Learning target: I can graph temperature-versus-time data from three hand-warmer prototypes, calculate peak rise, warming rate and time above a threshold, and decide which prototype meets the criteria and which characteristics to combine.
A student engineering club tested three iron-powder hand-warmer prototypes in a room at 22 °C, reading each pouch's temperature every 30 minutes for 5 hours. The numbers are a teaching dataset: invented to be realistic, not measured in a lab. Plot all three curves on the blank graph, then answer the questions. Show every calculation with units. Use the criteria table to judge the prototypes; the club's constraints are listed with it.
You will need: This worksheet, Pencil, Ruler, Calculator (optional)
| Kind | Statement | How it is checked |
|---|---|---|
| Criterion 1 | Peak temperature at least 42 °C | Highest reading in the table |
| Criterion 2 | Stays at or above 38 °C for at least 3 hours | Time from the first reading at or above 38 °C to the last reading at or above 38 °C |
| Constraint A | Never above 50 °C (skin safety) | No reading above 50 °C |
| Constraint B | No more than 25 g of iron per pouch (cost) | Mass of iron used |
| Time (min) | A: 10 g, thin pouch (°C) | B: 20 g, thin pouch (°C) | C: 20 g, thick pouch (°C) |
|---|---|---|---|
| 0 | 22 | 22 | 22 |
| 30 | 41 | 44 | 33 |
| 60 | 43 | 49 | 39 |
| 90 | 40 | 47 | 42 |
| 120 | 36 | 44 | 43 |
| 150 | 32 | 41 | 43 |
| 180 | 28 | 38 | 42 |
| 210 | 25 | 34 | 41 |
| 240 | 23 | 30 | 40 |
| 270 | 22 | 26 | 38 |
| 300 | 22 | 23 | 36 |
| Peak temperature (°C) | Time of peak (min) | Rise above room temperature (°C) |
|---|---|---|
| Prototype A | ||
| Prototype B | ||
| Prototype C |
| First reading at or above 38 °C (min) | Last reading at or above 38 °C (min) | Time at or above 38 °C (hours) |
|---|---|---|
| Prototype A | ||
| Prototype B | ||
| Prototype C |
| Criterion 1: peak ≥ 42 °C | Criterion 2: ≥ 38 °C for ≥ 3 h | Constraint A: never > 50 °C | Constraint B: ≤ 25 g iron |
|---|---|---|---|
| Prototype A | |||
| Prototype B | |||
| Prototype C |
A warming rate is a change in temperature divided by the time it took: (reading at 30 min − reading at 0 min) ÷ 30 min, in °C per minute. Write the subtraction on one line and the division on the next. For time above 38 °C, run your finger down a prototype's column and circle every reading that is 38 or more; the time is from the first circled row to the last circled row. Divide minutes by 60 to get hours (for example, 150 min ÷ 60 = 2.5 h).
Prototype A read 40 °C at 90 min and 36 °C at 120 min, so it crossed below 38 °C somewhere between those readings. Assuming the temperature fell at a steady rate between the two readings, calculate the minute at which A reached exactly 38 °C and revise its time above 38 °C. Then do the same for prototype B between 180 and 210 min. Write a sentence on how reading every 10 minutes instead of every 30 would change the certainty of the club's time measurements, and what it would cost in effort.