Question 22 temperature 30°C. The temperature of the coffee cup can be modelled by the differential equation A cup of boiling water has initial temperature 100°C, and it sits in a room of dT k(В - Т), dt where B is the temperature of the room and T is the temperature of the water after t minutes. (a) What is the limiting temperature of the coffee? (b) Solve the differential equation and show that the solution is T = 30 + 70e-kt where k is a constant. (c) It took 20 minutes for the water to cool by 40°. How long approximately will it take for the water to cool down to half of it's original temperature?
Question 22 temperature 30°C. The temperature of the coffee cup can be modelled by the differential equation A cup of boiling water has initial temperature 100°C, and it sits in a room of dT k(В - Т), dt where B is the temperature of the room and T is the temperature of the water after t minutes. (a) What is the limiting temperature of the coffee? (b) Solve the differential equation and show that the solution is T = 30 + 70e-kt where k is a constant. (c) It took 20 minutes for the water to cool by 40°. How long approximately will it take for the water to cool down to half of it's original temperature?
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:Question 22
temperature 30°C. The temperature of the coffee cup can be modelled by the differential equation
A cup of boiling water has initial temperature 100°C, and it sits in a room of
dT
k(В - Т),
dt
where B is the temperature of the room and T is the temperature of the water after t minutes.
(a)
What is the limiting temperature of the coffee?
(b) Solve the differential equation and show that the solution is
T = 30 + 70e-kt
where k is a constant.
(c)
It took 20 minutes for the water to cool by 40°. How long approximately will it take for the
water to cool down to half of it's original temperature?
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