A thermometer that has been sitting in a cold storeroom is brought into a warm kitchen. Newton's Law of Cooling can be used to model how the temperature rises in the thermometer as it approaches the kitchen's temperature: dT dt k (T - T∞) where k is the thermometer's proportionality constant and T∞ is the ambient temperature.

Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter19: Temperature, Thermal Expansion And Gas Laws
Section: Chapter Questions
Problem 4PQ
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The temperature initially reads 5°C when brought into the 25°C kitchen, and it reads 20°C after five minutes. Using the correct solution for temperature, when will the thermometer show approximately the correct temperature (say, 24.9°C)?

A thermometer that has been sitting in a cold storeroom is brought into a warm kitchen. Newton's Law of Cooling can be used
to model how the temperature rises in the thermometer as it approaches the kitchen's temperature:
dT
dt
k (T - T∞)
where k is the thermometer's proportionality constant and T∞ is the ambient temperature.
Transcribed Image Text:A thermometer that has been sitting in a cold storeroom is brought into a warm kitchen. Newton's Law of Cooling can be used to model how the temperature rises in the thermometer as it approaches the kitchen's temperature: dT dt k (T - T∞) where k is the thermometer's proportionality constant and T∞ is the ambient temperature.
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