Explain convection in liquids and gases in terms of density changes and describe experiments to illustrate convection

2.3.2 Convection

Learning objective

Explain convection in liquids and gases in terms of density changes and describe at least one experiment that clearly demonstrates convection.

Core explanation (exam‑style)

• When a fluid (liquid or gas) is heated it expands, its density falls and it becomes lighter than the surrounding fluid.
• The lighter (lower‑density) parcel is pushed upward by the surrounding heavier fluid; the cooler, denser fluid moves down to replace it.
• This upward‑and‑downward motion – a continuous loop called a convection cell – transfers heat through the bulk movement of the fluid.

1. Why density changes cause motion

1.1 Liquids (practically incompressible)

• Density change is almost entirely due to thermal expansion.
• For a small temperature change

  \$\rho \approx \rho{0}\bigl[1-\beta\,(T-T{0})\bigr]\$

  where β is the coefficient of volumetric expansion (≈ 2.1 × 10⁻⁴ K⁻¹ for water).

• Heating → T↑ → ρ↓ → fluid rises.
  

  Cooling → T↓ → ρ↑ → fluid sinks.

1.2 Gases (compressible)

• Density depends on both temperature and pressure. At (approximately) constant atmospheric pressure the ideal‑gas relation gives a useful qualitative picture:

  \$\rho \approx \frac{pM}{RT}\$

  (p = pressure, M = molar mass, R = gas constant, T = absolute temperature).

• Increasing T (while p stays roughly constant) reduces ρ, so the warm parcel rises; a cooler parcel (higher ρ) sinks.

2. Convection cells

A convection cell is a closed loop of fluid motion driven by the density differences described above.

3. Everyday examples

• Radiator heating a room – warm air rises, cool air descends, creating a circulating draft.
• Ocean surface currents – water heated at the equator rises, moves poleward, cools, sinks, and returns as deep‑water flow.
• Atmospheric circulation – differential heating of the Earth’s surface drives the Hadley, Ferrel and Polar cells.
• Mantle convection – very slow but massive currents that drive plate tectonics.
• Convection ovens – hot air circulates, cooking food more evenly than still air.

4. Experiments that clearly demonstrate convection

Experiment 1 – Heated water in a clear beaker

1. Fill a transparent beaker with room‑temperature water.
2. Drop a few drops of food‑colouring near the side (not the centre).
3. Place a small electric heater (e.g., a coil) at the bottom and switch it on.
4. Observation: The coloured water is drawn downwards toward the heater, then rises in a visible plume.
5. What it shows: Warm water (lower density) rises; cooler water (higher density) descends, forming a convection current.

Experiment 2 – Candle flame and a light piece of paper

1. Light a candle on a stable, draft‑free surface.
2. Hold a thin piece of paper a few centimetres above the flame.
3. Observation: The paper is pulled upward toward the flame.
4. What it shows: The flame heats the surrounding air, lowering its density; the warm air rises and draws the paper upward.

Experiment 3 – Colour‑water convection tank (hot–cold ends)

1. Set up a rectangular transparent tank (≈ 20 cm × 10 cm × 10 cm) filled with water.
2. Attach a heating element to one end of the bottom and an ice pack (or cold plate) to the opposite end.
3. Inject a thin vertical line of coloured dye in the centre using a syringe.
4. Observation: The dye bends into a circulating roll that moves from the hot side (rising) to the cold side (sinking).
5. What it shows: A temperature gradient creates a density gradient, producing a steady convection roll.

Key observations table

5. Optional deeper discussion (supplementary)

• Buoyancy force (optional formula):

  \$F{\text{buoy}} = (\rho{\text{ambient}}-\rho_{\text{parcel}})\,g\,\Delta V\$

  Useful for A‑Level work; not required for IGCSE.

• In liquids the coefficient of volumetric expansion β varies with temperature; for water β≈2.1 × 10⁻⁴ K⁻¹ near 20 °C.
• In gases the ideal‑gas relation can be rearranged to show that at constant pressure, ρ∝1/T, giving a clear inverse relationship between temperature and density.
• Rayleigh‑Bénard convection (pattern of hexagonal cells) is an advanced example where a fluid layer heated from below forms regular convection cells.

6. Summary checklist (exam‑style)

• Convection occurs only in fluids (liquids or gases).
• Heating → expansion → density ↓ → fluid rises.
• Cooling → contraction → density ↑ → fluid sinks.
• Resulting density difference creates a buoyancy force that drives a closed circulation (convection cell).
• Liquids: density change ≈ thermal expansion (incompressible).
• Gases: density change described qualitatively by ρ ≈ pM/(RT) (compressible).
• Typical classroom demonstrations: coloured‑water in a heated beaker, candle‑flame air currents, heated‑cooled convection tank.
• Real‑world applications: radiators, ocean & atmospheric currents, mantle convection, convection ovens.