Explanation Given information: Let the time taken for the temperature difference ( y − T 0 ) to decrease by a factor e − 1 be τ sec. k = 1 τ is called the characteristic time. Formula used: Newton’s law of cooling y ' ( t ) = − k ( y − T 0 ) Calculation: Let the time taken for the temperature difference ( y − T 0 ) to decrease by a factor e − 1 be τ sec. Therefore, by newton’s law of cooling y ' ( t ) = − k ( y − T 0 ) Solution to the above differential equation is y ( t ) = T 0 + C e − k t ......... ( 1 ) Therefore, from ( 1 ) y − T 0 = C e − k t ....... ( 2 ) When the temperature difference ( y − T 0 ) decreases by a factor e − 1 in time τ sec

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 9.2, Problem 12E

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Show that τ is the time required for the temperature difference (y−T0) to decrease by the factor e−1≈0.37.

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Chapter 9.2, Problem 11E

Chapter 9.2, Problem 13E

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Show that τ is the time required for the temperature difference ( y − T 0 ) to decrease by the factor e − 1 ≈ 0.37 .

Solution Summary: The author explains how Newton's law of cooling reduces the temperature difference by a factor e-1betau sec.

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Show that τ is the time required for the temperature difference (y−T0) to decrease by the factor e−1≈0.37.

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