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The change in temperature of an iron bar brought about by

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

Solution for problem 6E Chapter 3.3

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 6E

The change in temperature of an iron bar brought about by a transfer of heat is given by  where  is the amount of heat transferred, m is the mass of the bar, and c is the specific heat of iron. Assume that c = 448 J/kg°C and  are known with negligible uncertainty. Assume the mass is m = 0.54±0.01 kg. Estimate  and find the uncertainty in the estimate.

Step-by-Step Solution:
Step 1 of 3

Solution 6E

Step1 of 2:

Let us consider be the change in temperature of an iron bar brought about by a transfer of heat.

Where,

= the amount of heat transferred.

       = 1210 J.

   m = mass of the bar.

       = 0.540.01 Kg.

    c = the specific heat of iron.

       = 448 J/Kg0C.

We need to find the uncertainty in the estimate.

Step2 of 2:

From the given information we have = 1210, m = 0.54, c = 448,  

Consider,

                      = 1210/(0.54)(448)

               = 1210/241.92

      = 5.0016

Hence, = 5.0016.

Again consider,

Differentiate above equation with respect to “m” then

     

           =

         ...

Step 2 of 3

Chapter 3.3, Problem 6E is Solved
Step 3 of 3

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

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