The Warm Beaker Mystery
A teacher sets out three identical beakers for a lab on thermal energy. Beaker A holds 200 mL of water at 60 °C. Beaker B holds 400 mL of water at 40 °C. Beaker C holds 200 mL of water at 40 °C. All three sit on the same lab bench at 22 °C for 30 minutes. A student predicts that Beaker A will end up coolest because it starts hottest, and that Beakers B and C will finish at the same temperature since they start at the same temperature. The teacher wants students to reason from heat-transfer ideas rather than intuition, and to notice which quantities (temperature vs. thermal energy) the prediction conflates.
1. Evaluate the student's two predictions using the concepts of thermal energy and rate of heat transfer. Which parts are right, wrong, or incomplete?
Read the worked answer
Prediction 1 (A ends coolest) - wrong. All three beakers lose heat to the room, so all temperatures fall toward 22 °C. Starting hottest does not make a sample end coldest; it usually means it has the largest temperature gap to the room and therefore loses heat fastest at first. After 30 minutes A may still be warmest, not coolest.
Prediction 2 (B and C finish equal) - plausible but not guaranteed. They start at the same temperature and cool toward the same room temperature, so their final temperatures should be close. But B has twice the water, so it has roughly twice the thermal energy to shed for a given temperature drop. With equal exposed surface geometry, B cools more slowly per degree and may finish slightly warmer.
Key distinction: temperature is not thermal energy. B has more thermal energy than C at the same temperature because it has more mass. The student conflated 'hot' with 'holds the most heat.'
2. The teacher wants students to test whether surface area affects cooling rate. Describe a controlled modification and identify the variable that must be held constant.
Read the worked answer
Modification: Put the same volume of water at the same starting temperature into two containers with different exposed surface areas - for example, a tall narrow beaker and a wide shallow dish - and record temperature over time.
Held constant: water volume (mass), starting temperature, room temperature, and time of measurement. Only surface area should differ.
Reasoning: Newton's law of cooling says the rate of heat loss depends on the temperature difference and on how much surface is available for transfer. If surface area increases while everything else is fixed, the water should cool faster. Students compare the slopes of the temperature–time graphs, not just the final readings, because a single endpoint can hide a faster early cooling rate.