Phase diagram of water

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Lower ‘control rods’ into reactor to absorb excess neutrons Materials used: 113 Cd (σ c = 20,000 barns) 10 B (σ c = 4,000 barns) cross section is for thermal neutrons (~0.025 eV) [σ c (max) ~ π(λ/2π) 2 ∼ 2.6 10 7 barns] (withdraw control rods if reactivity gets too low) In practice control would be virtually impossible but for the existence of ‘delayed’ neutrons Delayed neutrons are released only after the β-decay of a fission product Typically, about 1% of neutrons produced by fission are delayed by 10-20 seconds, which is enough time for small adjustments in the position of the control rods (automatically controlled) eg 87 Br β − t 1/2 54.5 s n 87 Kr * 86 Kr 137 I β − t 1/2 21.8 s n 137 Xe * 136 Xe Neutron Population Growth η is number of neutrons emitted per neutron absorbed Because of losses the mean number is k, where k < η k is the effective multiplication factor If all neutrons were prompt the neutron population would grow like dn/dt = n(k−1)/τ = nq/τ where q=(k−1) and τ is the average neutron lifetime in the reactor So n = n o exp{qt/τ} eg q = 0.001, τ = 0.001 second gives n = n o exp(t), so after 10 s n/n o increases by a factor of 22,000 In 235 U the mean lifetime of the groups of delayed neutrons is about τ d = 9 s and they represent a fraction β = 0.65% of the total neutron emission 235 U delayed neutrons If q
Safety Features in a PWR • The control rods can be lowered fully in the case of an emergency • Should the pressure drop in the primary loop and the water start to boil, the creation of bubbles (voids) decreases the moderation and also the absorption. The effect on the moderation is the more significant and the chain reaction stops and the reactor is no longer critical • The moderation is also decreased if the core temperature rises, as this increases the Doppler broadening of the 238 U resonances, which decreases the resonance escape probability p • A loss-of-coolant accident (LOCA) in which the water in the primary loop is lost requires additional emergency cooling to be available. The outer containment vessel provides a final barrier and worked successfully in the Three Mile Island accident Power Output of Nuclear Reactor Reaction rate R = (Neutron Flux)×(Cross-section)×(Number of Nuclei) Flux φ = Neutrons m −2 s −1 Number of Nuclei = N Cross-section σ = effective area, unit is barn = 10 −28 m 2 Example: Reactor core contains 10 4 kg of uranium enriched to 2% in 235 U. Cross-section for neutron induced fission of 235 U = 579 barns. Flux φ = 10 18 m −2 s −1 . Calculate the power output. Number of 235 U nuclei = 10 4 (1000/238)(6 ×10 23 )(0.02) = 5.0×10 26 R = φσN = 10 18 ×579×10 −28 ×5.0×10 26 = 2.9×10 19 s −1 Energy per fission = 200 MeV = 200×10 6 ×1.6×10 −19 = 3.2×10 −11 J So power output = 3.2×10 −11 ×2.9×10 19 = 0.93 GW th . 10 4 kg U(2%) 5.0×10 26 × 3.2 ×10 −11 J = 1.6 × 10 16 J ≡ 0.5 GW th y Fast Breeder Reactors (FBR) Predicted fossil reserves ~ 8.10 22 J Fission reactors (thermal neutron) ~ 4.10 21 J Fast breeder reactors (fast neutrons) ~ 2.10 23 J fast breeder reactors are possible long-term solution to world’s energy needs (~10 3 years) - ~50 times fission reactor energy reserve Fission reactors consume 235 U so < 1% uranium utilised Fast breeder reactors have small core of highly enriched fissile fuel with no moderator. Emitted fast neutrons convert surrounding 238 U to fissile 239 Pu quicker than fuel consumed by fast neutron induced fission in core. Basic reactions β − β − α n + 238 U 239 U 239 Np 239 Pu 235 U t 1/2 =23.5m t 1/2 =2.35d t 1/2 =24,000y ‘fertile’ ie spawns Pu ‘fissile’ ie chain reaction
Page 1 and 2: Thermal Power Origins of Steam Powe
Page 3 and 4: Frictional losses across turbine bl
Page 5 and 6: Types of Fossil Fuel Power Stations
Page 7 and 8: B/A Fusion Binding Energy of Nuclei
Page 9: Macroscopic cross-sections for natu
Page 13 and 14: Environmental Impact of Nuclear Pow

Phase diagram of water

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