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.
time at 90°C of Design 2 and durability of Design 1
B.
time at 90°C of Design 3 and durability of Design 1
C.
temperature variation of Design 2 and size of Design 3
D.
temperature variation of Design 3 and size of Design 2

Answer 1

To evaluate which combination of designs from the three groups best meets the desired criteria and constraints for the hot pack, let's analyze the options provided:

1. Design 1:

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

2. Design 2:

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

3. Design 3:

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

Now we consider each of the options:

A. Time at 90°C of Design 2 (40 minutes) and durability of Design 1 (24 hours).

• This combination maximizes time at 90°C while ensuring high durability.

B. Time at 90°C of Design 3 (30 minutes) and durability of Design 1 (24 hours).

• This has a lower time at 90°C compared to Design 2.

C. Temperature variation of Design 2 (0-7°C) and size of Design 3 (8 cm × 5 cm).

• This offers a good balance between size and temperature variation but does not address time and durability.

D. Temperature variation of Design 3 (0-7°C) and size of Design 2 (10 cm × 6 cm).

• This does not change temperature variation meaningfully and uses a larger size.

Considering the desired criteria — maximizing time at or above 90°C, maintaining a constant temperature, ensuring durability, and being small enough to fit in shoes, gloves, or pockets — option A (time at 90°C of Design 2 and durability of Design 1) is the best combination.

So, the best choice is: A. Time at 90°C of Design 2 and durability of Design 1.