Part Three: Thermodynamics 第三部:熱力學 Steam turbine converts the energy of high-pressure steam to mechanical energy and then electricity. 蒸汽渦輪機把高壓蒸汽的能量先變成機械能，再成電力。

1 度電 = 瓩-小時 (KWH) = 1000  3600 焦耳 = 3.6 MJ 電費: 每度電 2.1元到 5.1元 World energy consumption (2008): ~ 151012 (15 trillion / tera) watts., mostly from fossil fuels 世界的能源消耗量 (2008): ~ 151012 (15兆) 瓦，大部份都來自化石燃料。 Applications of the laws of thermodynamics 熱力學定律的應用: Combustion engines 內燃機. Sun  Heat flows on Earth  Climate. 太陽  熱在地球上流動  氣象 Global warming. 地球暖化 Big bang: Heat flow in the universe. 大爆炸: 熱在宇宙中流動 1 度電 = 瓩-小時 (KWH) = 1000  3600 焦耳 = 3.6 MJ 電費: 每度電 2.1元到 5.1元

List of countries by electricity consumption Rank   Country   Electricity consumption (MW·h/yr)   Year of Data   Source   Population   As of   Average power per capita (watts per person)   —  World 16,830,000,000 2005 CIA Est.[3] 6,464,750,000 297 1  United States 3,816,000,000 CIA[1] 298,213,000 1,460 2  China 3,640,000,000 2009 [4] 1,315,844,000 277  European Union[5] 2,820,000,000 2004 CIA Est. 459,387,000 700 3  Russia 985,200,000 2007 143,202,000 785 4  Japan 974,200,000 CIA 128,085,000 868 5  Germany 593,400,000 82,329,758 2009 (CIA Est.) 822.22 6  Canada 540,200,000 32,268,000 1,910 7  India 488,500,000 1,103,371,000 50.5 8  France 451,500,000 60,496,000 851 9  South Korea 368,600,000 47,817,000 879 10  Brazil 368,500,000 186,405,000 226 11  United Kingdom 348,700,000 59,668,000 667 12  Italy 307,100,000 58,093,000 603 13  Spain 243,000,000 43,064,000 644 14  South Africa 241,400,000 47,432,000 581 15  Taiwan (Republic of China) 221,000,000 2006 22,894,384 1,101 16  Australia 219,800,000 20,155,000 1,244 17  Mexico 183,300,000 107,029,000 195 2.2億 百萬瓦。小時／年

Part Three: Thermodynamics 第三部:熱力學 Temperature and Heat 温度和熱量 The Thermal Behavior of Matter 物質的熱行為 Heat, Work, and the First Law of Thermodynamics 熱，功，和熱力學第一定律 The Second Law of Thermodynamics 熱力學第二定律

16. Temperature & Heat 温度&熱量 Heat , Temperature & Thermodynamic Equilibrium 熱量，温度 & 熱力學平衡 2. Heat Capacity & Specific Heat 熱容量 & 比熱 3. Heat Transfer 熱傳遞 4. Thermal Energy Balance 熱能的平衡

engine & brakes hot 引擎 & 剎車都還熱 How does this photo reveal heat loss from the house? 這圖片如何揭露房子的熱損耗? And how can you tell that the car was recently driven? 你又如何曉得車子不久前被開過? IR photo 紅外線圖片: engine & brakes hot 引擎 & 剎車都還熱 Studies of thermal properties 熱的研究: Thermodynamics: Relations between macroscopic properties. 熱力學: 巨觀屬性之間的關係。 Statistical mechanics: Atomic description. 統計力學: 以原子觀來描述。

16.1. Heat , Temperature & Thermodynamic Equilibrium 熱量，温度 & 熱力平衡 State at which macroscopic properties of system remains unchanged over time. 巨觀屬性不隨時間改變的系統狀態。 Examples of macroscopic properties: L, V, P, , , … 巨觀屬性的例子： 長度，體積，壓力，密度，電阻，… 2 systems are in thermal contact if heating one of them changes the other. 如果把兩個系統中的一個加熱，其它一個會有變化，那這兩個系統就說有熱接觸。 Otherwise, they are thermally insulated. 否則，它們之間是熱絕緣。 A,B in eqm B,C in eqm A,C in eqm  Two systems are in thermodynamic equilibrium  they have the same temperature 兩個系統在熱力平衡中  它們温度相同 0th law of thermodynamics : 2 systems in thermodynamic equilibrium with a 3rd system are themselves in equilibrium. 熱力學第零定律: 兩個系統分別和第三個系統成熱力平衡，則它們彼此也在熱力平衡中。

Gas Thermometers & the Kelvin Scale 氣體温度計 & 克氏溫標 Constant volume gas thermometer T  P 定容氣體温度計 Kelvin scale 克氏溫標: P = 0  0 K = absolute zero 絕對零度 Triple point of water 水的三相點  273.16 K 真空 Triple point 三相點: T at which solid, liquid & gas phases co-exist in equilibrium 固，液，氣三相共存於平衡狀態的温度 氣體 水銀 輭管 Mercury fixed at this level by adjusting h  P  T. 調整 h  P  T.來維持水銀面於此。 All gases behave similarly as P  0. 所有氣體在 P  0 時，性質都差不多。

Temperature Scales 溫標 Celsius scale 攝氏 ( C ) : Melting point of ice 冰融點 at P = 1 atm  TC = 0 C. Boiling point of water 水沸點 at P = 1 atm  TC = 100 C.  Triple point of water 水的三相點 = 0.01C Fahrenheit scale 華氏 ( F ) : Melting point of ice 冰融點 at P = 1 atm  TF = 32 F. Boiling point of water水沸點 at P = 1 atm  TF = 212 F. Rankine scale 蘭氏 ( R ) :

Supplement 附錄 Conditions for thermodyn. Eqm. 熱力平衡的條件 P V = n R T Isolated ideal gas 與外界隔離的理想氣體 P, V, n, T P V = n R T P j V j = n j R T j j = 1, 2 Fixed, thermally conducting partition 固定，可導熱的間隔 P1 , V1 , n1 , T1 P2 , V2 , n2 , T2 ( Local eqm. 局部平衡 ) T 1 = T 2 P j V j = n j R T j j = 1, 2 Movable, thermally conducting partition 可移動，可導熱的間隔 P1 , V1 , n1 , T1 P2 , V2 , n2 , T2 T 1 = T 2 & P 1 = P 2 P j V j = n j R T j j = 1, 2 Porous, movable, thermally conducting partition 可滲透，可移動，可導熱的間隔 P1 , V1 , n1 , T1 P2 , V2 , n2 , T2 T 1 = T 2 , P 1 = P 2 &  1 =  2 Same as no partition 跟沒有間隔一樣  = n / V

Heat & Temperature 熱(量)&温度 A match will burn your finger, but doesn’t provide much heat. 一枝火柴會燒傷你的手指，卻不能提供多少熱量。  Heat ~ amount 熱(量) ~ 數量 Temperature ~ intensity 温度 ~ 強度 Brief history of the theory of heat 熱理論短史: Heat is a fluid (caloric theory: 1770s) that flows from hot to cold bodies. 熱是一種流體 (熱流(卡路里)理論: 1770年代) ， 由高往低温處流動。 B.Thompson, or Count Rumford, (late 1790s): unlimited amount of heat can be produced in the boring of canon  heat is not conserved. 湯普生，即林福伯爵 (1790末): 炮管搪 (鏜)孔時可產生無限的熱  熱不守恆 J.Joule (1840s): Heat is a form of energy. 焦耳 (1840年代): 熱是一種能。 Heat is energy transferred from high to low temperature regions. 熱(量)是從高傳到低温處的能(量)。

16.2. Heat Capacity & Specific Heat 熱容量 & 比熱 Heat capacity C of a body : 一個物體的熱容量 C Q = heat transferred to body. 傳到物體的熱 Specific heat c = heat capacity per unit mass 比熱 c = 單位質量的熱容量 1 calorie (15C cal) = heat needed to raise 1 g of water from 14.5C to 15.5C. 1 卡路里 (15C cal) = 把一公克的水從14.5C 升至 15.5C所需熱量。 1 BTU (59F) = heat needed to raise 1 lb of water from 58.5F to 59.5F. 1 英熱單位 (59F BTU) = 把一英磅的水從 58.5 F 升至 59.5 F 所需熱量。

c = c(P,V) for gases  cP , cV . 一些常見材料的比熱* 比熱 鋁 水泥 銅 鐵 玻璃 水銀 鋼 石(花岡) 水: 液態 冰，10C 木 除非特別標明，温度範圍都是 0 C 到100 C c = c(P,V) for gases  cP , cV .

Example 16.1. Waiting to Shower 等洗澡 After everyone in your family has taken a shower, the temperature in the water heater drops to 18C. 你家裏的每一個人都洗過澡之後，熱水器的温度就掉到 18C. If the heater holds 150 kg of water, how much energy will it take to bring it up to 50C? 如果熱水器裝着 150公斤 的水，要多少能量才可以把它升到 50C ? If the energy is supplied by a 5.0 kW electric heating element, how long will that take? 如果能源是一個 5.0 kW 的電熱元件，要等多久?

The Equilibrium Temperature 平衡温度 Heat flows from hot to cold objects until a common equilibrium temperature is reached. 熱從高到低温處流動，直到各處温度均為同一平衡温度為止。 For 2 objects insulated from their surroundings: 對兩件與外界絕熱的物體來說: When the equilibrium temperature T is reached: 當達到平衡温度 T 時 

GOT IT? 16.1. A hot rock with mass 250 g is dropped into an equal mass of pool water. 一塊質量為 250g 的熱石頭掉入一盤同質量的水中。 Which temperature changes more? Explain. 那一個的温度變化較大? 解釋之。 crock = 0.20 cal / g C cwater = 1.0 cal / g C  Trock changes more

Example 16.2. Cooling Down 冷下來 An aluminum frying pan of mass 1.5 kg is at 180C, when it was plunged into a sink containing 8.0 kg of water at 20C. 一個質量1.5 kg 的鋁製平底鍋在温度為 180C 時， 被投入一個盛着 8.0 kg ， 20C 水的槽裏。 Assuming none of the water boils & no heat is lost to the environment, find the equilibrium temperature of the water & pan. 假設水沒有蒸發，且熱也沒有散失，求水和鍋的平衡温度。

16.3. Heat Transfer 熱傳遞 Common heat-transfer mechanisms: 常見的熱傳遞機制: Conduction 傳導 Convection 對流 Radiation 輻射

Conduction 傳導 Conduction: heat transfer through direct physical contact. 傳導: 熱靠物體的直接接觸來傳遞。 Mechanism: molecular collision. 機制: 分子碰撞 Heat flow 熱流量 H , [ H ] = watt 瓦 : Thermal conductivity 熱導率 k , [ k ] = W / mK

熱導率 空氣 鋁 水泥 (隨混比改變) 銅 玻璃纖維 玻璃 鵝絨 氦 鐵 鋼 保麗龍 水: 木(松) Conductor 導體 insulator絕緣體

Example 16.3. Warming a Lake 湖水加温 A lake with flat bottom & steep sides has surface area 1.5 km2 & is 8.0 m deep. 有一個底部平坦，週邊陡峭的湖。其面積是 1.5 km2 ，深度是 8.0 m。 The surface water is at 30C; the bottom, 4.0C. 湖面的水温是 30C; 湖底則是 4.0C. What is the rate of heat conduction through the lake? 湖內的熱傳導速率為何? Assume T decreases uniformly from surface to bottom. 假設 T 從湖面到湖底等速下降。 Power of sunlight is ~ 1 kW / m2 .

  applies only when T = const over each (planar) surface For complicated surface, use 截面形狀複雜時，需用 Prob. 72 & 78. Composite slab 複合平板 : H must be the same in both slabs to prevent accumulated heat at interface H 必需在兩塊板內都一樣才能避免熱累積在界面中 Thermal resistance : 熱阻: [ R ] = K / W  Resistance in series 阻力串聯 

GOT IT? 16.2. H, A, x same for all three H ,A, x 三個都一樣 Rank order the 3 temperature differences. 為這3個温差排序 H, A, x same for all three H ,A, x 三個都一樣  k T = const 涼 燙

Insulating properties of building materials are described by the R-factor ( R-value ) . = thermal resistance of a slab of unit area 單位面積板塊的熱阻 U.S.

Example 16.4. Cost of Oil The walls of a house consist of plaster ( R = 0.17 ), R-11 fiberglass insulation, plywood (R = 0.65 ), and cedar shingles (R = 0.55 ). The roof is the same except it uses R-30 fiberglass insulation. In winter, average T outdoor is 20 F, while the house is at 70 F. The house’s furnace produces 100,000 BTU for every gallon of oil, which costs $2.20 per gallon. How much is the monthly cost?

例 16.4. 油費 一幢房子的牆璧由石膏板( R = 0.17 ) ， R-11 玻璃纖維隔熱綿， 三夾板 (R = 0.65 ) ，和杉木牆面板 (R = 0.55 ) 拼成。 屋頂也一樣，祇是改用R-30 玻璃纖維隔熱綿。 冬天時，平均 T 戶外是 20 F ，室內是 70 F 。 房子的火爐每加侖油可產生 100,000 BTU ，油價是每加侖 $2.20。 每月的油費是多少 ?

Convection 對流 涼 T      rises 上升 燙 Convection = heat transfer by fluid motion 對流 = 源自流體流動的熱傳遞 T      rises 上升 燙 Convection cells in liquid film between glass plates (Rayleigh-Bénard convection, Benard cells) 玻璃片之間液體的對流細胞 ( 瑞利-比那對流，比那細胞 )

Examples 範例 : Boiling water 燒水. Heating a house 房子加熱. Sun heating earth  Climate, storms. 太陽加熱地球  氣候，暴風。 Earth mantle  continental drift 地殼  大陸漂移 Generation of B in stars & planets. 為恆星及行星產生磁場

Radiation 輻射 Glow of a stove burner  it loses energy by radiation 火爐發光  它的能量以輻射散失 Stefan-Boltzmann law for radiated power: 輻射功率的史特凡-波茲曼定律  = Stefan-Boltzmann constant 史特凡-波茲曼常數 = 5.67108 W / m2 K4. A = area of emitting surface 發射面積. 0 < e < 1 is the emissivity ( effectiveness in emitting radiation). 是發射率 (輻射的發射効率 ) e = 1  perfect emitter & absorber ( black body ). 完美發射體 &吸收體 (黑體) Black objects are good emitters & absorbers. 黑的東西是好的發射體 &吸收體 Shiny objects are poor emitters & absorbers. 亮的東西是不好的發射體 &吸收體

Stefan-Boltzmann law 史特凡-波茲曼定律 : Wien‘s displacement law 維恩位移定律 : max = b / T  P  T4  Radiation dominates at high T. 輻射在高温時為主導 Wavelength of peak radiation becomes shorter as T increases. 輻射高峯的波長隨 T 增大而變短 Sun ~ visible light. 太陽 ~ 可見光 Near room T ~ infrared. 室温 ~ 紅外線

GOT IT 懂嗎 ? 16.3. Name the dominant form of heat transfer from 指出下列熱傳遞的主導機制 a red-hot stove burner with nothing on it. 上無一物的紅熱爐灶。 a burner in direct contact with a pan of water. 火爐上放一煱水。 the bottom to the top of the water in the pan once it boils. 水開後從水底到水面 輻射 Radiation 傳導 conduction 對流 convection

Example 16.5. Sun’s Temperature 太陽的温度 The sun radiates energy at the rate P = 3.91026 W, & its radius is 7.0 108 m. 太陽以 P = 3.91026 W 的功率輻射能量，它的半徑是 7.0 108 m. Treating it as a blackbody ( e = 1 ), find its surface temperature. 把它當成是一個黑體 ( e = 1 ) ，找出它的表面温度。  = 5.67108 W / m2 K4

Conceptual Example 15.1. Energy-Saving Windows 省能窗户 Why do double-pane windows reduce heat loss greatly compared with single-paned windows? 為甚麼雙層玻璃窗的隔熱効果比單層的大很多 ? Why is a window’s R-factor higher if the spacing between panes is small? 為甚麼窗户的 R-因子會在玻璃間隔小的時候增大? And why do the best windows have “low-E” coatings? 為甚麼最好的窗户都有 “低 E” 外鏌 ? Thermal conductivity (see Table 16.2) 熱導率 (見表 16.2) : Glass 玻璃 k ~ 0.8 W/mK Air 空氣 k ~ 0.026 W/mK Layer of air reduces heat loss greatly & increases the R-factor . 加一層空氣可以減少散熱和增大 R-因子。 This is so unless air layer is so thick that convection current develops. 這需要空氣層不能太厚，以免產生對流。 “low-E” means low emissivity, which reduces energy loss by radiation. “低 E” 表示低放射率，以減少幅射散熱。

Making the Connection 連起來 Compare the for a single pane window made from 3.0-mm-thick glass with that of a double-pane window make from the same glass with a 5.0-mm air gap between panes. 比較一片 3.0-mm 厚的單層玻璃窗和一片用同樣玻璃，中留 5.0-mm 空隙的雙層玻璃窗。 Glass 玻璃 k ~ 0.8 W/mK Air 空氣 k ~ 0.026 W/m  K

16.4. Thermal Energy Balance 熱能的平衡 A house in thermal-energy balance. 一幢熱能已達平衡的房子 System with fixed rate of energy input tends toward an energy- balanced state due to negative feedback. 以固定速率引進能量的系統，都會因為負回饋而趨於能量平衡的狀態。 Heat from furnace balances losses thru roofs & walls. 從火爐來的熱能彌補了從屋頂和牆璧的流失。

Example 16.6. Hot Water 熱水 A poorly insulated electric water heater loses heat by conduction at the rate of 120 W for each C difference between the water & its surrounding. 一個隔熱不良的電熱水器由傳導的方式，以 温差每 C 120W 的功率失熱。 It’s heated by a 2.5 kW heating element & is located in a basement kept at 15 C. 它是由一個 2.5 kW 加熱元件加熱；而放置它的地下室則保持在 15 C 。 What’s the water temperature if the heating element operates continuously. 如果熱元件一直維持加熱，水温是多少？ Conductive heat loss 熱傳導流失 T = ? Electrical energy in 電能進 Heating element 加熱元件

Example 16.7. Solar Greenhouse 太陽能温室 A solar greenhouse has 300 ft2 of opaque R-30 walls, 一個太陽能温室有 300 ft2 的不透明 R-30 牆， & 250 ft2 of R-1.8 double-pane glass that admits solar energy at the rate of 40 BTU / h / ft2. 和 250 ft2 的 R-1.8 雙層玻璃 (其太陽能穿透率為 40 BTU / h / ft2)。 Find the greenhouse temperature on a day when outdoor temperature is 15 F. 找出一天戶外温度為 15 F 時，温室的温度。

Application: Greenhouse Effect & Global Warming 應用：温室効應和地球暖化 Average power from sun : 從太陽來的平均功率 入射陽光 Total power from sun : 從太陽來的總功率 Power radiated (peak at IR) from Earth : 自地球輻射掉的功率 (峰點在紅外線) 外放紅外線  natural greenhouse effect 自然温室効應 Mars : none 火星 : 無 (96% CO2 , P ~ .01 atm, T ~ 46C ) Venus : huge 金星 : 巨 (96% CO2 , P ~100 atm, T ~ 460C ) C.f.  T   15 C Greenhouse gases : H2O, CO2 , CH4 , … passes incoming sunlight, absorbs outgoing IR. 温室氣體: H2O, CO2 , CH4 , …把進來的陽光放行，出去的紅外線吸收。

0.6 C increase during 20th century. 二十世紀期間增加 0.6 C 。 二氧化碳濃度百萬分之一體積比 CO2 increased by 36% 二氧化碳增加 36% 工業年代開始 年 温度偏差 0.6 C increase during 20th century. 二十世紀期間增加 0.6 C 。 1.5 C – 6 C increase by 2100. 公元 2100 年時增加 1.5 C – 6 C。 年