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

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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.

Expert Solution

Step 1

Given Data:

$\frac{dT}{dt} = K [M (t) - T (t)]$

Where K is constant.

$K = 0.05 {(\min)}^{- 1} M (t) = 293 kelvins . T (0) = 364 kelvins . h = 0.1 \min$

To Find:

The temperature of the body after 30 minutes and 60 minutes.

Step by step

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