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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,  is the mass of the bar, and  is the specific heat of iron. Assume that  and  are known with negligible uncertainty. Assume the mass is   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

     

           =

                =  

              =

        =

                                                             =

             =

        = 

   = -9.2623

Hence, = -9.2623.

The estimate of uncertainty is given by

                 =  

            = (9.2623)(0.01)

= 0.0926

Hence,

Therefore, The estimate of uncertainty is 0.0926.


Conclusion:

The estimate of uncertainty is 0.0926.

 

 

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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