5. Newton's Law of Cooling states that if an object with temperature T(t) is placed in a room with ambient temperature T,, then T(t) obeys a differential equation of the form T'(t) = k(T – T.), where k is a constant depending on the physical properties of the object. Suppose that you put a pot of stew, initially at 90 degrees Fahrenheit, into a 35-degree refrigerator. (a) What is the temperature T(t) of the stew after t minutes? (b) Suppose that after half an hour, the stew is at 70 degrees Fahrenheit. What is the constant k in our problem? (c) How long will it take for the stew to cool to 50 degrees Fahrenheit?

5. Newton's Law of Cooling states that if an object with temperature T(t) is placed in a room with ambient temperature T,, then T(t) obeys a differential equation of the form T'(t) = k(T – T.), where k is a constant depending on the physical properties of the object. Suppose that you put a pot of stew, initially at 90 degrees Fahrenheit, into a 35-degree refrigerator. (a) What is the temperature T(t) of the stew after t minutes? (b) Suppose that after half an hour, the stew is at 70 degrees Fahrenheit. What is the constant k in our problem? (c) How long will it take for the stew to cool to 50 degrees Fahrenheit?

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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Question

Please answer all three parts. Thanks in advance.

5. Newton's Law of Cooling states that if an object with temperature T(t) is placed in a
room with ambient temperature T,, then T(t) obeys a differential equation of the form
T'(t) = k(T – T.),
where k is a constant depending on the physical properties of the object.
Suppose that you put a pot of stew, initially at 90 degrees Fahrenheit, into a 35-degree
refrigerator.
(a) What is the temperature T(t) of the stew after t minutes?
(b) Suppose that after half an hour, the stew is at 70 degrees Fahrenheit. What is the
constant k in our problem?
(c) How long will it take for the stew to cool to 50 degrees Fahrenheit?

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