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, dT - = K[M(t) - T(t)], where K is a constant. Let K = 0.05 (min) ¹ and the temperature of the medium be constant, dt M(t) = 293 kelvins. If the body is initially at 364 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.) 5)60min= 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 temperature of the medium M(t) and the temperature of the body. That is, dT - = K[M(t) - T(t)], where K is a constant. Let K = 0.05 (min) ¹ and the temperature of the medium be constant, dt M(t) = 293 kelvins. If the body is initially at 364 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.) 5)60min= kelvins.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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,
dT
- = K[M(t) - T(t)], where K is a constant. Let K = 0.05 (min)¹ and the temperature of the medium be constant,
dt
M(t) = 293 kelvins. If the body is initially at 364 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.)
(b)60min=
kelvins.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20afbc89-01bf-4e47-910c-436b829d66ac%2F164b81d8-29ec-4884-891d-1cf6139920da%2Fdl9gwzs_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,
dT
- = K[M(t) - T(t)], where K is a constant. Let K = 0.05 (min)¹ and the temperature of the medium be constant,
dt
M(t) = 293 kelvins. If the body is initially at 364 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.)
(b)60min=
kelvins.
Expert Solution
Step 1
Given Data:
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,
Where K is constant.
To Find:
The temperature of the body after 30 minutes and 60 minutes.
Step by step
Solved in 6 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
