An instrument at an initial temperature of 40 degrees C is placed in a room whose temperature is 20 degrees C. For the next 5h the room temperature Qo(t) gradually rises and is given by Qo(e) = 20 + 10t, where t is measured in hours. (a) Use Newton's Law of Cooling = -k(T - Qo), with k = 1, to determine the temperature of the instrument T(t) at any time t> 0. (b) Is there any time when the instrument equals the room temperature? Sketch the graph of T and Qo on the same plot.
An instrument at an initial temperature of 40 degrees C is placed in a room whose temperature is 20 degrees C. For the next 5h the room temperature Qo(t) gradually rises and is given by Qo(e) = 20 + 10t, where t is measured in hours. (a) Use Newton's Law of Cooling = -k(T - Qo), with k = 1, to determine the temperature of the instrument T(t) at any time t> 0. (b) Is there any time when the instrument equals the room temperature? Sketch the graph of T and Qo on the same plot.
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:An instrument at an initial temperature of 40 degrees C is placed in a room whose
temperature is 20 degrees C. For the next 5h the room temperature Qo(t) gradually rises
and is given by Qo(t) = 20 + 10t, where t is measured in hours.
(a) Use Newton's Law of Cooling = -k(T- Qo), with k = 1, to determine the
temperature of the instrument T(t) at any time t> 0.
(b) Is there any time when the instrument equals the room temperature? Sketch the graph
of T and Qo on the same plot.
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