Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the dT temperature of the medium M(t) and the temperature of the body. That is, -=K[M(t) - T(t)], where K is a constant. Let K = 0.04 (min) ¹ and the temperature of the medium be constant, M(t) = 295 kelvins. If the body is initially at 361 kelvins, use Euler's method with h = 0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes. dt (a) The temperature of the body after 30 minutes is (Round to two decimal places as needed.) kelvins.
Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the dT temperature of the medium M(t) and the temperature of the body. That is, -=K[M(t) - T(t)], where K is a constant. Let K = 0.04 (min) ¹ and the temperature of the medium be constant, M(t) = 295 kelvins. If the body is initially at 361 kelvins, use Euler's method with h = 0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes. dt (a) The temperature of the body after 30 minutes is (Round to two decimal places as needed.) kelvins.
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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(b) The temperature of the body after 60 minutes is __ Kelvins.
(Round to two decimal places as needed)
![Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the
temperature of the medium M(t) and the temperature of the body. That is, = K[M(t)- T(t)], where K is a constant. Let K = 0.04 (min) ¹
dT
1
dt
and the temperature of the medium be constant, M(t) = 295 kelvins. If the body is initially at 361 kelvins, use Euler's method with h = 0.1 min
to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.
(a) The temperature of the body after 30 minutes is
(Round to two decimal places as needed.)
kelvins.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faaed6e9c-dce1-4b09-8cf0-c81cdcf3a73f%2F9c082631-698c-4fc8-bc46-f6060b96aa5f%2Fg0ux8o_processed.png&w=3840&q=75)
Transcribed Image Text:Newton's law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the
temperature of the medium M(t) and the temperature of the body. That is, = K[M(t)- T(t)], where K is a constant. Let K = 0.04 (min) ¹
dT
1
dt
and the temperature of the medium be constant, M(t) = 295 kelvins. If the body is initially at 361 kelvins, use Euler's method with h = 0.1 min
to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.
(a) The temperature of the body after 30 minutes is
(Round to two decimal places as needed.)
kelvins.
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