5. Newton's Law of Cooling states that an object will cool down (or heat up) at a rate proportional to the difference between the temperature of the object and the ambient temperature. (a) Write a differential equation that models the rate at which a cup of coffee will cool down. Let k be the constant of proportionality, y(t) the temperature of the coffee at time t (in minutes) and T the ambient temperature. (b) Now suppose suppose the cup of coffee is made with boiling hot water and set in a room where the temperature is 20° C and the coffee cools to 90° C in 2 minutes. How long will it take the coffee to cool to 60° C?
5. Newton's Law of Cooling states that an object will cool down (or heat up) at a rate proportional to the difference between the temperature of the object and the ambient temperature. (a) Write a differential equation that models the rate at which a cup of coffee will cool down. Let k be the constant of proportionality, y(t) the temperature of the coffee at time t (in minutes) and T the ambient temperature. (b) Now suppose suppose the cup of coffee is made with boiling hot water and set in a room where the temperature is 20° C and the coffee cools to 90° C in 2 minutes. How long will it take the coffee to cool to 60° C?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please solve it on paper
based on the answer key the answer should be:
a. ?′ = ?(? − ?) [ or ?′ = ?(? − ?) ]
b. About 10.4 minutes
Transcribed Image Text:5. Newton's Law of Cooling states that an object will cool down (or heat up) at a rate proportional to the
difference between the temperature of the object and the ambient temperature.
(a) Write a differential equation that models the rate at which a cup of coffee will cool down. Let k be
the constant of proportionality, y(t) the temperature of the coffee at time t (in minutes) and T the
ambient temperature.
(b) Now suppose suppose the cup of coffee is made with boiling hot water and set in a room where the
temperature is 20° C and the coffee cools to 90° C in 2 minutes. How long will it take the coffee to cool to
60° C?
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