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I.3 守恆原理

I.3 守恆原理. I.3.1 能量守恆 I.3.2 動量守恆 I.3.3 角動量守恆. I.3.1 能量守恆. 一個隔絕系統內的能量，可以在動能，位能，熱能甚至質量之間互相轉換，但該系統之總能量維持不變。 K ( 動能 ) = 1/2 mv 2 U ( 位能 ) = mgh 重力位能 = 1/2 kx 2 彈性位能. Ex. 3-1 木塊 - 彈簧系統. Ex. 3-2 單擺. I.3.2 質能互換. E = mc 2 Q =  mc 2 Q ：反應中所釋放或吸收的能量

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I.3 守恆原理

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  1. I.3 守恆原理 • I.3.1 能量守恆 • I.3.2 動量守恆 • I.3.3 角動量守恆

  2. I.3.1 能量守恆 • 一個隔絕系統內的能量，可以在動能，位能，熱能甚至質量之間互相轉換，但該系統之總能量維持不變。 • K (動能) = 1/2 mv2 • U (位能) = mgh 重力位能 = 1/2 kx2彈性位能

  3. Ex. 3-1 木塊-彈簧系統

  4. Ex. 3-2 單擺

  5. I.3.2 質能互換 • E = mc2 • Q = mc2 • Q：反應中所釋放或吸收的能量 • m：反應物在反應後增加或減少之質量 • 化學反應 • 核分裂反應 • 核融合反應

  6. Nuclear Binding Energy

  7. Ex. 3-3 化學反應 2H2＋O2 2H2O Q = 4.85×105 J 反應物質量M = 2(2.0g)＋32.0g = 0.036㎏ 質量變化率:

  8. 核分裂反應的發現 • 德國物理學家 Otto Hahn 及 Fritz Strassmann 在1939年研究輻射問題時所發現 • 中子 + 鈾235 氪 + 鋇 + 中子

  9. A nuclear fission

  10. Ex. 3-4 核分裂反應－ 鈾235 235U＋ n  140Ce＋ 94Zr ＋ 2n 鈾 中子 鈰 鋯 235.04U 1.00867U 139.91U 93.91U 反應前後之質量差m = ( 235.04＋1.00867 ) － (139.91＋93.91＋2 ×1.00867 ) = 0.211u 釋放能量Q =  mc2= 0.211u ×932 = 197 Mev

  11. Ex. 3-4 Nuclear Fission 釋放能量Q = 197 Mev （一般化學反應僅數個電子伏特） m = 235.04u＋1.00867u = 236.65u 質量變化率f = m/m = 0.00089 ~ 0.1﹪

  12. 核融合反應 氘 + 氘  氦3 + 中子 + 能量 氘 + 氚  氦4 + 中子 + 能量

  13. 氘氚核融合反應

  14. A nuclear fusion

  15. Ex. 3-5 核融合反應－氘(重水) D ＋ D  T ＋ p 氘 氚 質子 2.01410u 3.01605u 1.00783u m = 2×2.01410－3.01605－1.00783 = 0.00432u

  16. Ex. 3-5 Nuclear Fusion

  17. I.3.3 核反應器(Nuclear Reactors) • 連鎖反應 (Chain Reactions) • 核彈 • 核能電廠 • 核反應器之基本結構 • 恆星的融合反應(太陽) • 地球上試驗的融合反應 • 磁圍阻 • 慣性圍阻

  18. 連鎖反應 (Chain Reaction) 核彈 核能電廠

  19. Chain Reactions • 核彈 • 實際上每次分裂釋出2.5個中子 (平均值) • 核能電廠 • 每次分裂釋出一個中子 • Critical (臨界) • Subcritical (次臨界) • Supercritical (超臨界)

  20. Atomic Bomb, Hydrogen Bomb and the Plutonium • Ne: 2.3 days Pu: 24000y • Both are 

  21. 原子彈

  22. Hiroshima from the ground

  23. Nagasaki after the Bomb

  24. 氫彈

  25. Hell opens up

  26. Ballistic missile submarine: a threat to world peace

  27. Submarine-launched ballistic missile

  28. 核反應器之基本結構 • 燃料棒－3﹪235U (0.07%) • 控制棒－B、Cd • 緩衝劑－水

  29. Reactor Core

  30. The Nuclear Fuel Cycle

  31. Olympic Dam Pit Head

  32. In-Situ Leach Mining

  33. Radioactive Wastes

  34. Depleted Uranium

  35. The Pressurized Water Reactor (PWR)

  36. The Boiling Water Reactor (BWR)

  37. Ex. 3-6 壓水式反應器 300℃ + 150 atm

  38. Nuclear Power Plant Accidents • 1952 Dec. 12, Chalk River, nr. Ottawa, Canada • 1957 Oct. 7, Windscale Pile No. 1, north of Liverpool, England • South Ural Mountains: • 1976 nr. Greifswald, East Germany • 1979 March 28, Three Mile Island, nr. Harrisburg, Pa. • 1986 April 26, Chernobyl, nr. Kiev, Ukraine • 1999 Sept. 30, Tokaimura, Japan

  39. Nuclear Power Plant Accidents • 1952 Dec. 12, Chalk River, nr. Ottawa, Canada: a partial meltdown of the reactor's uranium fuel core resulted after the accidental removal of four control rods. Although millions of gallons of radioactive water accumulated inside the reactor, there were no injuries. • 1957 Oct. 7, Windscale Pile No. 1, north of Liverpool, England: fire in a graphite-cooled reactor spewed radiation over the countryside, contaminating a 200-square-mile area.

  40. Nuclear Power Plant Accidents • South Ural Mountains: explosion of radioactive wastes at Soviet nuclear weapons factory 12 mi from city of Kyshtym forced the evacuation of over 10,000 people from a contaminated area. No casualties were reported by Soviet officials. • 1976 nr. Greifswald, East Germany: radioactive core of reactor in the Lubmin nuclear power plant nearly melted down due to the failure of safety systems during a fire.

  41. Nuclear Power Plant Accidents • 1979 March 28, Three Mile Island, nr. Harrisburg, Pa.: one of two reactors lost its coolant, which caused overheating and partial meltdown of its uranium core. Some radioactive water and gases were released.

  42. Nuclear Power Plant Accidents • 1986 April 26, Chernobyl, nr. Kiev, Ukraine: explosion and fire in the graphite core of one of four reactors released radioactive material that spread over part of the Soviet Union, eastern Europe, Scandinavia, and later western Europe. 31 claimed dead. Total casualties are unknown. Worst such accident to date.

  43. Nuclear Power Plant Accidents • 1999 Sept. 30, Tokaimura, Japan: uncontrolled chain reaction in a uranium-processing nuclear fuel plant spewed high levels of radioactive gas into the air killing one worker and seriously injuring two others. Japan's worst nuclear accident.

  44. 太陽的融合反應 • 太陽的輻射功率 = 3.9 ×1026 W • 如為化學反應，以太陽質量，僅能維持1000年；如為重力收縮~107年，但太陽的壽命已有50億年，不可能是核分裂，因為沒那麼多鈾。 • 結論: 融合反應（P-P cycle）

  45. 氘氚核融合反應

  46. A nuclear fusion

  47. P-P cycle － 1 點火溫度：一千五百萬度 氫氦

  48. P-P cycle － 2 • 氫燒完之後呢? 星球的演變 • 恆星是製造重元素的工廠 • 2個 (質子) 發生融合的機率~10-26，因此不會如同氫彈般爆炸。但恆星內部的氫密度極高，既使反應機率極低，仍可維持穩定的融合反應。另一方面，此反應之速率太慢，在地球上無法進行。

  49. 地球上試驗的融合反應 • D－T cycle ( 點火溫度：4千6百萬度) • D－D cycle ( 點火溫度：4億度) • 全電荷產物反應 (不需熱交換，但點火溫度更高) Heat Cycle

  50. D－T cycle D ＋ T  4He ＋ n n ＋ 6Li 4He ＋ T（氚）

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