In 2016 there were 450 nuclear power plants with a total installed power capacit

Question

In 2016 there were 450 nuclear power plants with a total installed power capacity of 400 GWe worldwide. Assume all are run with 3.5% enriched LEU fuel, have an average thermal efficiency of 30% and a capacity factor of 80%. Assume all power generated by the fission stems from 235U, whose fission products and energies are given in table 10-5 below.

all the rest. roin ft gion of one uranium is availah Tabla 5: Typical Energy Released in 235 Fragment Kinetic Energies 170 MeV KE of 2 or 3 neutrons emitted Prompt y-rays 5 gammas) 7 B-particles Fission Fragment Decay Antineutrinos -Gammas Total 207 MeV

Explanation / Answer

Per fission of U-235 we get (170 +5 ) Mev as thermal energy where as the other beata nad gama decays are not useful to generate energy

30% thermal efficiency => 175 *0.3 = 52.5 mev is converted

400 GW power

80 % capacity = 320 GW

energy produce per year = 320e+9 *3600*24*365*3600 = 1.01e+19 J

                               = 1.01e+19/ 1.609e-19 ev

                               = 6.28 e+31 Mev

    No U-235 atoms required to produce the energy = 6.28e+31/52.5 = 1.2e+30

     1mole 235 gm of U-235 has 6.02e+23 atoms

                mass of U-235 = 1.2e+30/6.02e+23 *(235) = 4.68 e+8 gms per plant

for 450 plants   = 4.68e+8*450

                         = 2.12 e+11 gms

                          = 2.12e+7 kgs

                          = 2.12 e+4 tons of U-235

Natural U contains 0.7 % of U-235

natural U required = 2.12e+4*100/0.7 = 3.03e+6 tons

The assumtion that the KE of the framents and the neutrons is fully converted to thermal energy, this may increase or decrease the actual energy produced.

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