19. 2nd Law of Thermodynamics 熱力學第二定律 Reversibility & Irreversibility 1. 可逆性和不可逆性 The 2nd Law of Thermodynamics 2. 熱力學第二定律 Applications of the 2nd Law 3. 第二定律的應用 Entropy & Energy Quality 4. 熵和能量品質

Most energy extracted from the fuel in power plants is dumped to the environment as waste heat, here using a large cooling tower. 發電廠內從燃料抽取的能量，大部份都被當成廢熱而丟到環境裏； 圖中用的是一個大型冷卻塔。 Why is so much energy wasted? 為甚麼浪費這麼多能量？ 2nd law: no Q  W with 100% efficiency 第二定律：沒有 Q  W可以達到 100% 効率。

Efficiencies 効率 Engine 引擎 Efficiency 効率 Gasoline 汽油 18~20% Diesel 柴油 up to 可達 40% Steam 蒸氣 ~8% Gas Turbine 氣渦輪 up to 可達 40% Power Plant 發電廠 Efficiency 効率 Coal 燃煤 36% Nuclear 核子 30%

19.1. Reversibility & Irreversibility 可逆性和不可逆性 時間 Block slowed down 質塊因摩擦力 by friction: 而慢下來: Irreversible 不可逆 Bouncing ball: 彈跳的球: reversible 可逆 Examples of irreversible processes: 不可逆程序範例: Beating an egg, blending yolk & white 打一個蛋，蛋黄蛋白混成一團 Cups of cold & hot water in contact 幾杯冷和熱水貼在一起 Spontaneous process: 自發性程序: order  disorder 有序  無序 ( statistically more probable ) (统計上較有可能)

GOT IT? 19.1. Which of these processes are irreversible: 以下那些程序是不可逆的： stirring sugar into coffee, (a) 把糖攪進咖啡中， building a house, (b) 建一幢房子， demolishing a house with a wrecking ball, (c) 用鐵球撞毀一幢房子， demolishing a house by taking it apart piece by piece, (d) 把房子逐塊拆下， harnessing the energy of falling water to drive machinery, (e) 利用水下墮的能量驅動機器， harnessing the energy of falling water to heat a house? (f) 利用水下墮的能量加熱房子？

19.2. The 2nd Law of Thermodynamics 熱力學第二定律 Heat engine extracts work from heat reservoirs. 熱引擎從熱庫取熱。 gasoline & diesel engines 汽油和柴油引擎 fossil-fueled & nuclear power plants 化石燃料和核子發電廠 jet engines 噴射引擎 熱庫 Perfect heat engine: coverts heat to work directly. 完美熱引擎: 把熱直接變成功。 2nd law of thermodynamics ( Kelvin-Planck version ): There is no perfect heat engine. 熱力學第二定律 ( 凱爾文- 普朗克 版 ) ： 沒有完美熱引擎。 No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work. 沒有任何程序的淨効果可以是從單一個熱庫吸收熱量，然後把它全部變成功。 Heat dumped 倒掉的廢熱

cylinder compressed adiabatically 氣缸絕熱地壓縮 ( T rises to Th adiabatically T 絕熱地升至Th ) gas in contact with Th , expands isothermally to do work; heat Qh = Wh absorbed 氣缸與Th 接觸，氣體等温膨脹作工；吸進 Qh=Wh的熱 cylinder expands adiabatically 氣缸絕熱地膨脹 ( T drops to Tc adiabatically T 絕熱地降至Tc ) cylinder in contact with Tc , gas compressed isothermally heat Qc = Wc dumped 氣缸與Tc 接觸，氣體等温壓縮；倒出 Qc = Wc 的熱 simple heat engine 簡單熱引擎 Efficiency 効率 (any engine) 任何引擎 (any cycle) 任何循環 (Simple engine) 簡單引擎

Carnot Engine (Cycle) 卡諾引擎 (循環) Ideal gas 理想氣體： AB: Heat abs. 吸收了熱 B  C: Work d. 做了功 C  D: Heat rej. 排出熱 D  A:  Work d. 被做了功 Adiabatic processes 絕熱程序：  Isothermal expansion 等温膨脹 : T = Th , W1 = Qh > 0 Adiabatic expansion 絕熱膨脹 : Th  Tc, W2 >0 Isothermal compression 等温壓縮 : T = Tc , W3 =  Qc < 0 4. Adiabatic compression 絕熱壓縮 : Tc  Th , W4 =  W2 < 0

Example 19.1. Carnot Engine 卡諾引擎 A Carnot engine extracts 240 J from its high T reservoir during each cycle, & rejects 100 J to the environment at 15C. 一部卡諾引擎每週期從它的高 T 熱庫提取 240 J ，再於 15C 向外丟出 100 J 。 How much work does the engine do in each cycle? 引擎每週期作功多少？ What’s its efficiency? 它的功率為何？ What’s the T of the hot reservoir? 高温熱庫的 T 為何？ work done 所作功 Efficiency 功率 

Engines, Refrigerators, & the 2nd Law 引擎，冷凍機，和第二定律 Carnot’s theorem 卡諾定理 : All Carnot engines operating between temperatures Th & Tc have the same efficiency. 所有在温度 Th & Tc 之間運作的卡諾引擎都有同樣的効率。 No other engine operating between Th & Tc can have a greater efficiency. 沒有其他在温度 Th & Tc 之間運作的引擎可以有更大的効率。 Refrigerator: extracts heat from cool reservoir into a hot one. 冷凍機: 從冷庫抽送熱量到一個熱庫。 work required 所需功

完美冷凍機：不用對它作功就可以把熱量從低移到高温熱庫。 perfect refrigerator: moves heat from cool to hot reservoir without work being done on it. 完美冷凍機：不用對它作功就可以把熱量從低移到高温熱庫。 2nd law of thermodynamics ( Clausius version ): There is no perfect refrigerator. 熱力學第二定律 (克勞修斯 版 ) ： 沒有完美冷凍機。 No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature. 沒有任何程序的淨効果可以是把熱從一個較低温的物體送到一個較高温的物體。

Perfect refrigerator  Perfect heat engine 完美冷凍機  完美熱引擎 實在的熱引擎 完美熱引擎 完美冷凍機 Perfect refrigerator  Perfect heat engine 完美冷凍機  完美熱引擎 Clausius  Kelvin-Planck 克勞修斯  凱爾文- 普朗克

Carnot engine is most efficient 卡諾引擎效率最高 完美熱引擎 Hypothetical engine 假想引擎, e = 70% Carnot refrigerator卡諾冷凍機, e = 60% Carnot engine is most efficient 卡諾引擎效率最高 eCarnot = thermodynamic efficiency 熱力效率 eCarnot  erev > eirrev

19.3. Applications of the 2nd Law 第二定律的應用 Power plant 發電廠 温度 Turbine渦輪機 Generator發電機 Electricity電 fossil-fuel 化石燃料 : Th = 650 K Nuclear 核能 : Th = 570 K Tc = 310 K 温度 水蒸氣 Boiler鍋爐 Condenser冷凝器 水 温度 Heat source熱源 入 出 Cooling water 冷卻用水 Waste water 廢水 Actual values 實在數值 : efossil ~ 40 % enuclear ~ 34 % ecar ~ 20 % Prob 54 & 55

Application: Combined-Cycle Power Plant 應用: 聯合-循環發電廠 Turbine engines: high Th ( 1000K  2000K ) & Tc ( 800 K ) … not efficient. 渦輪機: 高 Th ( 1000K  2000K ) & Tc ( 800 K ) … 無効率。 Steam engines : Tc ~ ambient 300K. 蒸氣機 : Tc ~ 周圍的 300K. Combined-cycle 聯合-循環 : Th ( 1000K  2000K ) & Tc ( 300 K ) … e ~ 60%

Example 19.2. Combined-Cycle Power Plant 聯合-循環發電廠 The gas turbine in a combined-cycle power plant operates at 1450 C. 一個聯合-循環發電廠內的氣渦輪機在1450 C下運作。 Its waste heat at 500 C is the input for a conventional steam cycle, with its condenser at 8 C. 它的 500 C 廢熱輸入另一個冷凝器在 8 C 的傳统蒸氣循環。 Find e of the combined-cycle, & compare it with those of the individual components. 求此聯合-循環的 e ，並與其個別組件的值比較。 氣渦輪機燃燒温度 氣渦輪機 中介温度 蒸氣循環 冷卻水温度

Refrigerators 冷凍機 1st law Max. theoretical value (Carnot cycle) Coefficient of performance (COP) for refrigerators : 冷凍機的績效系數 1st law Max. theoretical value (Carnot cycle) 理論最大值(卡諾循環) COP is high if Th  Tc . Th  Tc 時 COP 高 W = 0 ( COP =  ) for moving Q when Th = Tc . 若 Th = Tc ，移動 Q 時 W = 0 ( COP =  ) 。

Example 19.3. Home Freezer 家用冰箱 A typical home freezer operates between Tc =  18C to Th = 30 C. 家用冰箱通常都在 Tc =  18C 到 Th = 30 C 之間運作。 What’s its maximum possible COP? 它可能的最大 COP 值為何？ With this COP, how much electrical energy would it take to freeze 500 g of water initially at 0 C? 在這COP 值之下，需要多少電能才可以把 500 g 在 0 C 的水凝固？ Table 17.1 2nd law: only a fraction of Q can become W in heat engines. 第二定律：熱引擎中祇有一部份 Q 能變成 W 。 a little W can move a lot of Q in refrigerators. 冷凍機內一點 W 可以產生很多 Q 。

Heat Pumps 熱泵 Heat pump: moves heat from Tc to Th . Heat pump as AC : 以熱泵作冷氣機 Heat pump as heater : 以熱泵作暖爐 Ground temp ~ 10C year round 土地温度整年都 ~ 10C

GOT IT? 19.2. A clever engineer decides to increase the efficiency of a Carnot engine by cooling the low-T reservoir using a refrigerator with the maximum possible COP. 一個聰明的工程師决定要提高卡諾引擎的効率，方法是用一部具有最大 COP可能值的冷凍機來冷卻 低温熱庫。 Will the overall efficiency of this system 這系統的整體效率會 exceed 超過， be less than 低於， equal that of 等於 the original engine alone 原來引擎本身的值？ see Prob 32 for proof 證明可參考 Prob 32

19.4. Entropy & Energy Quality 熵和能量品質 機械，電能 最高質 2nd law: Energy of higher quality can be converted completely into lower quality form. 第二定律：高質能量可以完全變成較低質能量 But not vice versa. 反之卻不成。 高温 Energy quality Q measures the versatility of different energy forms. 能量品質 Q 衡量各種能量的可用性。 低温 最低質

Conceptual Example 19.1. Energy Quality, End Use, & Cogeneration 能量品質，終端使用，和共發電 You need a new water heater, & you’re trying to decide between gas & electric. 你需要一個新的熱水器；現正在瓦斯和電熱兩者之間作一選擇。 The gas heater is 85% efficient, meaning 85% of the fuel energy goes into heating water. 瓦斯熱水器的効率是 85% ，亦即 85% 的燃料能可以用來熱水。 The electric heater is essentially 100% efficient. 電熱水器的効率可說是 100% 。 Thermodynamically, which heater makes the most sense? 從熱力學來看，那一個熱水器比較值得用? Ans. 答 Only 1/3 of fuel energy is converted to electricity at a power plant. 發電廠祗把燃料能的 1/3 轉成電能。 With this in mind, the gas heater is a better choice. 在這考量下，瓦斯熱水器是較佳選擇。 Cogeneration 共發電 : Waste heat from electricity generation used for low Q needs. 發電時產生的廢熱用在低 Q 的需求上。

Making the Connection 連起來 If the electricity comes from a more efficient gas-fired power plant with e = 48%, 假設電力來自効率較佳，e = 48%，的天然氣發電廠， compare the gas consumption of your two heater choices. 比較上述兩種熱水器的瓦斯消耗。 Gas heater: 1 unit of fuel energy becomes 0.85 unit of heat. 瓦斯熱水器: 1單位的燃料能可變成 0.85單位的熱。 Electric heater: 1 unit of fuel energy becomes 0.48 unit of electric energy, 電熱水器: 1單位的燃料能可變成 0.48單位的電能， then becomes 0.48 unit of heat. 再變成 0.48單位的熱。 Electric heater consumes 0.85/0.48 = 1.8 times the fuel consumed by gas heater. 電熱水器消耗 0.85/0.48 = 1.8 倍瓦斯熱水器所需的燃料。

Entropy 熵  Carnot cycle (reversible processes): 卡諾循環 (可逆程序) Qh = heat absorbed 所吸熱 Qc = heat rejected 所排熱 Qh , Qc = heat absorbed 所吸熱  lukewarm: can’t do W, Q  微温：不能作功， Q  C = Carnot cycle 卡諾循環 絕熱線 C = any closed path 任何閉口路徑 壓力 Irreversible processes can’t be represented by a path. 不可逆程序不能以路徑表達。 等温線 體積 S = entropy 熵 [ S ] = J / K Contour = sum of Carnot cycles. 路徑 = 所有卡諾循環之和

Entropy 熵  Carnot cycle (reversible processes): 卡諾循環 (可逆程序) Qh = heat absorbed 所吸熱 Qc = heat rejected 所排熱 Qh , Qc = heat absorbed 所吸熱  lukewarm: can’t do W, Q  微温：不能作功， Q  C = Carnot cycle 卡諾循環 絕熱線 C = any closed path 任何閉口路徑 壓力 Irreversible processes can’t be represented by a path. 不可逆程序不能以路徑表達。 等温線 S = entropy 熵 [ S ] = J / K 體積

S = 0 over any closed path  S21 + S12= 0  S21 = S21 Entropy change is path-independent. 熵變量與路徑無關。 ( S is a thermodynamic variable ) ( S 是一個熱力變數)

Entropy in Carnot Cycle 卡諾循環的熵 Ideal gas 理想氣體： Heat absorbed: 吸收的熱 Heat rejected: 排出的熱 Adiabatic processes 絕熱程序： 

Irreversible Heat Transfer 不可逆熱傳遞 Cold & hot water can be mixed reversibly using extra heat baths. 冷和熱水可以用額外的熱庫來達成可逆性混合。 T1 = some medium T. 某個中介T 。 reversible processes 可逆程序 T2 = some medium T. 某個中介T 。 Actual mixing, irreversible processes 原來的混合，不可逆程序

Adiabatic Free Expansion 絕熱性自由膨脹 隔板 Adiabatic 絕熱  Qad.exp. = 0 氣 真空   拿走隔板  提取功 S can be calculated by any reversible process between the same states. S 可從兩態之間任何可逆程序計算 isothermal 等温 p = const. p = 定值 Can’t do work 不能作功 Q degraded. Q 被貶。

Entropy & Availability of Work 熵與可用的功 Before adiabatic expansion, gas can do work isothermally 絕熱膨脹之前，氣體可以在等温下作功 After adiabatic expansion, gas cannot do work, while its entropy increases by 絕熱膨脹之後，氣體不能作功，它的熵則增加了  In a general irreversible process 在一個廣泛的不可逆程序中 Coolest T in system

Example 19.4. Loss of Q Q的損耗 A 2.0 L cylinder contains 5.0 mol of compressed gas at 300 K. 一個 2.0 L 氣筒灌了 5.0 mol 在 300 K 的壓縮氣體。 If the cylinder is discharged into a 150 L vacuum chamber & its temperature remains at 300 K, 如果氣筒往一個 150 L真空倉放氣，而且它的温度保持在 300 K ， how much energy becomes unavailable to do work? 有多少能量變成不能作功？ 閥關上 真空 氣 之前 閥打開 之後

A Statistical Interpretation of Entropy 熵的統計詮釋 Gas of 2 distinguishable molecules occupying 2 sides of a box 由可存在盒子兩邊的兩個可分辨分子所組成的氣體 Microstates 微觀態 Macrostates 巨觀態 probability of macrostate 巨觀態的或然率 1/4 2 ¼ = ½ 1/4

probability of macrostate Gas of 4 distinguishable molecules occupying 2 sides of a box 由可存在盒子兩邊的 4 個可分辨分子所組成的氣體 Microstates 微觀態 Macrostates 巨觀態 probability of macrostate 巨觀態的或然率 1/16 = 0.06 4 1/16 = ¼ =0.25 6 1/16 = 3/8 = 0.38 4 1/16 = ¼ =0.25 1/16 = 0.06

Gas of 100 molecules 100個分子的氣體 Gas of 1023 molecules 1023 個分子的氣體 Equal distribution of molecules 分子平均分佈或然率 Statistical definition of entropy : 熵的统計定義：  # of micro states = 微觀態數目

Entropy & the 2nd Law of Thermodynamics 熵與熱力學第二定律 in any closed system 任何密閉系統中 S can decrease in an open system by outside work on it. S 可以在一個開放系統中因外界對它作功而減少。 However, S  0 for combined system. 不過，如果把”外界”也算進來，整個系统還是 S  0 。  S  0 in the universe 整個宇宙 S  0 Universe tends to disorder 宇宙趨向混亂 Life 生命 ?

GOT IT? 19.3. In each of the following processes, does the entropy of the named system increase, decrease, or stay the same? 在下列每個程序中，熵在提到的系统裏是 增加，減少，或是 不變？ a balloon inflates 氣球充氣 cells differentiate in a growing embryo, forming different organs 細胞在成長中的胚胎裏分化，形成各種器官 an animal dies, its remains gradually decays 一個動物死了，它的遺體慢慢腐爛 an earthquake demolishes a building 一場地震把一幢建築物毁了 a plant utilize sunlight, CO2 , & water to manufacture sugar 一棵植物用陽光， CO2 ，和水來制做糖 a power plant burns coal & produces electrical energy 一所發電廠燒煤來產生電能 a car’s friction based brakes stop the car. 以摩擦力為主的剎車把車子停下來。       