Choosing a Wall Material for a Soup Container
A Year 7 class is designing a reusable "keep-warm" lunch container for a school competition. Each team may choose one wall material from the technician's data sheet. The container must keep 200 mL of soup above 50 °C for two hours, weigh less than 400 g empty, survive a dishwasher cycle at 70 °C, cost under $6 per unit for a class set, and be accepted in kerbside recycling. The data sheet lists: aluminium (thermal conductivity 205 W/m·K, density 2.7 g/cm³, melts 660 °C, $4.20, recyclable); stainless steel (16 W/m·K, 7.9 g/cm³, 1400 °C, $5.80, recyclable); polypropylene (0.22 W/m·K, 0.9 g/cm³, softens near 100 °C, $1.10, recyclable); expanded polystyrene foam (0.035 W/m·K, 0.03 g/cm³, softens near 90 °C, $0.80, not accepted in kerbside recycling); and borosilicate glass (1.0 W/m·K, 2.5 g/cm³, 1400 °C, $3.50, recyclable). One team argues for the foam because it has by far the lowest conductivity.
1. Evaluate each material against the five constraints and recommend a solution.
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No single-listed material satisfies all five constraints.
- Aluminium: cheap, light, recyclable, but conductivity of 205 W/m·K means heat leaves the soup very quickly through the wall - the 50 °C target after two hours will fail.
- Stainless steel: still 16 W/m·K in a single wall, dense (7.9 g/cm³) so it pushes the 400 g limit, and at $5.80 it sits right at the budget edge.
- Polypropylene: 0.22 W/m·K, 0.9 g/cm³, $1.10, recyclable and survives 70 °C comfortably. It meets the cost, weight, dishwasher and recycling constraints but is only a moderate insulator.
- Foam: best insulator by far, but fails the recycling constraint and softens near 90 °C, which is marginal in a dishwasher and risky with hot soup.
- Glass: recyclable and cheap, but dense and vulnerable to thermal shock when boiling soup hits a cold wall.
The defensible recommendation is polypropylene as the structural wall plus an air gap (a double wall), because still air is one of the best insulators available and costs almost nothing in materials. That fixes polypropylene's one weakness without breaking any constraint.
2. Explain, using conduction, convection and radiation, why the air gap improves performance.
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Heat moves from the hot soup to the cooler room in three ways at once.
Conduction carries heat through the container wall. The rate depends on the material's conductivity and the wall's thickness, so a low-conductivity polymer slows it, and adding a gas gap means the heat must cross a poor conductor (air, about 0.026 W/m·K) as well as the wall.
Convection in the air gap is the risk: if the gap is wide and open, air circulates, carrying heat from the inner wall to the outer wall and defeating the purpose. The gap must therefore be narrow or divided into small cells so the air is trapped and cannot circulate.
Radiation still crosses a gap - infrared travels through air - so a shiny, low-emissivity surface facing the gap reflects radiation back towards the soup.
A lid matters too: without one, hot water vapour escapes and carries latent heat away, which no wall material can prevent.
3. A team uses foam anyway and their container cracks and is rejected by the recycling collection. Explain the failures using the data sheet and suggest how foam could still be used legitimately.
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Two separate failures are predictable from the data. First, the service temperature: foam softens near 90 °C, and although the dishwasher runs at 70 °C, the soup is poured close to boiling and the wall is thin, so the inner face can exceed the softening point, deform and crack. Second, the foam is explicitly not accepted in kerbside recycling, so the container fails the recycling constraint no matter how well it insulates.
A legitimate use is to move the foam out of the food-contact wall: use a polypropylene inner cup (food-safe, dishwasher-safe, recyclable) with a removable foam sleeve that only touches the outside. The sleeve never contacts hot liquid, so softening is not an issue, and it can be separated from the cup at disposal so the recyclable part enters kerbside collection while the sleeve goes to a specialist stream. This keeps the insulation benefit while satisfying the constraint that actually caused the rejection.