Explanation Given: A piece of metal is heated to 300 ° Celsius and then placed in a cooling liquid at 50 ° Celsius. After 4 minutes, the metal has cooled to 175 ° . Formula used: Use the newton law of cooling: F ( t ) = T 0 + C e − k t …… (1) where, F ( t ) , is the temperature after cooling of the material. T 0 , is the constant temperature of the new surrounding in which the material is kept. t , is the time for which the material is cooled down. And, C and k are constants. Calculations: Now for the first cooling time: F ( t ) = 300 T 0 = 50 t = 0 Put values in equation (1): F ( t ) = T 0 + C e − k t 300 = 50 + C e − k ⋅ 0 250 = C e 0 C = 250 Now for the second cooling time: F ( t ) = 175 T 0 = 50 t = 4 C = 250

Mathematics with Applications and Mylab Math with Pearson EText -- Title-Specific Access Card Package

12th Edition

ISBN: 9780134862668

Author: Lial, Margaret L.

Publisher: Pearson Education Canada

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Chapter 4, Problem 63RE

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To calculate: The temperature of the piece of metal after 12 minutes.

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Chapter 4, Problem 62RE

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