Which Cup Keeps the Cocoa Warm?
A Grade 6 team is choosing cups for a winter field trip and decides to test four options. Each cup is filled with 250 mL of water from the same kettle, and temperature is recorded at 0, 10, 20, and 30 minutes. The room is 21 °C, except that the knit-sleeve trial is run on a different afternoon when the room is 24 °C. Results:
- Bare ceramic mug: 82 °C to 58 °C
- Ceramic mug with knit sleeve: 82 °C to 66 °C
- Double-walled steel travel mug with lid: 85 °C to 71 °C
- Foam cup with lid, lid slightly loose: 82 °C to 69 °C
The team's poster reads, "The steel travel mug is the best insulator because it ended at the highest temperature." Their teacher asks them to check whether the data actually support that sentence before the poster goes to the science fair next week.
1. Evaluate the poster's claim using the data. Show the reasoning you would put on the poster.
Read the worked answer
Final temperature alone cannot settle the claim, because the cups did not all start at the same temperature. Compare temperature drops:
- Bare mug: 82 - 58 = 24 °C lost
- Knit sleeve: 82 - 66 = 16 °C lost
- Steel travel mug: 85 - 71 = 14 °C lost
- Foam cup: 82 - 69 = 13 °C lost
The steel mug started 3 °C hotter, so part of its higher final temperature comes from its starting point, not from better insulation. By temperature drop, the foam cup actually lost the least heat. The sleeve trial is also unfair in the other direction: it ran in a warmer room (24 °C vs 21 °C), and a warmer room slows heat loss, so a 16 °C drop there would likely be larger at 21 °C. The defensible statement is: "Under these conditions the foam cup and the steel mug lost the least heat; the bare mug lost the most." The original sentence overstates what the evidence shows.
2. Redesign the investigation so the comparison is fair. Name at least three specific changes and explain what each one controls.
Read the worked answer
- Equal starting temperature: fill all cups first, then wait and stir until every cup reads the same value (for example 82 °C) before starting the clock. This removes starting temperature as an explanation for different final readings; comparing drops is a backup if exact matching fails.
- Same room and same day: run all four trials side by side in one room. This controls the room temperature difference that affected the sleeve trial.
- Same lid condition: either give all cups identical lids or test lids as a separate variable. A loose lid on the foam cup lets warm, moist air escape and biases the result against foam.
- Same volume, same thermometer, same reading times, and at least three repeats per cup to reduce random error from a single reading. The redesign keeps only the cup design different, so any remaining difference in cooling can reasonably be attributed to the cup itself.
3. Use energy-transfer ideas to explain why the knit sleeve slows cooling even though the sleeve does not add any heat.
Read the worked answer
Heat moves from the warmer cocoa to the cooler surroundings whenever there is a temperature difference, and the bigger the difference, the faster the transfer. The sleeve does not warm the drink; it slows the escape of energy. Knit fabric traps small pockets of air, and still air is a poor conductor, so conduction through the cup wall is reduced. Trapping air next to the cup also limits convection, the circulation that keeps replacing warmed air with cooler air. Because less energy leaves each minute, the cocoa stays hot longer, though it still cools steadily and will eventually reach room temperature. This also explains the pattern in the data: the bare mug, with nothing slowing transfer, lost 24 °C, while cups that slowed transfer lost 13 to 16 °C.