1、19.2nd Law of Thermodynamics 熱力學第二定律1.Reversibility&Irreversibility1.可逆性和不可逆性2.The 2nd Law of Thermodynamics2.熱力學第二定律3.Applications of the 2nd Law3.第二定律的應用4.Entropy&Energy Quality4.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
2、 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 引擎引擎Efficiency 効率効率Gasoline 汽油1820%Diesel 柴油up to 可達 40%Steam 蒸氣8%Gas Turbine 氣渦輪up to 可達 40%Power Plant 發電廠發電廠Efficiency 効率
3、効率Coal 燃煤36%Nuclear 核子30%19.1.Reversibility&Irreversibility 可逆性和不可逆性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Spontaneo
4、us process:自發性程序:order disorder 有序 無序(statistically more probable)(统計上較有可能)時間時間GOT IT?19.1.Which of these processes are irreversible:以下那些程序是不可逆的：(a)stirring sugar into coffee,(a)把糖攪進咖啡中，(b)building a house,(b)建一幢房子，(c)demolishing a house with a wrecking ball,(c)用鐵球撞毀一幢房子，(d)demolishing a house by ta
5、king it apart piece by piece,(d)把房子逐塊拆下，(e)harnessing the energy of falling water to drive machinery,(e)利用水下墮的能量驅動機器，(f)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&di
6、esel 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。Perfect heat engine:coverts heat to work directly.完美熱引擎:把熱直接變成功。熱庫熱庫Heat dumped倒掉的廢熱No process is possible in wh
7、ich 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。simple heat engine簡單熱引擎 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 Q
8、h=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Efficiency効率Net Work Heat Inpute 淨功外加熱hchQQeQ1chQQ(any engine)任何引擎(Simple engine
9、)簡單引擎0UWQ(any cycle)任何循環Carnot Engine(Cycle)卡諾引擎(循環)1.Isothermal expansion 等温膨脹:T=Th,W1=Qh 02.Adiabatic expansion 絕熱膨脹:Th Tc,W2 03.Isothermal compression 等温壓縮:T=Tc,W3=Qc 04.Adiabatic compression 絕熱壓縮:Tc Th,W4=W2 eirrevCarnot refrigerator卡諾冷凍機,e=60%Hypothetical engine 假想引擎,e=70%完美熱引擎完美熱引擎19.3.Applica
10、tions of the 2nd Law 第二定律的應用Power plant發電廠fossil-fuel 化石燃料:Th=650 K Nuclear 核能 :Th=570 K Tc=310 K3101650fossilKeK 52%3101570nuclearKeK 46%Actual values 實在數值:efossil 40%enuclear 34%ecar 20%Prob 54&55Heat source熱源Boiler鍋爐Turbine渦輪機Generator發電機Electricity電Condenser冷凝器Waste water 廢水Cooling water冷卻用水温度温度
11、温度温度温度温度水蒸氣水蒸氣水水入入出出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
12、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 c
13、omponents.求此聯合-循環的 e，並與其個別組件的值比較。27381273 1450combinede 84%2735001273 1450turbinee 55%27381273500steame 64%氣渦輪機氣渦輪機燃燒温度燃燒温度氣氣渦渦輪輪機機蒸蒸氣氣循循環環中介温度中介温度冷卻水温度冷卻水温度Refrigerators 冷凍機Coefficient of performance(COP)for refrigerators:冷凍機的績效系數cQCOPWchcQQQchcTTTCOP is high if Th Tc.Th Tc 時 COP 高Max.theoretical v
14、alue(Carnot cycle)理論最大值(卡諾循環)1st lawW=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=18C to Th=30 C.家用冰箱通常都在 Tc=18C 到 Th=30 C 之間運作。Whats its maximum possible COP?它可能的最大 COP 值為何？With this COP,how much electrical energy
15、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？5.31273 183018 chcTCOPTTQL m334/0.5kJ kgkg167 kJTable 17.1QWCOP1675.31kJ31kJ2nd 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
16、凍機內一點 W 可以產生很多 Q。Heat Pumps 熱泵ccoolingQCOPWchcQQQinoutinTTTHeat pump as AC:以熱泵作冷氣機hheatingQCOPWhhcQQQininoutTTTHeat pump as heater:以熱泵作暖爐Ground temp 10C year round土地温度整年都 10CHeat pump:moves heat from Tc to Th.GOT IT?19.2.A clever engineer decides to increase the efficiency of a Carnot engine by cool
17、ing 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(a)exceed超過，(b)be less than低於，(c)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 3219.4.En
18、tropy&Energy Quality熵和能量品質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。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。最高質最高質最低質最低質機械，電能機械，電能高高温温低低温温Conceptual Example 19.1.Ener
19、gy Quality,End Use,&Cogeneration能量品質，終端使用，和共發電You need a new water heater,&youre 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 10
20、0%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?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。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
21、 mind,the gas heater is a better choice.在這考量下，瓦斯熱水器是較佳選擇。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 0.8
22、5 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。Entr
23、opy熵lukewarm:cant do W,Q 微温：不能作功，Q Carnot cycle(reversible processes):卡諾循環(可逆程序)cchhQTQT0chchQQTTQh=heat absorbed 所吸熱Qc=heat rejected 所排熱Qh,Qc=heat absorbed所吸熱0Cd QT C=any closed path 任何閉口路徑21d QST S=entropy 熵 S =J/KIrreversible processes cant be represented by a path.不可逆程序不能以路徑表達。等温線等温線體積體積壓壓力力絕熱線絕
24、熱線C=Carnot cycle 卡諾循環Contour=sum of Carnot cycles.路徑=所有卡諾循環之和Entropy熵lukewarm:cant do W,Q 微温：不能作功，Q Carnot cycle(reversible processes):卡諾循環(可逆程序)cchhQTQT0chchQQTTQh=heat absorbed 所吸熱Qc=heat rejected 所排熱Qh,Qc=heat absorbed所吸熱0Cd QT C=any closed path 任何閉口路徑21d QST S=entropy 熵 S =J/KIrreversible proces
25、ses cant be represented by a path.不可逆程序不能以路徑表達。等温線等温線體積體積壓壓力力絕熱線絕熱線C=Carnot cycle 卡諾循環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)S=0 over any closed path任何閉口路徑上，S=0 S21+S12=0 S21=S21 Entropy in Carnot Cycle 卡諾循環的熵Ideal gas 理想氣體：lnBhABhAVQQn R TV lnDcCDcCVQQ
26、n R TV Adiabatic processes 絕熱程序：11hBcCT VT V11cDhAT VT VCBDAVVVVABCABQQ ADCDCQQ Heat absorbed:吸收的熱Heat rejected:排出的熱lnBhAVn R TVlnCcDVn R TVABABChQSTlnBAVn RVDCADCcQSTlnCDVn RVABCS 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。fcTc
27、TdQST1cQTfhThTdQST2hQTchSSS 12chQQTT12ccQQTT1211cTTQ00S Actual mixing,irreversible processes原來的混合，不可逆程序reversible processes可逆程序T1=some medium T.某個中介T。T2=some medium T.某個中介T。21TTAdiabatic Free Expansion絕熱性自由膨脹.exp.0adW0vacuumpAdiabatic 絕熱 Qad.exp.=0.exp.0adU.exp.0adTS can be calculated by any reversi
28、ble process between the same states.dQST 1dQTQT21lnVn RV0WT211VVn RTdVTVp=const.p=定值Cant do work不能作功Q degraded.Q 被貶。S 可從兩態之間任何可逆程序計算真空真空提提取取功功拿拿走走隔隔板板氣氣隔板隔板isothermal等温 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21lnVWQn RTVAfter adiaba
29、tic 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QST21lnVn RVunavailableETSIn a general irreversible process在一個廣泛的不可逆程序中minunavailableETSCoolest T in systemExample 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
30、 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？21lnVn RTVminunavailableETS15025.08.314/300ln2.0LLmolJK molKL54 kJ閥閥打打開開之前之前氣氣閥閥關關上上真空真空之後之後A Statis
31、tical 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微觀態微觀態Macrostates巨觀態巨觀態probability of macrostate巨觀態的或然率巨觀態的或然率 1/42 =1/4Gas 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
32、微觀態微觀態Macrostates巨觀態巨觀態probability of macrostate巨觀態的或然率巨觀態的或然率 1/16=0.064 1/16=0.254 1/16=0.251/16=0.066 1/16=3/8=0.38Gas of 100 molecules100個分子的氣體Gas of 1023 molecules1023 個分子的氣體Equal distribution of molecules分子平均分佈或然率lnBSkStatistical definition of entropy:熵的统計定義：#of micro states=微觀態數目Entropy&the 2
33、nd Law of Thermodynamics熵與熱力學第二定律2nd Law of Thermodynamics:熱力學第二定律0S 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 0Universe tends to disorder宇宙趨向混亂Life 生命?
34、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)a balloon inflates氣球充氣(b)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(c)an animal dies,its remains gradually decays一個動物死了，它的遺體慢慢腐爛(d)an earthquake demolishes a building 一場地震把一幢建築物毁了(e)a plant utilize sunlight,CO2,&water to manufacture sugar一棵植物用陽光，CO2，和水來制做糖(f)a power plant burns coal&produces electrical energy一所發電廠燒煤來產生電能(g)a cars friction based brakes stop the car.以摩擦力為主的剎車把車子停下來。
