Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 43 - Energy from the Nucleus - Problems - Page 1333: 47b

Answer

The energy released is 9.00 $\times 10^{6}$ J/kg.

Work Step by Step

In the reation, two oxygen atoms combine with one carbon atom and produce carbon dioxide. Mass of Oxygen is 16 u & mass of Carbon is 12 u. $\therefore$ Total initial mass is $2(16.0 \mathrm{u})+(12.0 \mathrm{u})=44$ u. Converting the mass into kg units, we get, $$ (44 \mathrm{u})\left(1.661 \times 10^{-27} \mathrm{kg} / \mathrm{u}\right)=7.31 \times 10^{-26} \mathrm{kg} $$ Thus, 7.31 $\times 10^{-26}$kg of initial reactants was used. From previous question, we know the amount of energgy produced per carbon atom which can be also simplified as each combustion event produces $6.58 \times 10^{-19} \mathrm{J}$ so the energy produced per unit mass of reactants is $\left(6.58 \times 10^{-19} \mathrm{J}\right) /\left(7.31 \times 10^{-26} \mathrm{kg}\right)=9.00 \times 10^{6} \mathrm{J} / \mathrm{kg}$
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