6. Newton's law of cooling states that the temperature of an object changes at a rate proportional e difference between the temperature of the object and the temperature of its surroundings. to (a) Multiple Choice: The temperature of a cup of coffee obeys Newton's law of cooling. The initial temperature of the coffee is 150°F and, one minute later, it is 135°F. The ambient temperature of the room is 70° F. If H(t) represents the temperature of the coffee at time t, and k is a positive constant, the correct differential equation that models this situation is: (Select the correct answer). dH i. =k(T-135) dt dH
6. Newton's law of cooling states that the temperature of an object changes at a rate proportional e difference between the temperature of the object and the temperature of its surroundings. to (a) Multiple Choice: The temperature of a cup of coffee obeys Newton's law of cooling. The initial temperature of the coffee is 150°F and, one minute later, it is 135°F. The ambient temperature of the room is 70° F. If H(t) represents the temperature of the coffee at time t, and k is a positive constant, the correct differential equation that models this situation is: (Select the correct answer). dH i. =k(T-135) dt dH
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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Transcribed Image Text:Short Answer, True/False, and Multiple Choice Questions
6.
Newton's law of cooling states that the temperature of an object changes at a rate proportional
to e difference between the temperature of the object and the temperature of its surroundings.
(a) Multiple Choice:
The temperature of a cup of coffee obeys Newton's law of cooling. The initial temperature of
the coffee is 150°F and, one minute later, it is 135°F. The ambient temperature of the room is
70°F. If H(t) represents the temperature of the coffee at time t, and k is a positive constant, the
correct differential equation that models this situation is: (Select the correct answer).
dH
i.
=k(T-135)
dt
dH
ii. =k(T-150)
dt
dH
iii. =k(T-70)
dt
dH
iv. =kT(T-150)
dt
dH
V. =kT(T-70)
dt
Answer:
(b) Multiple Choice:
In the previous problem, after a long period of time, the temperature of the coffee approaches:
(Select the correct answer and Explain in one sentence.)
i. 120°F
ii. 100°F
iii. 70°F
iv. 65°F
v. 0°F
Answer:
Explanation in One Sentence
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