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17. Thermal Behavior of Matter 物質的熱行為

17. Thermal Behavior of Matter 物質的熱行為. Gases 氣體 Phase Changes 相變 Thermal Expansion 熱膨脹. What unusual property of water is evident in this photo? 這照片顯露了水的那一種特性？. Ice is less dense than water. 冰的密度比水低。. 17.1. Gases 氣體. The Ideal Gas Law : 理想氣體定律 ：.

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17. Thermal Behavior of Matter 物質的熱行為

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  1. 17. Thermal Behavior of Matter 物質的熱行為 Gases 氣體 Phase Changes 相變 Thermal Expansion 熱膨脹

  2. What unusual property of water is evident in this photo? 這照片顯露了水的那一種特性？ Ice is less dense than water. 冰的密度比水低。

  3. 17.1. Gases 氣體 The Ideal Gas Law: 理想氣體定律： k = 1.381023 J / K = Boltzmann’s constant 波爾茲曼常數 N = number of molecules 分子數目 NA = 6.0221023 = Avogadro’s number 阿佛加德羅數字 =number of atoms in 12 g of 12C 12克12C裏面的原子數 n = number of moles (mol) 摩爾數 1 mole of matter contains NA molecules. 一摩爾包含 NA 個分子 A piston-cylinder system. 一個活塞-氣缸系统。 = 8.314 J / K mol = Universal gas constant 通用氣體常數 All gases become ideal if sufficiently dilute. 在充份稀釋後，所有氣體都會變成理想。

  4. Example 17.1. STP 標準温壓 What volume is occupied by 1.00 mol of an ideal gas at standard temperature & pressure (STP), where T = 0C, & p = 101.3 kPa = 1 atm? 在標準温壓下 ( T = 0C, & p = 101.3 kPa = 1 atm )， 1.00 mol 理想氣體的體積為何？ ( last figure subject to round-off error ) 末位數含四捨五入誤差

  5. Kinetic Theory of the Ideal Gas 理想氣體的運動理論 • Kinetic theory 運動理論 ( Newtonian mechanics 牛頓力學 ): • Gas consists of identical “point” molecules of mass m. • 氣體由全部一樣，質量為 m 的〝點〞分子組成。 • No interaction between molecules, except when they collide. • 分子之間除碰撞時無相互作用。 • Random motion. 隨機運動。 • Collisions with wall are elastic. 與容壁的碰撞都是彈性的。 表面積

  6. Molecule i collides with right-hand wall (RHW). 分子 i 碰上右壁 Momentum transfer to wall is 動量轉移為 in No intermolecular collision • Next collision with RHW occurs at 無分子互撞 下次碰撞右壁的時間為 Average force of i on RHW: i 加於右壁的平均力為 out Random motion  隨機運動  Ideal gas law is recovered if 欲得理想氣體定律，祗需 T~ K

  7. Example 17.2. Air Molecule 空氣分子 Find K of a molecule in air at room temperature ( 20C = 293K), 找出在室温 (20C = 293K) 空氣中一個分子的 K ， & determine the speed of a N2 molecule with this energy. 再决定一個能量為此值的氮分子(N2)的速率。 Thermal speed: 熱速率

  8. Distribution of Molecular Speeds 分子速率的分佈 Maxwell-Boltzmann Distribution: (elastic collisions between free particles) 麥克斯韋-波爾茲曼分佈: ( 自由粒子間的彈性碰撞 ) 80 K 分子數 High-E tail extends rapidly with T 高-E 尾巴隨 T快速延展 • chemical reaction easier at high T 化學反應在高 T 時較易進行 • cooling of liquid 液體冷卻 ( by escape of high-E molecules) ( 緣於高-E分子逃逸 ) 300K vth vth 分子速率

  9. Real Gases 實在的氣體 • Important corrections to the ideal gas model 理想氣體模型的重要修正: • finite size of molecules  available V reduced. • 分子大小非零  可用 V 變小。 • Attractive interaction between molecules (van der Waals forces)  reduced P. • 分子的互吸作用 (范得瓦力)  P 變小  minimum volume 最小體積 van der Waals equation 范得瓦方程式

  10. 17.2. Phase Changes 相變 Phase changes take place at fixed T = TCuntil whole system is in the new phase. 相變時温度固定在 T = TC，直至整個系统變成新相為止。 ( breaking / building bonds raises U but keeps K unchanged ) ( 打斷 ／建立化學鍵會提高 U 但保持 K 不變 ) Heat of transformation 相變熱 L = energy per unit mass needed to change phase. 相變時單位質量所需熱量 Lf= Heat of fusion ( solid  liquid ) 熔解熱 ( 固  液 ) Lv= Heat of vaporization ( liquid  gas ) 蒸發熱 ( 液  氣 ) Ls= Heat of sublimation ( solid  gas ) 昇華熱 ( 固  氣 )

  11. 相變熱 (大氣壓下) 物質 熔點 沸點 酒精，乙基 銅 鉛 水銀 氧 硫 水 鈾 • Same E to melt 1 g ice or heat water by 80 C 熔解 1 g 冰和水升温 80 C 需要同樣的熱量。 Water:水

  12. Conceptual Example 17.1. Water Phases 水相 You put a block of ice initially at －20C in a pan on a hot stove with a constant power output, 你把一塊原來在 －20C 的冰塊，放在一個功率固定的熱爐上的鍋子裏加熱， and heat it until it has melted, boiled, and evaporated. 等它融化，沸騰，而全部蒸發。 Make a sketch of temperature versus time for this experiment. 把這實驗用一個温度對時間的圖表達。 steam warming 蒸氣加温中 boiling沸騰中 water warming 水加温中 温度 melting 熔解中 ice warming 冰加温中 時間

  13. Making the Connection 連起來 If you start with 0.95 kg of ice at －20C and supply heat at the rate of 1.6 kW, 如果你開始時用一塊在 －20C 的 0.95 kg 冰塊，且以 1.6 kW 的速率加熱， how much time will it take until you’re left with only water vapor? 要多久你才會祗剩下水蒸氣？ Heat needed to warm ice to 0 C 把冰加温到 0 C 需熱 : Heat needed to melt ice at 0 C 在 0 C 把冰融解需熱 : Heat needed to warm water to 100 C 把水加温到 100 C 需熱 : Heat needed to vaporize water at 100 C 在 100 C 把水蒸發需熱 : Time needed : 需時 :

  14. GOT IT 懂嗎 ? 17.2. You bring a pot of water to boil & then forget about it. 你把一壺水燒開之後把它忘了。 10 min later you come back & find it still boiling. 10 分鐘後你回來發現它還在沸騰。 Is its temperature 它的温度是 (a) less, (b) greater than, or (c) equal to (a) 小於，(b) 大於， 還是 (c) 等於 100 C ?

  15. Example 17.3. Meltdown 熔毀 ! A nuclear power plant’s reactor vessel cracks, draining all cooling water. 一個核電廠的反應堆容器破裂，把全部的冷卻用水流光。 Although nuclear fission stops, radioactive decay continues to heat the reactor’s 2.5105 kg uranium core at the rate of 120 MW. 雖然核分裂已停止，放射性衰變卻繼續以 120 MW 的功率加熱反應堆內 2.5105 kg 的鈾核心。 Once the melting point is reached, how much energy will it take to melt the core? 一旦達到熔點，還需要多少能量才可以把核心熔解？ How long will the melting take? 熔解過程要多久？ Table 17.1: for U Time to melt the core: 核心熔解需時

  16. Example 17.4. Enough Ice 冰夠嗎 ? When 200 g of ice at 10 C are added to 1.0 kg of water at 15 C, is there enough ice to cool the water to 0 C? 把 200 g 的 10 C 冰加到 1.0 kg 的 15 C 水之後，有沒有足夠的冰把水冷到 0 C ？ If so, how much ice is left in the mixture? 如果夠，那剩餘的冰有多少？ Heat released to bring water down to 0 C 把水降到 0 C 放出熱能 Heat required to bring ice up to 0 C 把冰升到 0 C 需用熱能 Heat required to melt ice at 0 C 把冰在 0 C 熔掉需用熱能  more than enough ice 有足夠的冰 Ice needed: 需要的冰 • ice left = 剩下的冰

  17. Phase Diagrams 相變圖 AB: low P, s  g 低 P ，固  氣 Sublimation: solid  gas 昇華: 固體  氣體 e.g., dry ice 乾冰 ( s-CO2 ) PC Solid固態 Melting 熔解 C.P. 臨界點 CD: medium P, s  l  g 中 P ，固 液  氣 liquid液態 壓力 Critical point 臨界點 Supercritical fluid : l-g indistinguishable 超臨界流體: 液-氣不可分 Boiling 沸騰 Gas 氣態 Sublimation 昇華 GH: medium T, l  g 中T， 液  氣 T.P. 三相點 TC EF: high P, s  l / f 高 P ， 固  液／流 温度 Phase diagram: P vs T 相變圖: P 對 T Triple point: s-l-g coexist 三相點: 固 -液-氣共存 = 273.16K, 0.6 kPa for H2O Caution: Phase transition doesn’t occur instantaneously 注意: 相變不是瞬間發生的

  18. 17.3. Thermal Expansion 熱膨脹 Coefficient of volume expansion : 體積膨脹係數 Prob. 69 Coefficient of linear expansion : 線膨脹係數 Prob. 72

  19. 膨脹係數* 固體 液和氣體 鋁 黃銅 銅 玻璃 (派萊克斯) 冰 不脹鋼 鋼 空氣 酒精，乙基汽油 水銀 水，1C 水，20C 水，50C * 除非特別標明，都在室温附近。 † 不脹鋼含 64% 鐵和 36% 鎳；是一種特別為減少熱膨脹而配成的合金。

  20. GOT IT? 17.3. If a donut-shaped object is heated, will the hole get 如果一個甜圈餅形的物體受熱，它的洞會變 (a) larger, or (b) smaller ? (a) 大， 或 (b) 小？

  21. Example 17.5. Spilled Gasoline 溢出的汽油 A steel gas can holds 20 L at 10C. 一個鋼制汽油礶在 10C 時可裝 20 L 。 It’s filled to the brim at 10C. 它在 10C 時剛好裝滿。 If the temperature is now increased to 25C, 假如温度現在上升到 25C， by how much does the can’s volume increase? 礶子的體積增加多少？ How much gas spills out?有多少汽油溢出？ Table 17.2:   Spilled gas: 溢油量

  22. Thermal Expansion of Water 水的熱膨脹 At 1C Reason: Ice crystal is open  ice  water 原因: 冰晶體的結構開放  ice floats 冰浮水上 max water occurs at 4C water 最大值在 4C > 0 < 0 臨界點 液 固 At fixed T Tm , ice melts if P. 在固定的 T Tm 下， 冰會在 P 時熔解。 Application: skating. 應用: 溜冰 氣 三相點

  23. Application: Aquatic Life & Lake Turnover應用： 水中生態和湖水翻轉 Anomalous behavior of ice-water makes aquatic life in freezing weather possible. 冰-水的異常行為使得就算在冰寒的天氣下，仍然可以在水中生活。 If deep enough, bottom water stays at 4C even when surface is iced over. 如果水夠深，就算表面已經冰封，底部的水仍然會保持在 4C 。 In a lake where bottom water stays at 4C year round, 在一個底部的水整年都保持在 4C 的湖裏， surface & bottom water can mix (turnover) only in spring time when both are at 4 C. 表面和底部的水祇能在春天兩者均為 4C 時混合 (翻轉)。

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