A thermometer is removed from a room where the temperature is 70° F and taken outside, where the air temperature is 10° F. After a half a minute the thermometer reads 50° F. What is the reading of the thermometer at t = 1 minute? How long will it take for the reading on the thermometer to reach 15° F? Solve the problem as follows: a) construct a linear first-order DE that models the behaviour of Newton's Law of Cooling and state the initial condition; b) solve the DE and find the constant k using the fact that at half a minute the thermometer reads 50° F; c) what will the temperature T, be at t = 1 minute; d) how long will it take the thermometer to display a reading of 15° F; e) sketch a rough graph of the solution in Question 3 (b) which displays the behaviour of the thermometer readings over time. Label the axes and relevant points on the graph;
A thermometer is removed from a room where the temperature is 70° F and taken outside, where the air temperature is 10° F. After a half a minute the thermometer reads 50° F. What is the reading of the thermometer at t = 1 minute? How long will it take for the reading on the thermometer to reach 15° F? Solve the problem as follows: a) construct a linear first-order DE that models the behaviour of Newton's Law of Cooling and state the initial condition; b) solve the DE and find the constant k using the fact that at half a minute the thermometer reads 50° F; c) what will the temperature T, be at t = 1 minute; d) how long will it take the thermometer to display a reading of 15° F; e) sketch a rough graph of the solution in Question 3 (b) which displays the behaviour of the thermometer readings over time. Label the axes and relevant points on the graph;
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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Transcribed Image Text:A thermometer is removed from a room where the temperature is 70° F and taken outside, where the
air temperature is 10° F. After a half a minute the thermometer reads 50° F. What is the reading of the
thermometer at t = 1 minute? How long will it take for the reading on the thermometer to reach 15° F?
Solve the problem as follows:
a) construct a linear first-order DE that models the behaviour of Newton's Law of Cooling and
state the initial condition;
b) solve the DE and find the constant k using the fact that at half a minute the thermometer
reads 50° F;
c) what will the temperature T, be at = 1 minute;
d)
how long will it take the thermometer to display a reading of 15° F;
e)
sketch a rough graph of the solution in Question 3 (b) which displays the behaviour of the
thermometer readings over time. Label the axes and relevant points on the graph;
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