Answer:
- 4 minutes: 17.4 °C
- 9 minutes: 23.7 °C
Explanation:
You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.
Newton's law of cooling
Newton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...
T = 36 -26·(22/26)^(t/2)
At times of t=4 and t=9, the temperature readings will be ...
- 4 minutes: 36 -26(11/13)^(4/2) ≈ 17.4 °C
- 9 minutes: 36 -26(11/13)^(9/2) ≈ 23.7 °C
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Additional comment
The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.
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