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According to Newton’s law of cooling, the time t needed

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

Solution for problem 16E Chapter 3.4

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 16E

According to Newton’s law of cooling, the time t needed for an object at an initial temperature T0 to cool to a temperature T in an environment with ambient temperature Ta is given by

     

where k is a constant. Assume that for a certain type of container, k = 0.025 min-1. Let t be the number of minutes needed to cool the container to a temperature of 50°F. Assume that T0 = 70.1 ± 0.2°F and Ta = 35.7 ± 0.1 °F. Estimate t, and find the uncertainty in the estimate.

Step-by-Step Solution:

Answer:

Step 1 of 2</p>

In this question we are asked to find the estimate of Newton’s law cooling equation and the uncertainty in the estimate.

Newton’s law cooling equation  = -…………..(1)

Where

 t is the number of minutes needed to cool the container

is a initial temperature

 is an ambient temperature

 is a constant

is a cooling temperature

Given parameters:

 = 0.025 , = 70.1 ± 0.2°F, = 35.7 ± 0.1 °F and

The quantity which we are estimating has several measurements. In this question we are measuring the initial temperature  and ambient temperature . These quantity mentioned here is uncertain and independent measurements.

So here we can use the following basic formula.

       ……………...(2)

Where , ,........, are independent measurements and uncertainties are , ,.........,

Equation 2 is called the multivariate propagation of error formula.

Step 2 of 2

Chapter 3.4, Problem 16E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The answer to “According to Newton’s law of cooling, the time t needed for an object at an initial temperature T0 to cool to a temperature T in an environment with ambient temperature Ta is given by where k is a constant. Assume that for a certain type of container, k = 0.025 min-1. Let t be the number of minutes needed to cool the container to a temperature of 50°F. Assume that T0 = 70.1 ± 0.2°F and Ta = 35.7 ± 0.1 °F. Estimate t, and find the uncertainty in the estimate.” is broken down into a number of easy to follow steps, and 91 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 16E from chapter: 3.4 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 16E from 3.4 chapter was answered, more than 305 students have viewed the full step-by-step answer. This full solution covers the following key subjects: temperature, estimate, needed, assume, container. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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