2. (Separable and Newton's Law of Cooling) Let T(t) be the temperature of the room and T, the outside temperature (assumed to be constant in Newton's law). Then by Newton's law k(T - T,). In this problem, the rate at which a substance cools in air is directly proportional to the difference between the temperatures of the substance and that of air. The temperature of air, TA, is 30° and the substance cools from 100' to 70' in 15 minutes. How long does it take for the substance to cool from 100' to 50'? A. 45.30 minutes B. 43.60 minutes C. 35.39 minutes D. 33.59 minutes

2. (Separable and Newton's Law of Cooling) Let T(t) be the temperature of the room and T, the outside temperature (assumed to be constant in Newton's law). Then by Newton's law k(T - T,). In this problem, the rate at which a substance cools in air is directly proportional to the difference between the temperatures of the substance and that of air. The temperature of air, TA, is 30° and the substance cools from 100' to 70' in 15 minutes. How long does it take for the substance to cool from 100' to 50'? A. 45.30 minutes B. 43.60 minutes C. 35.39 minutes D. 33.59 minutes

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

2. (Separable and Newton's Law of Cooling) Let T(t) be the temperature of the room and T, the
outside temperature (assumed to be constant in Newton's law). Then by Newton's law
dt
k(T – T,). In this problem, the rate at which a substance cools in air is directly proportional to
the difference between the temperatures of the substance and that of air. The temperature of
air, TA, is 30° and the substance cools from 100° to 70° in 15 minutes. How long does it take for
the substance to cool from 100 to 50"?
A. 45.30 minutes
B. 43.60 minutes
C. 35.39 minutes
D. 33.59 minutes
Solution. Hints:
1. Find the general solution of the equation = k(T – T,) by separable.
2. Let t = 0 and T = 100° to find C.
3. Let t = 15 and T = 70 to find k.
4. Let T = 50° to find t.

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