Program Explanation Given information: The temperature of the cake initially is 210 ° C and the room temperature is 70 ° C . The another condition is the temperature of the cake is 100 ° C after 30 minute. Calculation: Consider the standard equation of Newton’s law of cooling as follows, d T d t = − k ( T − A ) Here, A is the temperature of the outside. The room temperature is 70 ° C therefore, the value of A = 70 . Separate the variables of the above differential equations, as follows: d T ( T − 70 ) = − k d t Integrate the equation on both the sides. ∫ d T ( T − 70 ) = − ∫ k d t Evaluate the above integral as follows, ln c ( T − 70 ) = − k t Further evaluate the above equation for the value of T , as follows: T = 70 + c e − k t ........(1) Apply the initial condition that the temperature of cake is 210 ∘ F at t = 0 to obtain the value of c . T = 70 + c e − k t 210 = 70 + c e − k ( 0 ) 140 = c c = 140 Now substitute 140 for c in equation (1) to obtain the temperature function. T = 70 + 140 e − k t ........(2) Apply the boundary condition that temperate of the cake is 140 ∘ F at t = 30 to obtain the value of k

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Chapter 1.4, Problem 49P

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Program Description: Purpose of the problem is to findthe time at which the temperature of the cake is 100°F.

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Chapter 1.4, Problem 48P

Chapter 1.4, Problem 50P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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Program Description: Purpose of the problem is to findthe time at which the temperature of the cake is 100 ° F .

Solution Summary: The author explains the problem of finding the time at which the temperature of the cake is 100°F.

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Program Description: Purpose of the problem is to findthe time at which the temperature of the cake is 100°F.

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Chapter 1 Solutions