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The heating capacity of a calorimeter is known to be 4

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

Solution for problem 7SE Chapter 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 7SE

The heating capacity of a calorimeter is known to be 4 kJ/°C, with negligible uncertainty. The number of dietary calories (kilocalories) per gram of a substance is given by C = cH(∆T)/m, where C is the number of dietary calories, H is the heating capacity of the calorimeter, ∆T is the increase in temperature in °C caused by burning the substance in the calorimeter, m is the mass of the substance in grams, and c = 0.2390 cal/kJ is the conversion factor from kilo- joules to dietary calories. An amount of mayonnaise with mass 0.40 ± 0.01 g is burned in a calorimeter. The temperature increase is 2.75 ± 0.02°C.

a. Estimate the number of dietary calories per gram of mayonnaise, and find the uncertainty in the estimate.

b. Find the relative uncertainty in the estimated number of dietary calories.

c. Which would provide a greater reduction in the uncertainty in C: reducing the uncertainty in the mass to 0.005 g or reducing the uncertainty in ∆T to 0.01°C?

Step-by-Step Solution:

Step 1:

The heating capacity of a calorimeter is known to be 4kJ/0C, with negligible uncertainty.The number of dietary calories per gram of a substance is given by C=cH (, where C is the dietary calories, H is the heating capacity, is the increase in the temperature in  0C, m is the

 mass of the substance in grams,and c=0.2390cal/KJ. An amount of mayonnaise with mass

0.40g is burned in a calorimeter. The temperature increase is 2.750C.

We have to find

The estimate of the number of dietary calories per gram of mayonnaise, and the uncertainty in the estimate.The relative uncertainty in the estimated number of dietary calories.Which provide a greater reduction in the uncertainty in C: reducing the uncertainty in the mass to 0.005g or reducing the uncertainty in to 0.01 0C.

Step 2:

Here the number of dietary calories per gram of a substance is given by

 

                     

                              C= cH (/m

           Here   H=4,

                       c= 0.2390,

                  ,

                 

                    m = 0.40 ,

                   .

          So

                                C = 

                                   = 

                                   =  6.57

To find the uncertainty in the number of dietary calories per gram of mayonnaise we have to find the uncertainty of C due to each factor.

                     

                                 =  

                                  =  2.39 g

             

                          =  

                                 =  

                                   =   -16.4312 g

                         

So the uncertainty due to all factors is

         

         =    

         =       0.17

 

So the  estimate of the number of dietary calories per gram of mayonnaise is

  C = ( 6.57Kcal.  And the uncertainty in the power loss is 0.17.

Step 3 of 4

Chapter 3, Problem 7SE is Solved
Step 4 of 4

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

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