A student constructs a hand warmer that becomes hot to the touch when activated. It is activated when a pouch filled with 100 mL of water bursts and combines with a solid substance in a dry bag, as in the model shown below.

Question

The student wants to continue using the same solid. However, he finds that the hot packs he constructs do not become warm enough, so he wants to modify his design. He conducts a test using the same solid but with different concentrations, as shown in the table below.

After further research, he found that temperatures above 70°C are too hot for human touch. He wants the hot pack to be as warm as possible, but not too hot to touch. Based on the information given, how much of the substance should the student use to best modify his hot pack?
40 g
25 g
35 g
45 g

Answer 1

To determine the best amount of the solid substance for the hand warmer, we need to consider the effectiveness of each concentration in producing heat while ensuring that the temperature does not exceed 70°C for safety. However, the specific relationships between the amount of the solid and the resulting temperatures are not provided in the problem statement.

Assuming that there is a correlation between the amount of solid and the temperature generated (with increased amounts generally leading to higher temperatures), we can approach the problem by analyzing the options available:

• 40 g
• 25 g
• 35 g
• 45 g

Since higher concentrations of the solid may produce higher temperatures, the best choice would balance providing sufficient warmth but staying below the 70°C threshold. It’s common to find that there is a point of diminishing returns or a maximum temperature achievable for different amounts of substance.

Given the available options, a middle-range amount such as 35 g appears to be a reasonable compromise between not being too weak (like 25 g) and avoiding excessive heat (like 45 g). Therefore, if the goal is to be warm but safe, 35 g seems to be the best choice without exceeding the temperature limit.

Final recommendation: Use 35 g of the solid substance.