Nuclear and Geothermal Energy PDF

ME165-2 Nuclear and Geothermal Energy 2.0 Energy from Nuclear Reactions Prepared by Engr. Estelito V. Mamuyac 29 August 2024  NUCLEAR BINDING ENERGY ▪ Nuclear binding energy – energy required to disassemble a nucleus into the same number of free unbound neutrons and prot...

ME165-2 Nuclear and Geothermal Energy 2.0 Energy from Nuclear Reactions Prepared by Engr. Estelito V. Mamuyac 29 August 2024  NUCLEAR BINDING ENERGY ▪ Nuclear binding energy – energy required to disassemble a nucleus into the same number of free unbound neutrons and protons it is composed of so that the nucleons are distant from each other which is enough to cause a strong nuclear force that prevents the particles from interacting. ▪ Nuclear binding energy is the “glue” that holds protons and neutrons together in the atomic nucleus.  NUCLEAR BINDING ENERGY  Figure provides an example of a mass defect. That is, the sum of the mass of the individual protons and neutrons differs from the overall mass of the nucleus.  The nucleus weighs less than the masses of the individual subatomic particles.  NUCLEAR EXCITATION ENERGY ▪ Excitation energy – energy required to elevate electron above an arbitrary baseline energy state (i.e. ground state)  ENERGY COMPUTATION – ELEMENTARY THEORY Note: 1 MeV = 1.60218 x 10-13 J For 1 atomic mass unit: 1 𝑢 C² = (1.66054 × 10−27 kg) × (2.99792 × 108 m/s)² = 1.49242 × 10−10 kg (m/s)² = 1.49242 × 10−10 J = 931.49 MeV E = MC2; thus, energy for 1 kg atomic mass = 5.61 × 1029 MeV  ENERGY COMPUTATION – ELEMENTARY THEORY For 13Al27 + 2He4---> 14 Si30 + H1 (Example from Lecture 1.3) 1 ∆m = Total MassProducts – Total MassReactants = 30.9816 – 30.9818 = -0.0002 amu Calculating for the energy released, or binding energy: E = ∆mc2 = -0.0002 amu x (931.49 MeV/amu) = -0.1863 MeV (the -/+ sign determines whether it’s endothermic or exothermic) E = 0.1863 MeV of energy was released from the reaction  ATOMIC MASS UNIT Atomic mass unit Atomic Sub-particles (amu) Neutron 1.00866 Proton 1.00728 Electron 0.000549 1 amu = 1.66054 x 10-27 kg  NUCLEAR BINDING ENERGY Example Problems: 1. A certain nuclear reaction gives off 22.1 MeV. Calculate the energy released in Joules. 2. The nuclear mass of Lithium-7 (7Li3) is reported as 7.016005 amu. Calculate its binding energy.  NUCLEAR REACTION  Nuclear Fission  The nucleus of an atom is split, causing energy to be released. Inside the nucleus of an atom, some of the mass takes the form of “binding energy”, the energy needed to hold the nucleus together. Splitting the nucleus of an atom, releases the binding energy.  If a massive nucleus like uranium-235 breaks apart, then there will be a net yield of energy because the sum of the masses of the fragments will be less than the mass of the uranium nucleus. If the mass of the fragments is equal to or greater than that of iron at the peak of the binding energy curve, then the nuclear particles will be more tightly bound than they were in the uranium nucleus, and that decrease in mass comes off in the form of energy according to the Einstein equation.  For elements lighter than iron, fusion will yield energy.  NUCLEAR REACTION - FISSION  Uranium-235 (235U) Fission  In one of the most remarkable phenomena in nature, a slow neutron can be captured by a uranium-235 nucleus, rendering it unstable toward nuclear fission.  A fast neutron will not be captured, so neutrons must be slowed down by moderation to increase their capture probability in fission reactors.  A single fission event can yield over 200 million times the energy of the neutron which triggered it!  NUCLEAR REACTION - FISSION  Uranium-235 (235U) Fission   Uranium-235 (235U) Fission NUCLEAR REACTION - FISSION If at least one neutron from each fission strikes another U-235 nucleus and initiates fission, then the chain reaction is sustained.  NUCLEAR REACTION - FISSION  Uranium-235 (235U) Fission  If the reaction will sustain itself, it is said to be "critical", and the mass of U-235 required to produced the critical condition is said to be a "critical mass".  A critical chain reaction can be achieved at low concentrations of U-235 if the neutrons from fission are moderated to lower their speed, since the probability for fission with slow neutrons is greater.  A fission chain reaction produces intermediate mass fragments which are highly radioactive and produce further energy by their radioactive decay. Some of them produce neutrons, called delayed neutrons, which contribute to the fission chain reaction.  NUCLEAR REACTION - FISSION Form of Energy Released Amount of Energy Released (MeV)  Energy from Uranium Fission Kinetic energy of two fission fragments 168 Immediate gamma rays 7 Delayed gamma rays 3-12 Fission neutrons 5 Energy of decay products of fission fragments... Gamma rays 7 Beta particles 8 Neutrons 12 Average total energy released 215 MeV  NUCLEAR REACTION - FUSION  Nuclear Fusion  Fusion, the exact opposite of fission, occurs by joining two light nuclei into one heavier nucleus, and clean nuclear energy is given off when they join.  Fusion could produce a self sustaining energy source.  Fusion, or a thermonuclear reaction, can starts only at temperatures of many millions of degrees – even hotter than the sun.  Such intense heat destroys anything on earth that tries to hold or contain it, and a heat source that hot is hard to control. The hydrogen bomb, a fusion reaction designed to explode, needed an atomic fission bomb to get it started.  NUCLEAR REACTION - FUSION  If light nuclei are forced together, they will fuse with a yield of energy because the mass of the combination will be less than the sum of the masses of the individual nuclei.  If the combined nuclear mass is less than that of iron at the peak of the binding energy curve, then the nuclear particles will be more tightly bound than they were in the lighter nuclei, and that decrease in mass comes off in the form of energy according to the Einstein relationship.  For elements heavier than iron, fission will yield energy.  NUCLEAR REACTION - FUSION  For potential nuclear energy sources for the Earth, the deuterium-tritium fusion reaction contained by some kind of magnetic confinement seems the most likely path. However, for the fueling of the stars, other fusion reactions will dominate. NUCLEAR REACTION - FUSION  Deuterium-Tritium Fusion  The most promising of the hydrogen fusion reactions which make up the deuterium cycle is the fusion of deuterium and tritium.  The reaction yields 17.6 MeV of energy but requires a temperature of approximately 40 million Kelvins to overcome the coulomb barrier and ignite it.  The deuterium fuel is abundant, but tritium must be either bred from lithium or gotten in the operation of the deuterium cycle.  NUCLEAR REACTION Hydrogen Fusion Reactions  Even though a lot of energy is required to overcome the Coulomb barrier and initiate hydrogen fusion, the energy yields are enough to encourage continued research.  Hydrogen fusion on the earth could make use of the reactions:  NUCLEAR REACTION - FUSION  Hydrogen Fusion Reactions  NUCLEAR REACTION  Deuterium Cycle of Fusion  The four fusion reactions which can occur with deuterium can be considered to form a deuterium cycle. The four reactions:  can be combined as  or, omitting those constituents whose concentrations do not change:  NUCLEAR FUEL BURNUP  In nuclear power technology, burnup (also known as fuel utilization) is a measure of how much energy is extracted from a primary nuclear fuel source.  It is measured both as the fraction of fuel atoms that underwent fission in %FIMA (fissions per initial metal atom) and as the actual energy released per mass of initial fuel in gigawatt-days/metric ton of heavy metal (GWd/tHM), or similar units.  Expressed as a percentage, burnup is simple: if 5% of the initial heavy metal atoms have undergone fission, the burnup is 5%. In reactor operations, this percentage is difficult to measure, so the alternative definition is preferred.  NUCLEAR FUEL BURNUP  This can be computed by multiplying the thermal power of the plant by the time of operation and dividing by the mass of the initial fuel loading.  For example, if a 3000 MW thermal (equivalent to 1000 MW electric) plant uses 24 metric tons of enriched uranium (tU) and operates at full power for 1 year, what is the average burnup of the fuel? Ave. BurnUp = (3000 MW X 365 d) / 24 metric tons = 45,625 MW-d/tHM (where HM stands for heavy metal, meaning actinides like Uranium, Plutonium, etc.).  NUCLEAR FUEL BURNUP  Converting between percent and energy/mass requires knowledge of κ, the thermal energy released per fission event. A typical value is 193.7 MeV (3.1X 10-11 J) of thermal energy per fission. With this value, the maximum burnup of 100%, which includes fissioning not just fissile content but also the other fissionable nuclides, is equivalent to about 909 GWd/t. Nuclear engineers often use this to roughly approximate 10% burnup as just less than 100 GWd/t.  TEXTBOOKS & REFERENCES References Textbooks  Nuclear Energy – An Introduction to the Concepts, Systems, and Applications of Nuclear Processes, Raymond L. Murray, 6th Ed., 2009 Web  http://en.wikipedia.org/wiki/Radioactive_decay