Question 13.8: A thermonuclear fusion reactor is assumed to be used for pow......
A thermonuclear fusion reactor is assumed to be used for power generation under the following conditions:
• Annual consumption of deuterium D is 20 kg/a and tritium T is 30 kg/a
• Corresponding number of D and T moles is n = 1 \times 10^{4} moles each
• Annual duration of the reactor operation \tau is 7560 h per year
• Energy conversion efficiency of the fusion reactor is \eta = 0.43
Avogadro number is N = 6.023 \times 10^{23} molecules/atoms per mole and the energy released in a D–T fusion reaction is E_{f} = 17.59 MeV.
Estimate (i) the annual amount of energy released in the reactor E_{yr}, and (ii) the average electric power output P_{el} of the reactor.
1. Amount of energy released in the fusion reactor during 1 year
E_{y r}=n~N\,E_{f}=1\times10^{4}\times6.023\times10^{23}\times17.59~\mathrm{MeV}=1.059\times10^{29}~\mathrm{MeV}/\mathrm{a}As 1 MeV =\,1.609\times10^{-13}\, J, hence
E_{_{yr}}=1.059\times10^{29}\,\,\mathrm{MeV}/{\bf a}\times1.609\times10^{-13}\,\mathrm{J/MeV}=1.704\times10^{16}\,\mathrm{J}/\mathrm{a}2. Average electric power output of the fusion reactor
P_{\mathrm{el}}=E_{\mathrm{{yr}}}\,\eta/\tau=(1.704\times10^{16}\,\mathrm{J}/\mathrm{a\times0.43})/(7560\,\mathrm{{h/a\times3600\,s/h}})=269.2\,\mathrm{{MW}}