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A nutritionist determines the caloric value of a 10.0 g sample of beef fat by burning...

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spock4 | Student, Undergraduate | (Level 1) Honors

Posted May 7, 2013 at 10:24 AM via web

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A nutritionist determines the caloric value of a 10.0 g sample of beef fat by burning it in a bomb calorimeter (at constant volume). The calorimeter held 2.500 kg of water, the heat capacity of the bomb is 1.360 kJ/degrees celcius, and the temperature of a calorimeter is increased from 25 degrees celcius to 56.9 degrees celcius. Calculate the number of Joules released per gram of beef fat. What is the dietary caloric value of beef fat in calories per gram?

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jerichorayel | College Teacher | (Level 1) Senior Educator

Posted May 15, 2013 at 5:36 PM (Answer #1)

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As the beef fat is burned, it transfers its energy to its surroundings. So the total amount of heat absorbed by the surroundings is equal to the heat absorbed the calorimeter plus the heat absorbed by the water. 

`Heat_(t o t a l) = Heat_(calo rimeter) + Heat_(water)`

Given:

Mass of the sample: `10.00 g`
Mass of water: `2.500 kg = 2500 grams`
Heat capacity of the bomb: `(1.360 kJ)/(C^(o))`
change in T = `56.9 - 25.0 =31.9 C^(o)`

Heat capacity of water = `4.185 (J)/(g ^(o) C)`

 

`Heat_(calo rimeter) =(1.360 kJ)/(degrees) C^(o) * 31.9C^(o)`

`Heat_(cal o rimeter) = 43.384 kJ = 43384 jou l es`

 

`Heat_(water) = 2500 kg *4.185 (J)/(g ^(o) C) * 31.9C^(o)`

`Heat_(water) = 333674 jou l es`

 

`Heat_(t o t a l) = Heat_(calo rimeter) + Heat_(water)`

`Heat_(t o t a l) =43384 +333674`

`Heat_(t o t a l) = 377 058 jou l es`

 

Number of joules released per gram of fat:

`(377 058 jou l es)/(10.0 grams) = 37705.8 (jou l e s)/(g) -> a n s w e r`

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