The Four-Hour Cooler Challenge
Eighth-grade teams must design a container that keeps a 200 mL milk carton at or below 10 °C for 4 hours. The milk starts at 4 °C, and the outdoor test area is 28 °C. Each container must hold at most 2 L, cost no more than $5.00, and be easy for one student to carry. Team A builds a cardboard box lined with aluminum foil. It costs $1.50 but leaks when ice melts, and the milk reaches 16 °C at 4 hours. Team B builds a foam box lined with reflective bubble wrap. It costs $4.80, holds 1.5 L, has a tight lid, and the milk reaches 9 °C at 4 hours. Team C builds a double plastic container with wool between the walls. It costs $3.20, but the lid fits loosely, and the milk reaches 11 °C at 4 hours. The class must choose the best prototype and recommend one improvement before the final test.
1. Which prototype best meets the criteria and constraints? Justify your choice by comparing each prototype with the temperature limit, cost limit, size limit, and usability.
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Team B is the best prototype. It keeps the milk at 9 °C, below the 10 °C limit, while Team A reaches 16 °C and Team C reaches 11 °C; both fail the temperature criterion. Team B costs $4.80, which is within the $5.00 limit, and its 1.5 L size is under the 2 L limit. It has a tight lid and is described as carryable, so it meets the usability constraint. Team A is cheapest but fails on temperature and leaks, which is a serious usability failure. Team C is under budget and fits the size limit, but the loose lid allows warm air to enter and lets cold air escape, and it still misses the temperature target. Team B is the only prototype that satisfies every stated criterion, even though it has the highest cost.
2. Team C claims that adding more wool would make its container the best. Evaluate this claim and propose a more effective change, using heat-transfer reasoning.
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Adding wool may help because wool traps air and reduces conduction, but Team C’s main problem is the loose lid. A loose lid allows convection: warm outside air can enter and cold air can escape, and water vapor can carry energy away. More wool will not fix that pathway. A more effective change is to seal the lid with foam tape or a gasket and add a layer of reflective bubble wrap inside the lid. The class should also test whether the wool stays dry; wet insulation conducts heat better than dry insulation. After fixing the lid, Team C could compare temperature change every 30 minutes with Team B. The claim that more wool alone makes it best is not supported because the prototype already fails the temperature limit and the lid is an uncontrolled heat pathway.
3. Describe a fair test the class should use to compare the improved prototypes, including at least two variables to control and one measurement to record over time.
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The class should test all containers at the same time in the same outdoor location, out of direct sunlight but exposed to the same 28 °C air. Each container should start with a 200 mL milk carton at 4 °C, measured with the same thermometer. The amount of ice or coolant, if used, should be the same mass in each design. Variables to control include starting milk temperature, amount of milk, amount of coolant, container placement, and test duration. Students should record milk temperature every 30 minutes for 4 hours, plus the final temperature and whether the container leaks. They should run at least three trials per prototype and average the results. A fair comparison uses the same measurement schedule and the same environmental conditions; otherwise a container placed in shade could appear better because of location rather than design.