; metals best (free electrons); Q/t = kAΔθ/L.
Convection: heated fluid expands, becomes less dense and rises; land and sea breezes; ventilation.
Radiation: infrared waves, no medium needed; dull black best absorber and emitter, shiny best reflector.
Vacuum flask: vacuum stops conduction and convection; silvering reduces radiation; stopper stops convection.
Greenhouse effect: short-wave radiation in, long-wave radiation trapped.
Kinetic theory: particles in random motion; average KE ∝ absolute temperature.
Gas pressure: molecular collisions with walls; p = ⅓ρc̄²; explains Boyle’s, Charles’s and pressure laws.
Evaporation (any temperature, surface, cools) vs boiling (SVP = external pressure, throughout).
SVP depends only on temperature; saturated vapours do not obey Boyle’s law; pressure raises boiling point.
Dew point and relative humidity: RH = SVP(dew point)/SVP(air) × 100%; wet-and-dry-bulb hygrometer.

Start here: Conduction

Put a metal spoon in a pot of boiling egusi soup: soon the handle is too hot to hold. Heat has travelled along the spoon although the spoon itself has not moved. This is conduction.

Conduction is the transfer of heat through a material from a region of higher temperature to one of lower temperature, by the vibration of particles passing energy to their neighbours, without the material as a whole moving.

How it happens: at the hot end, particles vibrate more vigorously and bump into neighbours, passing on energy. In metals there is an additional, much faster mechanism: free electrons move rapidly through the metal and carry energy from hot to cold regions. That is why metals are good conductors, and why good electrical conductors are usually good thermal conductors too.

Good conductors	Bad conductors (insulators)
Silver, copper, aluminium, iron, brass	Wood, plastic, cork, glass, wool, rubber, still air, water

Experiment: comparing conductors

Rods of equal length and thickness of copper, aluminium, iron and glass are coated with wax and one end of each is put in boiling water (Ingenhousz’s experiment). The wax melts furthest along the best conductor (copper).

Rate of conduction

For a slab of area A and thickness L with temperature difference Δθ across it: Q/t = kAΔθ/L, where k is the thermal conductivity (W m⁻¹ K⁻¹).

Worked example 14.1

A copper rod (k = 400 W m⁻¹ K⁻¹) of cross-section 0.01 m² and length 0.5 m has its ends at 100 °C and 50 °C. Find the rate of heat flow.

Q/t = 400 × 0.01 × 50/0.5 = 400 W.

400 J/s (400 W)

Applications: cooking pots are made of aluminium or steel (good conductors) with wooden or plastic handles (insulators); a woollen blanket traps still air (a poor conductor); a stone floor feels colder than a rug at the same temperature because it conducts heat away from your feet faster.

⚠️ Common mistake: saying the stone floor is "colder" than the rug. They are at the same temperature; the floor feels colder because it conducts heat away faster.

Try it yourself. Why do metal pots have wooden handles?

Show solution

Wood is a poor conductor, so little heat reaches the hand.

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Practice questions

1. Name the method of heat transfer in each: (a) handle of a pot gets hot, (b) sea breeze, (c) warmth from a fire across a room.

Show worked answer

(a) conduction, (b) convection, (c) radiation.

2. An aluminium plate (k = 200) 0.02 m thick, area 0.05 m², has a 40 K difference across it. Find the rate of heat flow.

Show worked answer

200 × 0.05 × 40/0.02 = 20,000 W.

3. Explain why roofs in hot regions are often painted white.

Show worked answer

White surfaces reflect most radiation and absorb little.

4. State two assumptions of the kinetic theory of gases.

Show worked answer

Any two: random motion; negligible molecular volume; no intermolecular forces except in collisions; elastic collisions; negligible collision time.

5. Give three differences between evaporation and boiling.

Show worked answer

Any temperature vs fixed; surface vs throughout; cooling vs constant temperature.

Key words

Conduction: Transfer of heat through a material without the material moving.
Convection: Transfer of heat by the bulk movement of a fluid.
Radiation: Transfer of heat by electromagnetic (infrared) waves.
Thermal conductivity: A measure of how well a material conducts heat.
Insulator: A poor conductor of heat, e.g. wood, plastic, air.
Convection current: The circulating flow of a fluid heated from below.
Land breeze: A night wind blowing from land to sea.
Sea breeze: A day wind blowing from sea to land.
Kinetic theory: The model that matter consists of particles in constant random motion.
Vapour: A gas below its critical temperature, which can be liquefied by pressure alone.
Saturated vapour: A vapour in dynamic equilibrium with its own liquid.
Saturated vapour pressure (SVP): The pressure exerted by a saturated vapour; depends only on temperature.

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