物质的热行为课件

1、物质的热行为17. Thermal Behavior of Matter 物質的熱行為 Gases 氣體 Phase Changes 相變 Thermal Expansion 熱膨脹物质的热行为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。物质的热行为17.1. Gases 氣體The Ideal Gas Law:理想氣體定律：A piston-cylinder system.一個活塞-氣缸系统。pVN k Tk = 1.381

2、023 J / K = Boltzmanns constant 波爾茲曼常數N = number of molecules 分子數目ANn NNA = 6.0221023 = Avogadros 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pVn RTARN k= 8.314 J / K mol = Universal gas constant通用氣體常數Al

3、l gases become ideal if sufficiently dilute.在充份稀釋後，所有氣體都會變成理想。物质的热行为Example 17.1. STP 標準温壓What volume is occupied by 1.00 mol of an ideal gasat standard temperature & pressure (STP), where T = 0C, & p = 101.3 kPa = 1 atm?在標準温壓下 ( T = 0C, & p = 101.3 kPa = 1 atm )， 1.00 mol 理想氣體的體積為何？pVn

4、RTn RTVp31.008.314/273.2101.3 10molJK molKPa3322.4210m22.42 L( last figure subject to round-off error ) 末位數含四捨五入誤差物质的热行为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

5、 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。1. Collisions with wall are elastic. 與容壁的碰撞都是彈性的。表面積物质的热行为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2x ix ipm vNo intermolecular collision Next collision with RHW occurs a

6、t無分子互撞 下次碰撞右壁的時間為2ix iLtvAverage force of i on RHW:i 加於右壁的平均力為iiipFt2x im vLFpAiiFA2ixim vA L2xiimvV2xmpNvV221xxiivvNRandom motion 隨機運動222xyzvvv213v22132pVNm v23N KIdeal gas law is recovered if欲得理想氣體定律，祗需21322Km vk TT Kinout0y ip物质的热行为Example 17.2. Air Molecule 空氣分子Find K of a molecule in air at roo

7、m temperature ( 20C = 293K),找出在室温 (20C = 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。32Kk T2331.38 10/2932JKK216.07 10J2272 141.66 10Nmukg264.65 10kg22 Kvm21262 6.07 104.65 10Jkg5222.61 10/ms2vv511/m s232vkTmThermal speed:熱速率3thk Tvm物质的热行为Distr

8、ibution 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 )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

9、子逃逸 )80 Kvth300Kvth分子數分子速率 22exp2mvn vC vk T 0n v dvN物质的热行为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22nRTa nPVnbVv

10、an der Waals equation范得瓦方程式minimum volume最小體積22a nPVnbnRTVnRTPV物质的热行为17.2. Phase Changes 相變Phase changes take place at fixed T = TC until 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 trans

11、formation 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 )QL m物质的热行为Water:水334/fLkJ kg80/cal g1/Ccal g K Same E to melt 1 g ice or hea

12、t water by 80 C熔解 1 g 冰和水升温 80 C 需要同樣的熱量。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物质的热行为Conceptual Example 17.1. Water Phases 水相ice warming冰加温中melting熔解中water warming水加温中boiling沸騰中steam warming蒸氣加温中You put a block of ice initially at 20C in a pan on a hot stove with a constant power output,你把一塊原來在 20C 的冰塊，放在一個功

13、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。時間時間温度温度物质的热行为Making the Connection連起來If you start with 0.95 kg of ice at 20C and supply heat at the rate of 1.6 kW,如果你開始時用一塊在 20C 的 0.95

14、 kg 冰塊，且以 1.6 kW 的速率加熱，how much time will it take until youre 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 : 0.952.05/20kgkJkg KKiceiceiceiceHmcT39 kJHeat needed to melt ice at 0 C在 0 C 把冰融解需熱 :2i wicefHmL 0.95334/kgkJkg317 kJHeat needed to vaporize water at 10

15、0 C 在 100 C 把水蒸發需熱 :Heat needed to warm water to 100 C 把水加温到 100 C 需熱 :waterwaterwaterwaterHmcT 0.954.18/100kgkJkg KK397 kJ2w vwatervHmL 0.952260/kgkJkg2140kJ29001.6kJtkW Time needed :需時 :1810 s0.5h物质的热行为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 m

16、in 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 ?物质的热行为Example 17.3. Meltdown 熔毀 !A nuclear power plants 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。Alt

17、hough nuclear fission stops, radioactive decay continues to heat the reactors 2.5105 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 2.5105 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 melt

18、ing take?熔解過程要多久？QL m82.8/fLkJ kgTable 17.1: for U582.8/2.5 10kJ kgkg20.7 GJTime to melt the core:核心熔解需時QTP9620.7 10120 10JW173 s3m物质的热行为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

19、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？QL m1.04.184/15waterQkgkJ kg KCQm cTHeat released to bring water down to 0 C把水降到 0 C 放出熱能62.8 kJ0.22.05/10iceQkgkJ kg KCHeat required to bring ice up to 0 C把冰升到 0 C 需用熱能4.1kJ0.2334/meltQkgkJ kgHeat required to melt

20、ice at 0 C把冰在 0 C 熔掉需用熱能66.8 kJ more than enough ice 有足夠的冰Ice needed:需要的冰62.84.1334/kJmkJ kg0.176 kg ice left = 剩下的冰20017624ggg物质的热行为Phase Diagrams 相變圖Phase diagram: P vs T 相變圖: P 對 TSublimation: solid gas昇華: 固體 氣體 e.g., dry ice 乾冰 ( s-CO2 ) Critical point : l-g indistinguishable 臨界點: 液-氣不可分AB: low

21、P, s g 低 P ，固 氣CD: medium P, s l g 中 P ，固 液 氣EF: high P, s l / g 高 P ， 固 液氣GH: medium T, l g 中T， 液 氣Caution: Phase transition doesnt occur instantaneously 注意: 相變不是瞬間發生的Triple point: s-l-g coexist三相點: 固 -液-氣共存 = 273.16K, 0.6 kPa for H2OSolid固態Gas 氣態liquid液態Melting熔解Sublimation 昇華Boiling 沸騰 C.P.臨界點T.P

22、.三相點壓力温度物质的热行为物质的热行为17.3. Thermal Expansion 熱膨脹Coefficient of volume expansion :體積膨脹係數/V VT1 dVV dTCoefficient of linear expansion :線膨脹係數/L LT3Prob. 69Prob. 72物质的热行为膨脹係數*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，1C水，20C水，50C* 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。物质的热行为GOT IT? 17.3. If a don

23、ut-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？LLT22RRT 1RRT 物质的热行为Example 17.5. Spilled Gasoline 溢出的汽油A steel gas can holds 20 L at 10C.一個鋼制汽油礶在 10C 時可裝 20 L 。Its filled to the brim at 10C.它在 10C 時剛好裝滿。If the temperature is now increased t

24、o 25C, 假如温度現在上升到 25C，by how much does the cans volume increase?礶子的體積增加多少？How much gas spills out? 有多少汽油溢出？Table 17.2:6112 10steelK6136 10steelK5195 10gasK/V VTVVT612036 102510canVLKCC0.0108 L512095 102510gasVLKCC0.285 LSpilled gas:溢油量0.2850.01080.275LLL物质的热行为Thermal Expansion of Water 水的熱膨脹Reason: I

25、ce 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 4C water 最大值在 4CAt 1C514.8 10waterK 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 0 0三相點臨界點液固氣物质的热行为Application: Aquatic Life & Lake Turnover應用： 水中生態和湖水翻轉Anomalous behavior of ice-wa

26、ter 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 4C 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 4C 。In a lake where bottom water stays at 4C year round,在一個底部的水整年都保持在 4C 的湖裏，surface & bottom water can mix (turnove

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