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(1)]. where K is a constant. Let K= 0.04 (min) ¯' and the temperature of the medium be constant, M(t) = 292 kelvins. If the body is initialy at 355 kelvins, use Euler's method wvith 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 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(1)]. where K is a constant. Let K= 0.04 (min) ¯' and the temperature of the medium be constant, M(t) = 292 kelvins. If the body is initialy at 355 kelvins, use Euler's method wvith 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 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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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Euler rule

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(1)]. where K is a constant. Let K= 0.04
(min) ¯' and the temperature of the medium be constant, M(t) = 292 kelvins. If the body is initialy at 355 kelvins, use Euler's method
wvith 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 kelvins.

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Given a differential equation that describes the Newton’s law of cooling.

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Now, start the iteration with n = 0,

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Now, we find the iteration that represents temperature at time t = 30.

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