Explanation Given: A thermometer is taken from an inside room to the outside. The temperature after 1 minute is T ( 1 ) = 55 ° F and after 5 minutes the temperature is T ( 5 ) = 30 ° F . Calculation: Consider the equation for the Newton’s Law of cooling. d T d t = k ( T − T 0 ) = k ( T − 5 ) (1) Here, k is a constant. Separate the variables in equation (1) and integrate. ∫ d T k ( T − 5 ) = ∫ k d t ln | T − 5 | = k t + c 1 | T − 5 | = e c 1 e k t T − 5 = C e k t Simplify the above equation. T = 5 + C e k t (2) Substitute 1 for t and T ( 1 ) = 55 ° F in equation (2). T ( 1 ) = 5 + C e k ( 1 ) 55 = 5 + C e k 50 = C e k 50 C = e k (3) Substitute 5 for t and T ( 5 ) = 30 ° F in equation (2)

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.7, Problem 14E

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Calculate the initial temperature of the inside room.

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Calculate the initial temperature of the inside room.

Solution Summary: The author calculates the initial temperature of the inside room, based on the Newton's Law of Cooling.

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Chapter 2 Solutions