Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 31 - Nuclear Energy; Effects and Uses of Radiation - Problems - Page 912: 35

Answer

5600 kg of natural water per hour.

Work Step by Step

We are told to assume an efficiency of $33\%$. This means that the reactions actually generate a power of 1150MW/0.33. Now that we know the average power for an hour, find the amount of energy. $$\frac{(1150\times10^6 J)/0.33}{s}\frac{3600s}{hour}\frac{MeV}{1.60\times10^{-13}J}=7.841\times10^{25}MeV/h$$ Change this to an amount of deuterium. If we assume that the two d-d reactions take place at equal rates, then 4 deuterons react to release 4.03MeV+3.27 MeV= 7.30 MeV. This is an average of 1.825 MeV per deuteron. $$(7.841\times10^{25}MeV/h)\frac{deuterium}{1.825MeV}=4.296\times10^{25} deuterons/h$$ Convert that figure to an amount of water. We know the fraction of deuterium vs regular H in natural water is $0.0115\%$. $$(4.296\times10^{25} deuterons/h)\frac{1H}{0.000115d}\frac{H_2O}{2H}\frac{0.018kg}{6.02\times10^{23}molecules}$$ $$\approx5600\;kg/h$$
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