A teacher asked her students to design a hot pack. The desired criteria and constraints for the hot pack are as follows:

Question

its temperature should remain at or above 90°C for as long as possible
its temperature should remain as constant as possible
it should be durable and leak proof
it should fit inside shoes, gloves, or a pant pocket
The students were instructed to mix calcium chloride crystals in plastic bags filled with water. They were split into three groups, and each group created a design. Each design used a different amount of calcium chloride crystals. The table shows the hot pack designs created by the three groups.

Amount of Time at 90°C (minutes) Variation in Temperature (°C) Durability of Pack (hours) Size of Pack
Design 1 20 0-5 24 10 cm × 6 cm
Design 2 40 0-7 20 10 cm × 6 cm
Design 3 30 0-7 15 8 cm × 5 cm

How could the designs be combined to best meet the criteria and constraints?
A.
temperature variation of Design 2 and size of Design 3
B.
temperature variation of Design 3 and size of Design 2
C.
time at 90°C of Design 3 and durability of Design 1
D.
time at 90°C of Design 2 and durability of Design 1

Answer 1

To determine the best combination of designs that meets the criteria and constraints of the hot pack (temperature above 90°C for as long as possible, low temperature variation, durability, and compact size), let's evaluate the options based on each design’s results:

1. Design 1:

   • Time at 90°C: 20 minutes
   • Variation in Temperature: 0-5°C
   • Durability: 24 hours
   • Size: 10 cm × 6 cm

2. Design 2:

   • Time at 90°C: 40 minutes (best for time)
   • Variation in Temperature: 0-7°C
   • Durability: 20 hours
   • Size: 10 cm × 6 cm

3. Design 3:

   • Time at 90°C: 30 minutes
   • Variation in Temperature: 0-7°C
   • Durability: 15 hours (least durable)
   • Size: 8 cm × 5 cm (smallest size)

Now analyzing each option:

A. temperature variation of Design 2 and size of Design 3

• Temperature Variation: 0-7°C (Design 2) - higher variation.
• Size: 8 cm × 5 cm (Design 3) - compact.

B. temperature variation of Design 3 and size of Design 2

• Temperature Variation: 0-7°C (Design 3) - similar to Design 2.
• Size: 10 cm × 6 cm (Design 2) - larger.

C. time at 90°C of Design 3 and durability of Design 1

• Time: 30 minutes (Design 3) - better than Design 1 but worse than Design 2.
• Durability: 24 hours (Design 1) - best durability.

D. time at 90°C of Design 2 and durability of Design 1

• Time: 40 minutes (Design 2) - best duration.
• Durability: 24 hours (Design 1) - best durability.

Among these options, D offers the best combination of meeting the criteria:

• It guarantees the longest time at 90°C (40 minutes from Design 2), ensuring that the hot pack remains effective for a longer time.
• It combines this with the best durability (24 hours from Design 1), which is essential for long-lasting use.

Therefore, the best answer is: D. time at 90°C of Design 2 and durability of Design 1.