Testing a Claim About a New Insulating Material
A company claims its new foam board has twice the insulating power of expanded polystyrene. A student decides to test this with two identical plastic cups, each containing 200 g of water at 70 °C. One cup is wrapped in a 1.0 cm layer of the new foam, the other in a 1.0 cm layer of polystyrene. Both cups are placed side by side on the same bench in a room at 22 °C. The student records the water temperature every 2 minutes for 20 minutes using the same thermometer, moving it from cup to cup. Results show the foam-wrapped cup cooling from 70 °C to 48 °C and the polystyrene cup cooling from 70 °C to 44 °C. The student concludes the claim is supported.
1. Critique the student's experimental design and identify at least three weaknesses that could affect the conclusion.
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Several weaknesses matter:
Using one thermometer for both cups. Moving the thermometer between cups takes time and may carry heat or cold, and each reading is delayed. Two thermometers, or a data logger with two probes, would be better. If two thermometers are used, they must be calibrated against each other.
No lids mentioned. Evaporation from the open water surface causes cooling that may differ between cups if the lids or covers differ. Evaporation is a major heat loss and must be controlled.
Position on the bench. The cups are side by side, so one may be closer to a draught, a radiator, or a sunny window. They should be swapped or placed symmetrically, and draughts screened.
Single trial. One run each gives no indication of repeatability. The experiment should be repeated, ideally with the materials swapped between cups to cancel any position effect.
Thickness and coverage. The claim is about the material, but the student has not checked that both layers are exactly 1.0 cm thick and cover the cups equally, including the base.
Any of these could produce a difference of a few degrees, which is the size of the effect being claimed.
2. The student's data show a 22 °C drop for foam and a 26 °C drop for polystyrene. Assess whether this supports the claim of 'twice the insulating power' and suggest how the data should be presented to make a fairer comparison.
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The claim is that the foam has twice the insulating power. A simple comparison of temperature drops gives 26/22 ≈ 1.18, so the polystyrene lost about 18% more temperature than the foam, not twice as much. On this evidence the claim is not supported.
However, comparing raw temperature drops is not the best measure. Heat loss depends on the temperature difference between the water and the room, which changes during the experiment. A fairer approach is to plot temperature against time for both cups and compare the initial rates of cooling at the same temperature difference, for example the gradient of each curve at 70 °C. The ratio of the gradients is a better measure of relative insulating power.
A further refinement is to calculate the heat lost: Q = mcΔθ, with m = 0.200 kg and c = 4200 J/(kg °C). The foam cup lost about 0.200 × 4200 × 22 ≈ 18 500 J and the polystyrene cup about 21 800 J. Dividing by the time and by the average temperature difference gives a heat-transfer rate per degree, which is the quantity the insulation controls.
Even after this analysis, the difference is small and could be within experimental error. The student should repeat the experiment and report whether the difference is consistent, rather than concluding from a single pair of runs.