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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 6. Assume that c = 448 J/kg °C and ∆Q = 1210 J are known with negligible uncertainty. Assume the mass is m = 0.75 ± 0.01 kg. Estimate ∆T, and find the relative uncertainty in the estimate.

EXERCISE 6: 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 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

    

 ...

Step 2 of 3

Chapter 3.3, Problem 16E is Solved
Step 3 of 3

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 =

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