3.2.5 A thermometer is removed from a room where the temperature is 21° C and is taken outside, where the air temperature is-12° C. After one-half minute the thermometer reads 11° C. What is the reading of the thermometer at t = 1 min? (Roundyour answer to two decimal places.)°CHow long will it take for the thermometer to reach -8° C? (Round your answer to two decimal places.)min

Answered: A thermometer is removed from a room…

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

3.2.5

A thermometer is removed from a room where the temperature is 21° C and is taken outside, where the air temperature is
-12° C. After one-half minute the thermometer reads 11° C. What is the reading of the thermometer at t = 1 min? (Round
your answer to two decimal places.)
°C
How long will it take for the thermometer to reach -8° C? (Round your answer to two decimal places.)
min

Expert Solution

Step 1

Sol:-

To solve this problem, we can use Newton's law of cooling, which states that the rate of change of the temperature of an object is proportional to the difference between the object's temperature and the temperature of its surroundings.

Let T(t) be the temperature of the thermometer at time t. Then, we have:

dT/dt = k(T - T_s)

where k is a constant of proportionality, T_s is the temperature of the surroundings (in this case, -12° C), and dT/dt is the rate of change of the temperature.