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.

Mass of Solid
(g) Initial
Temperature
(°C) Final
Temperature
(°C)
20 20 51
30 20 63
40 20 73
50 20 86
60 20 96

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?
A.
35 g
B.
25 g
C.
45 g
D.
40 g

Answer 1

To determine how much of the solid the student should use in order to achieve a final temperature that is warm but not too hot to touch, we look at the final temperatures corresponding to each mass of solid:

• 20 g: Final Temperature = 51°C
• 30 g: Final Temperature = 63°C
• 40 g: Final Temperature = 73°C
• 50 g: Final Temperature = 86°C
• 60 g: Final Temperature = 96°C

Since temperatures above 70°C are too hot for human touch, we must choose a final temperature that is 70°C or lower.

From the data, we see:

• At 40 g, the final temperature is 73°C (too hot).
• At 30 g, the final temperature is 63°C (acceptable).
• At 20 g, the final temperature is 51°C (acceptable).

However, to find the best modification, we want the highest temperature below 70°C. This would be the final temperature corresponding to 30 g, which is 63°C.

Therefore, the best option for the student is:

B. 30 g