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According to Newton’s law of cooling, the temperature T of

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 11E Chapter 3.2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 11E

Problem 11E

According to Newton’s law of cooling, the temperature T of a body at time t is given by T = Ta+ (T0 – Ta) e-kt, where Ta is the ambient temperature, T0 is the initial temperature, and k is the cooling rate constant. For a certain type of beverage container, the value of k is known to be 0.025 min-1.

a. Assume that Ta = 36°F exactly and that T0 = 72.0 ± 0.5°F. Estimate the temperature T at time t = 10 min, and find the uncertainty in the estimate.

b. Assume that T0 = 72°F exactly and that Ta = 36.0 ± 0.5°F. Estimate the temperature T at time t = 10 min, and find the uncertainty, in the estimate.

Step-by-Step Solution:

Answer :

Step 1 of 3:

        According to the Newton’s law of cooling, the temperature T of a body at time t is given by  

                   

                   Where,  is the ambient temperature

                                   is the initial temperature

                                    k is the cooling rate constant.

                       Here the value of k is 0.025


Step 2 of 3

Chapter 3.2, Problem 11E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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According to Newton’s law of cooling, the temperature T of