Question #160323
A family living in a villa consumes about 25 MWh of energy per year. We imagine that this energy could be produced in a fusion power plant that uses the nuclear reaction H + H -> He + n, where H stands for deuterium, He for helium-3 and n for neutron. We also assume that the efficiency of the fusion power plant is 30%. How many grams of deuterium are needed each year to produce energy for this family?
1
Expert's answer
2021-02-01T15:04:37-0500

The energy of this reaction is


Ep=3.27 MeVE_p=3.27\ MeV

Eyear=ηEpm2mD25(3600)=(0.3)(3.27)(1.61019)m2(3.34351027)m=0.00383 kg=3.83 gE_{year}=\eta E_p \frac{m}{2m_D}\\25(3600)=(0.3)(3.27)(1.6\cdot10^{-19})\frac{m}{2(3.3435\cdot 10^{-27})}\\m=0.00383\ kg=3.83\ g


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