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Refer to Exercise 6. Assume that c = 448 J/kg °C and ?Q =

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

Solution for problem 16E 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 16E

Refer to Exercise  Assume that  and  are known with negligible uncertainty. Assume the mass is . Estimate , and find the relative uncertainty in the estimate.

Step-by-Step Solution:

Solution:

Step 1 of 1:

The change in temperature of an iron bar about by a transfer of heat is

Where is the amount of heat transferred.

Here .

m is the mass of the bar.

Here  kg and

c is the the specific heat of iron.

Here c = 448 J/Kg0C.

Our goal is:

We need to find the estimate value of the and the relative uncertainty in the estimate.

Now we have to find the estimate value of the .

From the given information we have = 1210, m = 0.75, c = 448,  

Consider,

Substitute all the values in the above equation.

      =

 =

      = 3.6011

Therefore, = 3.6011.

Again consider .

Then,

Now we differentiate above equation with respect to “m” then

    

           =

                =

               =

         =

                                                              =

              =

    =

  = -4.8015

Therefore, = -4.8015.

Now we have to find the estimate of uncertainty.

Then the estimate of uncertainty is given by

                  =  

Here

            = (4.8015)(0.01)

= 0.0480

Hence,

Therefore, The estimate of uncertainty is 0.0480.


Conclusion:

The estimate of uncertainty is 0.0480.


 

Step 2 of 1

Chapter 3.3, Problem 16E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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Refer to Exercise 6. Assume that c = 448 J/kg °C and ?Q =