Suppose you have just poured a cup of freshly brewed coffee with temperature 90 C in a room where the temperature is 20 o C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation dT = k(T – Trom) dt where Trom- 20 o Cis the room temperature, and k is some constant. Suppose it is known that the coffee cools at a rate of 2 C per minute when its temperature is 70 o C. A. What is the limiting value of the temperature of the coffee? lim T(t) - B. What is the limiting value of the rate of cooling? dT lim 1 dt C. Find the constant k in the differentlial equation. D. Use Euler's method with step stze h= 3 minutes to estimate the temperature of the coffee after 15 minutes. T(15) =

Suppose you have just poured a cup of freshly brewed coffee with temperature 90 C in a room where the temperature is 20 o C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation dT = k(T – Trom) dt where Trom- 20 o Cis the room temperature, and k is some constant. Suppose it is known that the coffee cools at a rate of 2 C per minute when its temperature is 70 o C. A. What is the limiting value of the temperature of the coffee? lim T(t) - B. What is the limiting value of the rate of cooling? dT lim 1 dt C. Find the constant k in the differentlial equation. D. Use Euler's method with step stze h= 3 minutes to estimate the temperature of the coffee after 15 minutes. T(15) =

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.

Question

Suppose you have just poured a cup of freshly brewed coffee with temperature 90 C in a room where the
temperature is 20 o C.
Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature
difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t),
satisfies the differential equation
dT
k(T - Troom)
dt
where Troom= 20 o C is the room temperature, and k is some constant.
Suppose it is known that the coffee cools at a rate of 2o C per minute when its temperature is 70 o C.
A. What is the limiting value of the temperature of the coffee?
lim T(t) =
t 00
B. What is the limiting value of the rate of cooling?
dT
lim
0 dt
C. Find the constant k in the differential equation.
k =
D. Use Euler's method with step size h= 3 minutes to estimate the temperature of the coffee after 15
minutes.
T(15)

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