Explanation Given: The initial temperature of a metal bar is 20 ° C and the given conditions are T ( 0 ) = 20 ° C and T ( 1 ) = 22 ° C . Calculation: Consider the equation for the Newton’s Law of heating. d T d t = k ( T − M ) (1) Here, M is the temperature of the boiling water, T is the temperature of the rod and k is the constant. Substitute 100 ° C for M in the equation (1). d T d t = k ( T − 100 ) (2) Separate the variables and integrate both sides. ∫ d T ( T − 100 ) = ∫ k d t ln | T − 100 | = k t + C T − 100 = e k t + C T ( t ) = 100 + C 1 e k t (3) Substitute 0 for t and T ( 0 ) = 20 ° C in equation (3). T ( 0 ) = 100 + C 1 e k ( 0 ) 20 = 100 + C 1 − 80 = C 1 Substitute − 80 for C 1 in equation (3). T ( t ) = 100 − 80 e k t (4) Substitute 1 for t and T ( 1 ) = 22 ° C in equation (4)

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.7, Problem 15E

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Calculate the time that will be taken by the bar to reach 90° C and 98° C.

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Chapter 2.7, Problem 14E

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Chapter 2 Solutions

Advanced Engineering Mathematics

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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Calculate the time that will be taken by the bar to reach 90 ° C and 98 ° C .

Solution Summary: The author calculates the time that will be taken by the bar to reach 90° and 98°.

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Calculate the time that will be taken by the bar to reach 90° C and 98° C.

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Chapter 2 Solutions