Explanation Given: The equation of Newton’s law of cooling is given by, T = M + C e − k t Here, M is temperature of the kitchen. Calculation: Consider the above equation. T = M + C e − k t Since, initially ( t = 0 ) , the temperature of the water was at 100 ° C then above equation becomes as follows, 100 = M + C e − k ( 0 ) 100 = M + C C = 100 − M …… ( 1 ) Given that, after 5 min , the temperature of the water has decreased to 80 ° C . Since, the above equation becomes as follows, 80 = M + C e − 5 k …… ( 2 ) Finally, after another 5 min ( t = 10 minutes ) the temperature has dropped to 65 ° C . Since, the above equation becomes as follows, 65 = M + C e − 10 k …… ( 3 ) Substitute ( 100 − M ) for C in equation ( 2 ) . 80 = M + ( 100 − M ) e − 5 k 80 − M = ( 100 − M ) e − 5 k …… ( 4 ) Substitute ( 100 − M ) for C in equation ( 3 ) . 65 = M + ( 100 − M ) e − 10 k 65 − M = ( 100 − M ) e − 10 k …… ( 5 ) Square the equation ( 4 ) and divide with equation ( 5 ) as follows,

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 2.2, Problem 36E

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The temperature of the kitchen by assuming Newton’s law of cooling.

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Chapter 2.2, Problem 35E

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Fundamentals of Differential Equations and Boundary Value Problems

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The temperature of the kitchen by assuming Newton’s law of cooling.

To find: The temperature of the kitchen by assuming Newton’s law of cooling.

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Chapter 2 Solutions

To find:

The temperature of the kitchen by assuming Newton’s law of cooling.