Short Version : 16. Temperature & Heat 短版: 16.温度&熱量

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 ) :

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 .

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 

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

Specific Heat vs Thermal Conductivity 比熱對熱導率 c ( J/kgK ) k (W/mK ) Al 900 237 Cu 386 401 Fe 447 80.4 Steel 502 46 Concrete 880 1 Glass 753 0.8 Water 4184 0.61 Wood 1400 0.11

  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 

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.

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 )

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

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 Intensity @ top of atm : 1390 W/m2. Mean dist ./. Earth & sun : 1.5 1011m.

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 16.7. 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