Unit 46: Newton’s Law of Cooling
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q46.1) An apple pie cools on a windowsill. What will be its temperature after one hour if its initial temperature is 70°C, the surrounding air is 12°C, and its decay constant is 0.035min⁻¹?
***Q46.3) You buy a fancy bottle of beer while travelling and bring it home to consume with your family. Annoyingly, the brewer recommends the beer be consumed at cellar temperature (11°C) instead of fridge temperature (4°C). You place the bottle in your 4°C fridge and find that it cools from room-temperature (22°C) to 18°C in 20 minutes. How much longer should you leave it in the fridge to get it to ideal consumption temperature of 11°C?
**Q46.2) You toss a hot rock in the ocean and find that it cools from 100°C to 50°C in 10 seconds. What’s the rock’s decay constant if the temperature of the ocean is 4°C?