Overnight temperature model and frost
Overnight temperature model and frost
IP 1
7 marks
At 6 p.m. the temperature in a mountain village is \(4\,^\circ\mathrm{C}\). A simple model assumes that the temperature falls at a constant rate of \(1.5\,^\circ\mathrm{C}\) per hour until midnight, and then rises at a constant rate of \(0.75\,^\circ\mathrm{C}\) per hour.
- Find the temperature at midnight.[1]
- Frost forms when the temperature is below \(-2\,^\circ\mathrm{C}\). Using the model, find the length of time for which the temperature is below \(-2\,^\circ\mathrm{C}\).[3]
- Find the time at which the temperature returns to \(0\,^\circ\mathrm{C}\).[1]
- The temperature recorded at 9 a.m. was \(1.5\,^\circ\mathrm{C}\). Compare this with the model's value and comment on the assumption of a constant rate.[2]
Solution:
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Answer:(a) \(-5\,^\circ\mathrm{C}\) (b) \(6\) hours (10 p.m. to 4 a.m.) (c) 6.40 a.m. (d) model gives \(1.75\,^\circ\mathrm{C}\), \(0.25\,^\circ\mathrm{C}\) above the reading; the constant-rate assumption is reasonable but slightly overestimates the warming
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