Cooling cup investigation
A Form 5 student investigates which cup material keeps tea warm. She pours 200 cm³ of water at 80 °C into three identical-shaped cups: metal, plastic and foam. She records the time for the water to cool to 40 °C. Trial 1: metal 9 min, plastic 14 min, foam 26 min. Trial 2: metal 9 min, plastic 13 min, foam 24 min. In Trial 2 the foam cup was placed near an open window and the thermometer touched the bottom. The student concludes that metal is the best material for a thermos flask because it cooled fastest. The teacher says the investigation has a design flaw and that the conclusion does not follow.
1. Identify two controlled variables the student should keep constant and explain why each matters.
Read the worked answer
Two important controlled variables are the starting temperature and volume of water, and the shape and size of the cups.
- Starting temperature and volume: if one cup starts at 80 °C and another at 85 °C, or if volumes differ, the amount of thermal energy stored is different. The cooling time would then reflect the starting conditions, not the cup material.
- Cup shape and size: a wider cup exposes more surface area to the air, increasing cooling by convection and evaporation. Identical shapes make the material comparison fair.
Other valid controls include room temperature, draughts, lid use, and thermometer position. The open window in Trial 2 is a problem because moving air increases cooling, so the foam result is not a fair test of insulation alone.
2. Calculate the mean time to cool for each material and the mean cooling rate from 80 °C to 40 °C for foam and metal. Comment on the reliability of the foam result.
Read the worked answer
Mean time:
- Metal: (9 + 9) ÷ 2 = 9.0 min.
- Plastic: (14 + 13) ÷ 2 = 13.5 min.
- Foam: (26 + 24) ÷ 2 = 25.0 min.
The water cools by 80 − 40 = 40 °C.
- Metal rate = 40 ÷ 9.0 = 4.44 °C/min.
- Foam rate = 40 ÷ 25.0 = 1.60 °C/min.
Metal cools about 2.8 times faster than foam. The foam result is less reliable because Trial 2 was affected by the open window and the thermometer touching the bottom. The two foam trials differ by 2 min, which is a large range compared with metal. A repeat under controlled conditions is needed before trusting the foam mean.
3. Explain why the conclusion 'metal is best for a thermos' is invalid, and recommend a better design/test.
Read the worked answer
The conclusion confuses fastest cooling with best insulation. A thermos flask should slow heat loss, so the best material is the one that takes longest to cool, not the shortest. Metal is a good conductor, so it transfers heat quickly to the surroundings and cools fastest. Foam is a poor conductor and traps air, so it slows heat transfer. On the data, foam is the better insulator, not metal.
A better test would: use identical cups with lids, place all cups in the same still-air position away from windows, keep the thermometer in the water without touching the bottom, and record temperature every minute for at least three trials. The student should compare cooling curves and calculate an average rate for each material.