Phase diagram of water

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2 Gaseous Diffusion Uranium ore converted to UF 6 gas passed through very thin porous membranes. Light 235 U molecule diffuses faster than the heavier 238 U molecule. ~1400 stages to achieve 3-5% 235 U/ 238 U Enrichment 3 Ultracentrifuge Gaseous UF 6 is rotated at high angular velocity in a cascade of centrifuges, causing partial separation 4 Laser Separation Tuned lasers selectively ionise the lighter isotope in UF 6 vapour Positive ion attracted to charged collector plates – still being developed Energy Released by Fission Process Instantaneous Release (per fission) MeV Fission products 168 heat Neutrons 5 γ-rays 7 heat Delayed Release (per fission) MeV β-particles 8 heat γ-rays 7 heat Antineutrinos 12 lost from reactor Neutron Capture by 238 U β β n + 238 U 92 239 U 92 239 Np 93 239 Pu 94 23.5 m 2.3 d In practice many neutrons do not contribute to fission because they are absorbed by 238 U f(E) 0 2 4 6 Neutron energy (MeV) Neutron cross-sections on Uranium Barns 10 3 10 2 10 1 10 0 σ∼1/v Neutron Energy Distribution average energy Neutron energy density, f(E) f(E) ~ 0.77(E) 1/2 exp(−0.775E) On average, 2.44 neutrons are produced per fission Average neutron energy is ~ 2MeV fission by 235 U 92 capture by 238 U 92 fission by 238 U 92 10 −1 10 1 10 3 10 5 10 7 eV
Macroscopic cross-sections for natural uranium (Σ t = Σn i σ ti ) Factors affecting chain reaction 1) For each thermal neutron absorbed, η effective fast neutrons emitted η < ν, mean number produced (ν =2.42 for 235 U), because not all neutrons absorbed by fuel cause fission. Nat U (0.72% 235 U) η =1.33 2) Some fast neutrons cause fission before slowing down which increases the number of neutrons by the fast fission factor ε 3) The probability that a neutron will avoid resonance capture by 238 U the resonance escape probability p - depends on the moderator 4) The fraction of thermal neutrons that are absorbed by the fuel in the core (fuel, moderator, can) is called the thermal utilization factor f 5) There are a fraction l f of fast neutrons and a fraction l t of thermal neutrons that leak out of the reactor The neutron multiplication factor k is therefore given by: k = ηεpf(1− l f ) (1− l t ) For infinite core k ∞ = ηεpf Four factors formula Neutron Moderation Moderator is a medium for reducing the kinetic energy of neutrons from MeV to thermal level without losing many in the ‘resonant trap’ of 238 U m M For 180 deg scattering neutron E s = [(M − m)/(M + m)] 2 E i = [(A − 1)/(A + 1)] 2 E i For 0 deg scattering E s = E i Averaging, E s = ½{1 + [(A − 1)/(A + 1)] 2 }E s nucleus = [(A 2 + 1)/(A + 1) 2 ]E s (Averaging over all angles gives the same result) 1 H 12 C 238 U A 1 12 238 E s /E i 0.5 0.86 0.99 How many collisions required to reduce neutron energy from 2 MeV to 1 eV ? (factor of 2 10 6 ) Put (E s /E i ) n = 1/(2.10 6 ) = 5.10 −7 eg 1 H gives n ~ 21, 12 C gives n ~ 96 Moderating Ratio, MR Good moderators require • large σ elastic (σ el ) • low σ capture (σ c ) • significant loss in KE per collision • chemical stability (in hot, radioactive environment) Moderating ratio, MR = (1− E s /E i ) σ el /σ c Reactor Control H 2 O 62; D 2 O 4830; C 216 If the neutron flux increases to a higher level than that needed for a stable chain reaction, how can the reactor be controlled, ie how can equilibrium be restored?
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Phase diagram of water

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