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

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

1 answer

To determine the best combination of the designs to meet the criteria and constraints for the hot pack, let's analyze each option based on the desired outcomes:

  1. Time at 90°C: Longer duration at or above 90°C is preferred.
  2. Temperature Variation: The aim is for a small variation (as constant as possible).
  3. Durability: A more durable pack is preferable.
  4. Size: It should be small enough to fit into shoes, gloves, or pockets.

Now, let's evaluate each option:

A. Time at 90°C of Design 2 and durability of Design 1

  • Time at 90°C: 40 minutes (Design 2)
  • Durability: 24 hours (Design 1)
  • This combination provides a good balance with the best time at temperature and excellent durability.

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

  • Temperature Variation: 0-7°C (Design 2)
  • Size: 8 cm × 5 cm (Design 3)
  • This option sacrifices time and durability for a compact size but remains in a higher temperature variation.

C. Temperature variation of Design 3 and size of Design 2

  • Temperature Variation: 0-7°C (Design 3)
  • Size: 10 cm × 6 cm (Design 2)
  • This option still has a higher temperature variation and is not the most compact pack.

D. Time at 90°C of Design 3 and durability of Design 1

  • Time at 90°C: 30 minutes (Design 3)
  • Durability: 24 hours (Design 1)
  • This option combines good durability with a reasonable time at temperature but goes below the maximum time of Design 2.

Given these evaluations, Option A is the best choice because it combines the best time at 90°C with excellent durability, effectively meeting the criteria and constraints for the hot pack design.

Final Answer: A. time at 90°C of Design 2 and durability of Design 1