Why are black robes worn in extremely hot climates? 7 熱物理 Why are black robes worn in extremely hot climates?

黑袍下的秘密 6C higher, Nature 1980

熱物理 (Thermal Physics) 溫度與熱 熱膨脹 相變化（phase changes） 熱傳遞（Heat transfer） 氣體動力論（Kinetic Theory of gases） 引擎與致冷機

7.1 溫度與熱 The Celsius and Fahrenheit temperature scales Kelvin Scale TF = (9/5)TC+32° Kelvin Scale TC = T – 273.15° T3 = 273.16K triple point 水的三相點溫度

凱氏攝氏與華氏溫標

攝氏與華氏溫標

從最高溫到最低溫 0.5x10-9

溫度計 定容氣體溫度計 熱偶溫度計 Bimetallic strip Optical pyrometer

定容氣體溫度計

凱氏溫標的定義

熱偶溫度計 (thermocouple) -240 ° C– 2700 °C 康銅是一種銅鎳合金，由55%的銅和45%鎳(Cu55Ni45)所組成，它的特性是不易隨溫度變化而改變其性其，且電阻率高。 -240 ° C– 2700 °C

Bimetallic strip and Optical pyrometer 光測高溫計 集中於一幕屏（screen）上，幕屏後裝一紅色濾鏡，僅讓波長為0.65 microns之輻射能透過，俾使觀察者易觀察幕屏上之情形。同時另裝一標準鎢絲燈，其發出之輻射能亦可集中在幕屏上，以作為比較。調整變阻器以調整通過標準鎢絲燈之電流，使標準光源在幕屏上之亮度（brightness） 與輻射熱之亮度相等。此時變阻器之刻度即代表此輻射熱源之溫度。

熱（heat）的定義和單位 Heat is the energy that is transferred between a system and its environment because of a temperature difference that exists between them J = Joule（焦耳） Cal = calorie（卡洛里） Btu = British Thermal Unit

例一 A candy bar 350大卡 1 mile = 1.609 km 供100W燈泡使用4.1h 慢跑3 ~ 4mi

7.2 熱膨脹

Bimetallic strip switch

線膨脹與體膨脹

例二 熱應力 (Thermal stress)

例三 Delivering diesel oil from Las Vegas to Payson 9785 gal, temperature difference 41°F  = 9.510-4/C ° - diesel fuel  = 11 10-6/C ° - steel tank

例四 水的 ”熱漲冷縮”

7.3 相變化（phase changes） 固態 –> 液態 –> 氣態 –> 電漿態 固態 –> 液態 –> 氣態 –> 電漿態 -----------------溫度上升--------------> solid liquid vapor plasma (冰) (水) (水蒸氣) (H、O、e)

Phase diagram of water 水在一大氣壓下，以恆定率加熱時，其溫度隨時間之變化。

Phase diagram of water The liquid and vapor densities become closer and closer to each other until the critical temperature is reached where the two densities are equal and the liquid-gas line or phase boundary disappears.

比熱和潛熱 比熱（specific heat capacity）：使每公斤物質溫度上升1K或1℃所需之熱。 潛熱（latent heat）：相變化中，每公斤物質所吸收或釋出之熱。

潛熱表

例五 使-5℃，5公斤的冰塊變成150℃的水蒸氣所需的熱量Q

7.4 熱傳遞（Heat transfer） 傳導（conduction） 對流（convection） 輻射（Radiation）

傳導（conduction） H（Heat flow熱流）= KA T /L K：導熱率 A：截面積 T：溫差 L ：長度

導熱率

R-value R．30 insulating slab 5.1 in PU foam 23 in white pine 180 in glass 1.4 mi silver R=L/k –> H = A T /R

例六 人體組織的熱傳導 人以普通速度步行時，產生之熱流 為280W 人體表面積約1.5m2，且平均而言，熱係於皮膚之下0.03m處產生 導熱率則約與動物肌肉相同，為 0.2 W/mK

熱流 皮膚與體內之溫差僅數度，因此熱並非經由組織之傳導，而係經由血液輸送。

對流（convection）

Global Circulation

Climate

例七 暖氣與冰箱

例八 forced convection

例九 Sauna 皮膚溫度 = 33℃，室溫 = 29℃ 人體表面積 = 1.5m2 此人所產生之熱流約為2倍；另一半藉由輻射散失。

輻射（Radiation） 良輻射體亦為良吸收體 Stefan-Boltzmann Law 輻射功率 H = eAT4 e：輻射率 0 ≦ e ≦ 1 e = 1－完美輻射體(吸收體)－black body 光亮表面之e則極小

例十 人體的輻射 人體在紅外線波長範圍e ~1 人體在可見光波長範圍e = 0.82~0.65 皮膚溫度33℃ = 306K

例十一獵戶座的紅巨星 Betelgeuse 表面溫度2900 K，輻射功率4 ×1030 （太陽的一半） （太陽的10000倍） 火星軌道半徑

例十二 Hubble 望遠鏡的溫度調節設計 軌道衛星之日照被地球屏蔽時，其溫度與未被屏蔽時，有極大差異。 衛星表面的高反射金屬膜在日照下，可反射大部分來自太陽的輻射，把溫昇降至最低；而當其在地球陰影內時，亦可降低本身輻射之熱損耗。（poor absorber = poor emitter） Launched in 1990 and greatly extended in its scientific powers through new instrumentation installed during four servicing missions with the Space Shuttle, the Hubble, in its sixteen years of operations, has validated Lyman Spitzer Jr.'s (1914-1997) original concept of a diversely instrumented observatory orbiting far above the distorting effects of the Earth’s atmosphere and returning data of unique scientific value. Hubble's coverage of light of different colors (its "spectral range") extends from the ultraviolet, through the visible (to which our eyes are sensitive), and into the near-infrared. Hubble's primary mirror is 2.4 meters (94.5 inches) in diameter. Hubble is not large by ground-based standards but it achieves heroically in space. Hubble orbits Earth every 97 minutes, 575 kilometers (360 miles) above the Earth's surface.

例十三 太陽能熱水器 收集器內部，包括水管均漆有高吸收黑漆，提昇其對太陽輻射之吸收。 水管以銅製，提昇水管水的熱傳導。 收集器之玻璃蓋降低因空氣對流之熱損耗。

例十四輻射與動物的活動－狐猿（lemur） white sifaka

例十五紅外線照相能源分析（thermogram）

醫學、環境 交感神經因局部麻醉而阻斷 (35.75 vs 33.25 C )

7.5 氣體動力論 壓力、溫度與方均根速度 氣體的狀態方程式 （equation of state） 氣體分子的速率 Kinetic Theory of Gases

壓力、溫度與方均根速度 微觀與巨觀 Microscopic and macroscopic Pressure, temperature and RMS speed

動量、力與壓力

方均根速度

各種氣體的方均根速度

氣體的狀態方程式 PV = nRT –> P = nRT /V + C/V2 …… P：壓力 V：體積 n：莫耳數（mole） T：溫度 R：氣體常數 = 8.31

例十六 1 mole氣體的體積 STP: Standard Temperature and Pressure Conditions –> 0℃（273K） 1 atm = 1.013105Pa (N/m2)

mole and NA Avogadro’s number 1 mole 物質，包含N = 6.022 ×1023個原子

例十七 Hope Diamond 112 3/16 - carat Golconda, India, 1688 Smithsonian http://groups.google.com/group/talk.politics.misc/browse_thread/thread/bf820ef369a141f/8bbb8c46ee5a36c8?lnk=st&q=Hope+Diamond&rnum=1&hl=en#8bbb8c46ee5a36c8 WASHINGTON (AP) -- Researchers using computer analysis have traced the origin of the famed Hope Diamond, concluding that it was cut from a larger stone that was once part of the crown jewels of France. A French connection had been suspected for the Hope, but the new study shows just how it would have fit inside the larger French Blue Diamond and how that gem was cut, Smithsonian gem curator Jeffrey Post explained. The deep blue Hope Diamond is the centerpiece of the gem collection at the Smithsonian's National Museum of Natural History, famed for its claimed history of bad luck for its owners. It's been good fortune for the museum, though, drawing millions of visitors. Post said the new analysis of the diamond took a year, with researchers using sketches from pre-Revolutionary France, scientific studies of the French crown jewels and computer models. "This new Hope Diamond research would not have been possible 10 years ago," said Post. "What is exciting is that we are constantly learning new information about our collections as we apply new high-tech research methods. Even the Hope Diamond is grudgingly giving up some of its secrets." The research helps confirm the Hope Diamond as originating with a 115-carat stone found in India in 1668. That stone was sold to King Louis XIV of France who had it cut into the 69-carat French Blue. The French Blue was stolen during the French Revolution. Just over twenty years later, after the statute of limitations expired, a large blue diamond was quietly put up for sale in London, and eventually Henry Philip Hope purchased it. Finally donated to the Smithsonian by jeweler Harry Winston, the now 45.52 carat stone is the world's largest blue diamond. The team of researchers led by Post and Steven Attaway, engineer and gem cutter; as well as Scott Sucher and Nancy Attaway, gem cutting experts, compiled the new analysis. While the French Blue no longer exists, Post said the sketches of it from France were quite detailed and allowed preparation of a computer model of that stone. In 1700, French scientists had also studied several stones from the royal collection, determining their specific gravity and other details. Their analysis of other stones that still exist was quite accurate, Post said in a telephone interview, so the researchers felt the data on the French Blue was also probably accurate. After using the sketches and analysis to make the computer model of the French Blue, and at the same time measuring the Hope Diamond and entering that data into the computer, the researchers "virtually placed the Hope back inside the French Blue" Post said. "It turns out it actually fits perfectly in only one way, but at that orientation, when you saw how it fit, you could see why it was cut the way it is," Post said. "They cut he corners off the French Blue, changed slightly the angle of the bottom facets, and that produced the Hope Diamond," he said. Indeed, some of the facets of the current diamond may even be left over from the French Blue.

例十八 Rosser Reeves Ruby Sri Lanka Smithsonian 1 mole of Al2O3 = 2(26.9815g)＋ 3(15.9994g) =101.9612g Sri Lanka

氣體分子的速率 Maxwell’s speed distribution

不同溫度時之速率分布

例十九 Maxwell’s speed distribution (a) The average speed (b) The root-mean-square speed (c) The most probable speed

7.5 引擎與致冷機 熱與功 引擎的效率 沒有完美的引擎 致冷機的效能係數 沒有完美的致冷機

功(work) 理想氣體進行等溫 程序所作的功 理想氣體的狀態方程式 Work Done by an ideal gas at constant temperature

程序與等溫線 Process and Isotherms

Process 絕熱Adiabatic Process 等溫Isothermal Process 定壓Isobaric process 定容Isochoric process

其他程序

引擎 美國維吉尼亞州的North Anna核電廠 核三發電容量 1900MW 核四發電容量 2700MW

The Stirling Engine

The PV diagram efficiency An isothermal expansion (ab) A constant-volume process (bc) An isothermal compression (cd) A constant-volume process (da) efficiency

引擎的效率 efficiency  = = 一般摩托車之效率22﹪，所做功為2510 J，則廢熱Q為

致冷機

致冷機的效能係數 coefficient of performance K =

例二十 家用冰箱 K = 4.7，Q = 250 J（每循環） 電功 廢熱

Entropy 熵 Some one-way processes

敬請期待 電、磁、近代物理

彈性 物質受力（應力，Stress）後產生形變（應變，Strain），當應力移除後，物質回復原狀之性質即為彈性。

應力－應變圖 A：比例極限（proportional limit） B：屈服點（yield point）或彈性極限 在比例極限之內 應力（）＝ 比例常數 ×應變（ε）

應力的種類 拉張壓力 壓縮應力 剪(切)應力 壓力

Young’s Modulus Y–楊氏模數 S –切變模數 B –體模數

Ex. 4-1 骨骼的壓縮 承受重量 = 1640N/2= 820N 大腿骨長度 ＝ 0.55m 截面積 = 7.7×10-4m2

Ex. 4-2 鋼樑熱膨脹 L = 9.6m A = 0.10 m 溫度上升19℃時，膨脹2.2×10-3m