Design Challenge: A Self-Warming Cup for an Outdoor Choir Recording

0 / 10

Design Challenge: A Self-Warming Cup for an Outdoor Choir Recording

Use test data to size and improve a cup warmed by a chemical reaction.

Test 1: How much quicklime?

Read the passage and study Table 1. Then answer the questions.

Warm Drinks in a Cold Bandshell

1In December, the Westmoor Middle School choir recorded a winter song in the town's old stone bandshell, where the echo makes voices ring. Sound engineer Mr. Lars Engstrom set up microphones and a recorder that run on batteries, but the bandshell has no power outlets, so there was no way to plug in a kettle. Choir director Ms. Adaora Nwankwo wanted the singers to have warm drinks between takes, since many singers find that a warm drink feels good on the throat in cold air. Seventh graders Paloma Restrepo and Ishaan Venkataraman took on the job as a science club design challenge: build a cup that warms its own drink.

2Their cup has two parts. An inner cup holds 200 mL of drink. Around it, an outer chamber holds quicklime, a white powder also called calcium oxide, and a sealed pouch of water. Pressing a button on the bottom breaks the pouch. The water reaches the quicklime, and the two react to form a new substance, calcium hydroxide. A small vent lets steam escape from the outer chamber. Quicklime can burn skin and eyes, so the club's adviser, Dr. Yusuf Adeyemi, filled and sealed every outer chamber while wearing gloves and goggles. The students only pressed the buttons and read the thermometers.

3The club agreed on three criteria. Criterion 1: the drink reaches 45 °C or warmer by the 10-minute reading. Criterion 2: the drink stays at 60 °C or cooler at every reading, so no one burns a lip. Criterion 3: the outside of the cup stays below 45 °C, so it is safe to hold.

4In every test, the drink was 200 mL of water that started at 8 °C, the temperature of the air in the bandshell, and each pouch held 40 mL of water. In Test 1, the students changed only the mass of quicklime in the outer chamber. They read a thermometer in the drink and a thermometer taped to the outside of the cup every 5 minutes for 30 minutes and recorded the 10-minute reading and the highest readings.

Table 1. Test 1: Cups With No Sleeve (drink starts at 8 °C)
Quicklime (g)	Drink at 10 min (°C)	Highest drink (°C)	Highest outside (°C)
25	20	23	26
50	35	38	37
75	50	53	52
100	64	68	63

1.

Use Table 1.

With 75 g of quicklime, the drink warmed by °C in the first 10 minutes.

2.

Which path best describes the energy that warms the drink?

A. The steam from the vent carries thermal energy from the bandshell air back down into the drink.B. The reaction of quicklime and water releases thermal energy, which flows through the inner wall into the drink.C. Cold flows out of the drink into the quicklime, which leaves the drink warmer.D. Pressing the button gives the cup the thermal energy, which is stored in the drink until it is sipped.

3.

Which pattern does Table 1 show as the mass of quicklime increased?

A. The drink got warmer with each step up to 75 g, then cooler at 100 g.B. The drink got warmer, but the outside of the cup stayed at about 26 °C.C. Each extra 25 g made both the drink and the outside of the cup warmer.D. The drink warmed by about the same amount, whatever the mass of quicklime.

4.

Use criteria 1 and 2 in paragraph 3. Circle each design in Table 1 that meets both of these criteria for the drink.

5.

Suppose the club tested a cup with 60 g of quicklime and no sleeve. Predict its highest drink temperature.

A. About 44 °C, because each extra 25 g raised the highest drink temperature by about 15 °CB. About 30 °C, because 60 g is a little more than half of the largest amount in Table 1C. About 53 °C, because 60 g sits closer to 75 g than to 50 g in Table 1D. About 60 °C, because 60 g of quicklime warms the drink to a temperature equal to its mass

Test 2: Adding a sleeve

Read the paragraph and study Table 2. Use the three criteria in paragraph 3 and the new criterion below.

The 75 g cup failed criterion 3, so for Test 2 the club kept 75 g of quicklime and wrapped the cup in a sleeve. Everything else stayed the same as in Test 1. Because each song takes many takes, Ms. Nwankwo added criterion 4: the drink is still 40 °C or warmer at the 30-minute reading.

Table 2. Test 2: 75 g of Quicklime (drink starts at 8 °C)
Sleeve	Drink at 10 min (°C)	Highest drink (°C)	Highest outside (°C)	Drink at 30 min (°C)
None	50	53	52	35
Cardboard	51	54	40	36
Foam	53	56	33	46

6.

The foam sleeve kept the drink warmer and the outside of the cup cooler. Which explanation fits Table 2 best?

A. The foam slowed the flow of thermal energy from the cup out into the cold air.B. The foam reacted with the quicklime, so the reaction released more thermal energy.C. The foam added its own thermal energy to the drink once it touched the hot cup.D. The foam kept the cold air from flowing into the cup, so the drink lost no cold.

7.

Which design in Table 2 meets all four criteria?

A. No sleeve, because its drink was 50 °C at the 10-minute readingB. The cardboard sleeve, because its outside stayed at 40 °CC. The foam sleeve, because its drink was 46 °C at 30 minutes

8.

Ishaan wonders whether a finer quicklime powder would warm the drink faster. Which plan is a fair test of his idea?

A. 75 g of fine powder and 75 g of coarse powder, both in foam sleeves with 8 °C drinksB. 75 g of fine powder and 100 g of coarse powder, both in foam sleeves with 8 °C drinksC. 75 g of fine powder with an 8 °C drink and 75 g of coarse powder with a 20 °C drinkD. Fine powder with a foam sleeve and coarse powder with a cardboard sleeve, both 75 g

9.

After a recording session, Dr. Adeyemi opens a used cup and adds fresh water to its outer chamber. The cup does not warm up again. Which explanation fits the passage best?

A. The steam from the vent carried the quicklime out of the outer chamber.B. The quicklime had already reacted to form calcium hydroxide, a new substance.C. The fresh water was too cold to carry any thermal energy into the quicklime.D. The drink had soaked up the quicklime's heat, which is now stored in the drink.

10.

Paloma says, "Let's use 100 g of quicklime with the foam sleeve. More quicklime always makes a better warmer." Do you agree? Write a recommendation for the choir's cup. Support your claim with data from both tables and the criteria, and explain where the thermal energy comes from.