Case study·Standard multi-step (3/5)·No calculator
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Question
A hot liquid cools in a room at . At one instant its temperature is and its cooling rate is . Assume Newton's law of cooling holds approximately for the interval considered.
Total: 4 marks
(a) Find the excess temperature at that instant. (1 mark)
(b) Find the proportionality constant in . (1 mark)
(c) Estimate the cooling rate when the liquid is at . (1 mark)
(d) Explain why the rate decreases as the liquid approaches room temperature. (1 mark)
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