Which Cup Holds More Thermal Energy? The Four-Cup Ice Mystery

Investigation question: Four covered cups of water look identical from the outside. Which one can melt the most ice, which one holds the most thermal energy, and are those the same question?

Scientific purpose

Students receive four lidded foam cups that hide different amounts of water at different temperatures. Using only a scale and a thermometer they gather evidence, predict which cup will melt the most ice, and then test all four with equal masses of ice for the same time. The measured grams of ice melted reveal that the hottest cup does not win, that the amount of water matters as much as its temperature, and that an ice-cold cup with plenty of thermal energy melts almost nothing because there is no temperature difference to drive heat.

Why this helps students with this chapter

Students say 'thermal energy depends on mass and temperature' long before they believe it; when they must bet on a cup, almost everyone bets on the hottest one. Gathering the evidence themselves, committing to a ranking, and then weighing the meltwater makes the result their own. The ice-cold cup is the twist that separates thermal energy from heat: it has five times the water of the hottest cup, yet it can give the ice almost nothing because the two are at nearly the same temperature.

Standards connections

MS-PS3-4 (supports, the relationship among energy transferred, mass and temperature, used as background): This is a California Grade 6 PE, and the lab resembles its clarification example (ice melted by water samples). Here it supports the Grade 7 work: the investigation is designed for students rather than planned by them, and no one calculates the energy transferred, which the assessment boundary excludes.

MS-PS1-4 (practice, using a particle model to explain temperature, thermal energy and melting when energy is added): Students explain with particles why a larger, cooler cup can melt more ice than a smaller, hotter one, and why melting stops at 0 °C. This practices the particle reasoning of the PE; the full model of temperature and state over time is assessed in Lab 1.

Roles (rotate each session)

• Weigher: Tares the scale, weighs every cup and collection cup, and calls each mass aloud for the recorder.
• Thermometer reader: Reads each cup's temperature through the lid hole after the reading settles, wipes the thermometer between cups, and reads the final liquid temperatures.
• Recorder: Fills the evidence and results tables, subtracts to find each mass, and posts the group's results on the class chart.
• Timekeeper and skeptic: Runs the six-minute timer, checks that all four cups are treated the same way, and asks 'how do we know?' before the group commits to its prediction.

Materials

Estimated cost: About 15 to 25 per class with scales on hand; about 50 to 80 if scales must be bought (an estimate; Estimate: foam cups with lids about $8 per 50, clear cups about $3 per sleeve, two bags of ice about $6, small strainers about $2 each; kitchen scales about $10 to $15 each if the school has none.)

Safety

• Water above about 50 °C can scald. The teacher prepares all warm water, and no cup is warmer than 45 °C. Report a cup that feels hot.
• Spilled water and ice make floors slippery. Keep all pouring over the tray and wipe up at once.
• Keep the scale dry; water can damage it and cause a shock hazard with plug-in models. Use battery scales and set cups on a paper towel on the pan.
• Glass thermometers can break and cut. Do not stir with them; report any break to the teacher.
• Lab water and ice are not for drinking or eating; collection cups and spoons stay in the lab.

Teacher preparation and setup

1. Thirty minutes before class, fill a cooler with ice and water so the ice settles at 0 °C. Ice straight from a freezer is colder than 0 °C and can freeze some water onto itself, which spoils the ice-cold cup.
2. Weigh each empty foam cup with its lid and write the mass on the bottom; do the same for the clear collection cups.
3. Fill each group's cups shortly before class, weighing the water in: W gets 40 g of water at about 45 °C; X gets 200 g of water left out overnight at room temperature (about 22 °C); Y gets 200 g at about 35 °C; Z gets 200 g of ice-cold water strained from the cooler (about 0 to 2 °C), with no ice pieces. Mix warm water from hot and cold tap water and check it with a thermometer; students never receive water above 45 °C. Snap on the lids.
4. Keep a key card of what is in each cup out of sight until the reveal. Students' measured masses should match within a couple of grams; their temperatures will have drifted a little toward room temperature, especially the small cup W.
5. Run the test once yourself if you can, to check that six minutes of stirring brings every cup with leftover ice close to 0 °C with your cups and ice.

Investigation design

Student procedure

1. Read the case card: four cups labeled W, X, Y and Z, lids on. Your job is to predict which cup can melt the most ice, using only the evidence you can gather without looking inside. Do not open any lid until step 5.
2. Gather evidence. The weigher weighs each cup with its lid and subtracts the empty mass written on the bottom to find the mass of water. The thermometer reader slides the thermometer through the lid hole, waits until the reading settles, and calls it out. The recorder fills the evidence table.
3. Predict. As a group, rank the cups from most ice melted to least (q1) and write the rule you used (q2). The skeptic checks that every member can explain the ranking. Show the teacher your prediction before you continue.
4. Prepare the ice. Drain ice from the class cooler in the strainer for about one minute, then weigh four portions of 150 g each into the small bowls. Work quickly so the portions do not sit and melt.
5. Test. Each member takes one cup and one ice portion. On the timekeeper's 'go', everyone removes their lid, tips in the ice and starts stirring gently and steadily with a spoon. Keep stirring for six minutes.
6. At exactly 6:00, everyone pours their cup's liquid into its matching collection cup at the same time, holding the ice back with the spoon. Tip the cup until no more liquid comes out, but do not squeeze or shake the ice.
7. The reader measures the temperature of each collected liquid. The weigher weighs each collection cup and subtracts its empty mass. The recorder finds the ice melted: liquid collected minus starting water.
8. Post your four 'ice melted' values on the class chart, then copy the class results into your table. The teacher reveals what was put in each cup.
9. Empty all ice and water into the sink, dry the cups and spoons, and answer the analysis questions individually.

Expected observations

• Measured masses close to the prepared values (W about 40 g; X, Y and Z about 200 g). Measured temperatures drift a little toward room temperature: W may read 40 to 44 °C by the time it is measured; Z may read 1 to 4 °C.
• Grams of ice melted, roughly: Y most (about 75 to 95 g), X next (about 45 to 65 g), W much less (about 15 to 30 g), Z least (about 0 to 8 g). The ranking Y, X, W, Z should hold in nearly every group even though the exact values vary.
• Final liquid temperatures of about 0 to 3 °C in every cup that still had ice; colder in cups that melted less.
• Cup Z's small positive 'melt' is mostly water that clung to the drained ice, not real melting.

Likely difficulties

• Students forget to subtract the empty-cup mass, so the 'water' column is 5 to 10 g too high. The recorder should check that cups X, Y and Z come out near the same water mass.
• Pouring is slow or uneven, and ice keeps melting in the cups that are poured last. Pour all four at once on the timekeeper's call.
• Ice taken straight from a freezer instead of the 0 °C cooler can make cup Z's result negative, as some water freezes onto the very cold ice. Use the cooler, or treat a negative Z as a discussion point.
• Groups argue that W 'should have won' and suspect an error. Have them compare with the class medians: when the same surprising result repeats across groups, it is evidence, not a mistake.
• The small cup W cools quickly while waiting. Measure its temperature last before the test, or have the teacher fill W cups a few minutes later than the others.

Structured debrief

1. Reveal the cups: W held 40 g at about 45 °C, X 200 g at room temperature, Y 200 g at about 35 °C, Z 200 g of ice-cold water. Put the class medians on the board next to the predictions. Most groups will have ranked W first; ask what they now think the rule should be.
2. Ask where each gram of melted ice got its energy: from the water cooling down. Water can give energy to the ice only while it is warmer than the ice, so what matters is how much water there is and how far it can cool before it reaches 0 °C. W cooled a long way but had little water; Y cooled less far but had five times as much.
3. Spend the most time on Z. It has five times the water of W, its molecules are moving almost as energetically, so it holds more thermal energy than W, yet it melted almost nothing. Heat needs a temperature difference. This is the cleanest evidence in the unit that thermal energy and heat are different ideas.
4. Connect back to the slide 10 camper and the slide 5 bathtub: the big pot of lukewarm water, like cup Y, beats the small mug of nearly boiling water, and a tank at 0 °C, like cup Z, does nothing for the ice.

Recording sheet: what students fill in

Lab 2 recording sheet: The four-cup ice mystery

The cups hide different water. You may weigh them and take their temperature, but you may not look inside until the test. Every gram of ice that melts needs energy, and in this lab all of that energy comes from the water in the cup.

Analysis questions: answer key

Individual evidence of learning

Each student submits the evidence and results tables, their own copy of the class medians and individual answers to q4 through q11. The claim in q4 with its evidence, the particle explanation in q5, and the thermal-energy ranking in q9 are the main evidence that the student can separate temperature, thermal energy and heat.

Assessment criteria

Accessibility adaptations

• Provide a calculator and a subtraction frame (liquid collected − starting water = ice melted) for students who need support with the arithmetic.
• Students with limited fine-motor control can take the recorder or skeptic role; the pouring can be done by a partner while the student calls the timing.
• Use a talking or large-display scale and digital thermometer for students with low vision; the weigher and reader call every value aloud.
• Offer sentence frames for the claim: 'Cup ___ melted the most ice because ___. Cup ___ was the hottest, but ___.'

Low-cost alternative

Without scales, use identical ice cubes instead of weighed ice: add one cube at a time to each cup, stirring until it melts, and count how many cubes each cup melts completely before a cube survives for three minutes. Measure the water with a measuring cup (1 mL of water has a mass of about 1 g). The ranking is the same, though the counts are coarser.

Model limitations

This activity has not been physically tested by the authors; the expected grams melted are estimates from the masses and temperatures used, and real values will be lower because six minutes may not bring every cup all the way to 0 °C and some energy goes into warming the cup and spoon. Drained ice carries a film of water that adds a few grams to every cup's 'melt', and the room air adds a little energy through the foam. The lab measures the energy each cup can give to 0 °C ice, not its total thermal energy: total thermal energy cannot be measured with a thermometer and scale, which is exactly why q9 is answered by reasoning rather than measurement. The 'Which cup holds more thermal energy?' title is a question to investigate, and the answer turns out to differ from the ice-melting ranking.

Teacher notes

The prepared contents are W 40 g at about 45 °C, X 200 g at room temperature, Y 200 g at about 35 °C and Z 200 g at about 1 °C. The ideal-melt estimates in the q4 reasoning use 'grams melted is about grams of water times degrees above 0 °C, divided by 80', which is for teacher checking only; do not teach it as a formula, because the PEs' assessment boundaries exclude calculating energy. If a group's ranking differs from Y, X, W, Z, look first for a missed subtraction or a late pour. Post the class medians; slide 10's camper discussion, W5 (Twice the Ice) and W10 item 2 can refer back to them.