Explanation Given: The ambient temperature is T m and the time period is t . Formula used: Newton’s Law of Cooling/Warming: d T d t = k ( T − T m ) (1) Here, the constant of proportionality is k and rate of change of temperature is d T d t Calculation: Write the expression for Newton’s Law of Cooling/Warming. d T d t = k ( T − T m ) (1) Refer to the graph shown in Figure (1) to obtain the value of T m as ( 80 − 30 cos π t 12 ) Substitute ( 80 − 30 cos π t 12 ) for T m in equation (1)

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Chapter 1.3, Problem 6E

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A mathematical model for the temperature T(t) of a body within the given environment.

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A mathematical model for the temperature T ( t ) of a body within the given environment.

Solution Summary: The author explains the differential equation for the temperature T(t) of a body within the given environment.

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Chapter 1 Solutions