Basic Concepts: Systems, Properties & Equilibrium基本概念：系統、性質與平衡

What you'll be able to do本章學習成果

• Define system, surroundings, boundary, and distinguish closed systems from control volumes.定義系統、外界與邊界，並區分封閉系統與控制體積。
• Recognize what a property is and the kinds of equilibrium that define a state.辨識性質的意涵，以及定義狀態的各類平衡。
• State the state postulate and recognize equilibrium.陳述狀態假設並辨識平衡狀態。
• Define process, path, and cycle, and state the zeroth law and temperature scales.定義過程、路徑與循環，陳述第零定律與溫標。
• Describe how pressure is measured, convert among pressure units, and relate gage, absolute, and vacuum pressure.說明壓力的量測方式，換算各種壓力單位，並建立表壓、絕對壓力與真空壓力之間的關係。

Systems & boundaries系統與邊界

Thermodynamics is the science of energy. The system is whatever we choose to study; the surroundings are everything external; the boundary separates them.熱力學是能量的科學。系統是我們選擇研究的對象；外界是一切外部環境；邊界將兩者分隔。

• Closed system (control mass): a fixed amount of mass. No mass crosses the boundary, though energy still can.封閉系統（控制質量）：固定的質量。質量不穿越邊界，但能量仍可。
• Open system (control volume): a region in space through which both mass and energy can flow.開放系統（控制體積）：空間中的一個區域，質量與能量皆可穿越。

We treat matter as a continuum, ignoring atomic graininess — valid when the system is large compared with the molecular mean free path (Knudsen number ≤ 0.01).我們將物質視為連續體，忽略原子尺度的不均勻性——在系統遠大於分子平均自由路徑時成立（努森數 ≤ 0.01）。

Properties性質

A property is any characteristic of a system — pressure, temperature, volume, mass. Properties are either intensive (independent of size) or extensive (proportional to extent); dividing extensive by mass gives a specific intensive property. See Thermodynamic Properties: Fundamentals for the full definitions and interactive lab.性質是系統的任何特徵——壓力、溫度、體積、質量。性質分為強度性質（與大小無關）與廣延性質（與大小成比例）；廣延性質除以質量得到比強度性質。完整定義與互動實驗請見熱力學性質：基礎。

State & equilibrium狀態與平衡

The state is the condition of a system described by its properties. Thermodynamics deals with equilibrium states — no unbalanced driving forces. Full equilibrium requires: thermal (uniform T), mechanical (uniform p), phase (stable phases), and chemical (no net reaction).狀態是由性質描述的系統條件。熱力學處理平衡狀態——無不平衡驅動力。完全熱力學平衡需同時滿足：熱平衡（溫度均勻）、力學平衡（壓力均勻）、相平衡（穩定相量）與化學平衡（無淨反應）。

The state postulate狀態假設

Fix any two independent intensive properties (say $T$ and $p$, or $T$ and $v$) and every other property is determined. This is the principle the psychrometric chart and property tables rely on. At saturation, $T$ and $p$ are not independent — a different second property is needed.固定任意兩個獨立強度性質（如 $T$ 與 $p$，或 $T$ 與 $v$），其他所有性質即被確定。這正是濕空氣線圖與性質表的依據。在飽和區，$T$ 與 $p$ 並非獨立——需另選第二個性質。

Process & path過程與路徑

A process is any change from one equilibrium state to another; the path is the series of states passed through. A quasi-equilibrium process stays infinitesimally close to equilibrium — the idealization that lets us draw a process as a line on a diagram. Iso- prefixes name constant-property processes: isothermal (T), isobaric (p), isochoric (v). A cycle returns to its initial state.過程是從一個平衡狀態到另一個平衡狀態的任何變化；路徑是所經歷的一系列狀態。準平衡過程在整個過程中始終無限接近平衡——這一理想化使我們能在性質圖上以線段表示過程。等字頭命名定性質過程：等溫（T）、等壓（p）、等容（v）。循環使系統回到初始狀態。

Temperature & the zeroth law溫度與第零定律

Temperature is our measure of hotness — microscopically, of the random kinetic energy of molecules. The zeroth law is what makes it measurable: the “third body” is a thermometer. Bring it into equilibrium with a system, read a property that changes with hotness (a liquid's length, a wire's resistance, a voltage), and the reading can be compared with any other system the thermometer has touched.溫度是我們度量冷熱的尺度——微觀上，是分子隨機動能的尺度。第零定律使溫度可以被量測：那個「第三個物體」就是溫度計。讓它與系統達到熱平衡，讀取一個隨冷熱變化的性質（液柱長度、導線電阻、電壓），讀值即可與溫度計接觸過的任何其他系統相比較。

Two questions follow. What numbers do we assign — the temperature scales below — and which physical effect do we read — the instruments after that. Thermodynamic relations always take absolute temperature, just as they take absolute pressure.由此衍生兩個問題：我們要賦予什麼數值——下文的溫標；以及讀取哪個物理效應——其後的量測儀器。熱力學關係式一律採用絕對溫度，就如同採用絕對壓力一样。

Temperature scales溫標

Every practical scale is pinned to easily reproduced states of water at 1 atm: the ice point (ice and air-saturated water in equilibrium) and the steam point (liquid water and vapor, no air, in equilibrium).所有實用溫標都以 1 atm 下易於重現的水的狀態為基準：冰點（冰與飽含空氣的水平衡共存）與汽點（液水與水蒸氣平衡共存，無空氣）。

• Celsius (°C) — the SI relative scale. Ice point 0 °C, steam point 100 °C, one hundred equal divisions between.攝氏（°C）——SI 相對溫標。冰點 0 °C，汽點 100 °C，中間等分為一百格。
• Fahrenheit (°F) — the English-system relative scale. Ice point 32 °F, steam point 212 °F, 180 divisions between — so one Fahrenheit degree is $5/9$ of a Celsius degree.華氏（°F）——英制相對溫標。冰點 32 °F，汽點 212 °F，中間 180 格——故一華氏度為攝氏度的 $5/9$。

Both scales put their zero at an arbitrary place. A scale whose zero is physically meaningful — and whose definition does not depend on the properties of any particular substance — is a thermodynamic (absolute) temperature scale. The second law will supply the rigorous definition; the experiment below shows where its zero sits.這兩種溫標的零點都是任意選定的。零點具有物理意義——且定義不依賴任何特定物質性質——的溫標，稱為熱力學（絕對）溫標。其嚴謹定義將由第二定律給出；以下実驗則展示其零點所在。

Deriving the Kelvin scale克耳文溫標的由來

Fill a rigid bulb with gas and use its pressure as the thermometric property — a constant-volume gas thermometer. At low pressure every gas behaves ideally, so $P$ varies linearly with temperature. Plot $P$ against $T(°\mathrm{C})$ for different gases and different amounts of gas: the lines have different slopes, but every one extrapolates to $P=0$ at the same temperature, $-273.15\ °\mathrm{C}$. That common intercept is absolute zero, and it is independent of the substance used.將氣體封入剛性球體，以其壓力作為測溫性質——即定容氣體溫度計。低壓下所有氣體皆近似理想氣體，故 $P$ 隨溫度線性變化。對不同氣體、不同氣量繪製 $P$ 對 $T(°\mathrm{C})$ 的圖：各直線斜率不同，但每一条外推至 $P=0$ 時都落在同一溫度：$-273.15\ °\mathrm{C}$。這個共同的截點就是絕對零度，且與所用物質無關。

The Kelvin scale keeps the size of the Celsius degree and moves the zero to absolute zero:克耳文溫標保留攝氏度的大小，而將零點移至絕對零度：

Historically the kelvin was fixed by assigning the ice point 273.15 K; in 1954 the reference moved to the more reproducible triple point of water, set to exactly 273.16 K. Since 2019 the kelvin is defined by fixing the Boltzmann constant, $k_B = 1.380649\times10^{-23}$ J/K, which ties temperature directly to energy and to no substance at all. Note the unit is written K, not °K.歷史上，克耳文以冰點定為 273.15 K 而確定；1954 年參考點改為更易重現的水的三相點，定為恰好 273.16 K。自 2019 年起，克耳文改由固定波茲曼常數 $k_B = 1.380649\times10^{-23}$ J/K 定義，使溫度直接與能量連結，不再依賴任何特定物質。注意單位寫作 K，而非 °K。

The Rankine scale (R) is the English-system absolute scale: same zero as Kelvin, but with the Fahrenheit-sized degree.蘭金溫標（R）是英制的絕對溫標：零點與克耳文相同，但採用華氏度的大小。

Measuring temperature溫度量測

Any property that changes reproducibly with hotness can serve as a thermometer. Three dominate engineering practice.任何隨冷熱可重現地變化的性質都可用作溫度計。工程實務中以三種為主。

1 · Liquid-in-glass thermometer1 · 玻璃液體溫度計

A bulb of mercury or dyed alcohol feeds a fine capillary. The liquid expands more than the glass, so the column length tracks temperature; the stem is graduated against the fixed points. No power, no electronics — but slow, fragile, read by eye, and limited by the liquid (mercury freezes at −38.8 °C).裝有水銀或染色酒精的球部連接一根細毛管。液體的膨張大於玻璃，故液柱長度隨溫度變化；管身依固定點刻度。無需電源與電子元件——但反應慢、易碎、需目視讀值，且受液體性質限制（水銀在 −38.8 °C 凝固）。

2 · Thermocouple2 · 熱電偶

Join two wires of dissimilar metals at one end. Whenever that junction is at a different temperature from the other ends, a small voltage appears — the Seebeck effect. The EMF depends only on the two metals and on the temperature difference between the measuring junction and the reference junction, so the reference temperature must be known or compensated electronically. Standard pairs are lettered: type K (chromel–alumel, ≈ 41 µV/°C), J, T, and others. Thermocouples are cheap, rugged, fast, and span roughly −200 to 1350 °C — the workhorse of combustion and process measurement — at the cost of modest accuracy, typically ±1–2 °C.將兩根不同金屬的導線一端接合。當該接點與另一端溫度不同時，便產生微小電壓——即塞貝克效應。此電動勢僅取決於兩種金屬，以及量測接點與參考接點間的溫度差，因此參考溫度必須已知或以電子方式補償。標準金屬對以字母編號：K 型（鎘鎮－鎮鋁，約 41 µV/°C）、J 型、T 型等。熱電偶便宜、耐用、反應快，量測範圍約 −200 至 1350 °C——是燃燒與製程量測的主力——代價是精度普通，通常為 ±1–2 °C。

3 · Resistance temperature detector (RTD)3 · 電阻溫度檢測器（RTD）

The electrical resistance of a pure metal rises almost linearly with temperature. An RTD is a fine platinum wire or film whose resistance is measured with a bridge or ohmmeter; the industry standard Pt100 reads 100 Ω at 0 °C and about 138.5 Ω at 100 °C. Platinum is chemically inert and exceptionally stable, so RTDs are the most accurate and repeatable of the three (±0.1–0.3 °C), though slower, costlier, and limited to roughly −200 to 600 °C. Three- or four-wire connections cancel the resistance of the lead wires themselves.純金屬的電阻隨溫度近似線性上升。RTD 是一根細白金絲或白金薄膜，以電橋或歐姆表量測其電阻；工業標準的 Pt100 在 0 °C 為 100 Ω，100 °C 時約 138.5 Ω。白金化學惰性且極為穩定，故 RTD 是三者中最精確、重現性最佳的（±0.1–0.3 °C），但反應較慢、成本較高，範圍約限於 −200 至 600 °C。三線或四線式接法可消除引線本身的電阻。

Beyond these, thermistors (semiconductor resistors, very sensitive over a narrow range) and infrared pyrometers (non-contact, from emitted radiation) fill the gaps. Whatever the sensor, it reports the temperature of itself — the zeroth law is satisfied only once it has reached equilibrium with what you meant to measure.除此之外，熱敏電阻（半導體電阻，窄範圍內極靈敏）與紅外線高溫計（非接觸式，由輻射推算）填補其餘需求。無論哪種感測器，它回報的都是自身的溫度——唯有在它與你想量測的對象達到平衡之後，第零定律才真正成立。

Pressure壓力

Pressure is the normal force a fluid exerts per unit area. It is an intensive property, and — like temperature — it only means something thermodynamically when referred to a definite zero.壓力是流體在單位面積上施加的垂直力。它是強度性質；與溫度相同，唯有相對於明確的零點時，壓力在熱力學上才具有意義。

In a fluid at rest pressure grows with depth as the weight of the column above adds up, $\Delta P = \rho g \Delta h$ — the relation every pressure-measuring device below is built on.靜止流體中，壓力隨深度增加，因上方液柱重量累加所致：$\Delta P = \rho g \Delta h$——以下各種壓力量測裝置皆建立在此關係之上。

Measuring pressure壓力量測

Three classic instruments cover most of engineering practice: the barometer for atmospheric pressure, the manometer for small and moderate differences, and the Bourdon tube gage for everyday industrial readings.三種經典儀器涵蓋了工程實務的大部分需求：量測大氣壓的氣壓計、量測小至中等壓差的壓力計（U 型管），以及用於日常工業讀值的波登管壓力表。

1 · The mercury barometer1 · 水銀氣壓計

Torricelli's 1644 instrument: invert a sealed tube of mercury into an open dish. The column falls until its weight balances the atmosphere pressing on the free surface, leaving near-vacuum above. The height of that column is the atmospheric pressure — which is why atmospheric pressure is also called barometric pressure.托里切利於 1644 年發明的儀器：將裝滿水銀的密封管倒插入開口皿中。水銀柱下降，直到其重量與作用於自由液面的大氣壓平衡，管頂留下近乎真空。該液柱的高度就是大氣壓——這也是大氣壓又稱氣壓計壓力的原因。

2 · The manometer2 · U 型管壓力計

A U-tube partly filled with a working liquid — mercury, water, alcohol, or oil. One leg connects to the vessel, the other opens to the atmosphere; the fluid shifts until the height difference $h$ balances the pressure difference. Choosing a light fluid magnifies $h$ for small pressure differences, which is why manometers excel at low-pressure work.U 型管內部分充填工作液體——水銀、水、酒精或油。一端接容器，另一端通大氣；液體移動直到高度差 $h$ 與壓差平衡。選用較輕的液體可放大小壓差所對應的 $h$，這正是壓力計擅長低壓量測的原因。

3 · The Bourdon tube gage3 · 波登管壓力表

A hollow metal tube of flattened cross-section, bent into a C and sealed at the free end. Applying pressure inside tries to straighten it; the tiny deflection drives a linkage and needle. It is rugged, needs no liquid, and reads both positive pressures and vacuum — but because the case is open to the atmosphere it registers the difference from ambient, so a Bourdon gage reads gage pressure.一根截面扁平的中空金屬管，彎成 C 形且自由端封閉。內部加壓時管子有伸直的趨勢，此微小變形經連桿機構驅動指針。它堅固耐用、無需液體，且可量測正壓與真空——但由於表殼與大氣相通，所量得的是與環境的差值，因此波登管壓力表顯示的是表壓。

Modern practice adds pressure transducers — strain-gage diaphragms and piezoelectric elements that convert deflection into an electrical signal. They are more sensitive, faster, and easier to log than mechanical gages, but the reference-level question below is identical for all of them.現代實務另有壓力轉換器——應變計膜片與壓電元件，將變形轉換為電訊號。相較於機械式錶頭，它們更靈敏、反應更快且便於記錄，但以下的基準面問題對所有裝置一律相同。

Units of pressure壓力單位

The SI unit is the pascal, $1\ \mathrm{Pa} = 1\ \mathrm{N/m^2}$ — an inconveniently small quantity, since the atmosphere alone is about 101 325 Pa. Engineering therefore works in kPa, MPa, and bar, while barometry and US industrial practice keep their own units.SI 單位為帕斯卡，$1\ \mathrm{Pa} = 1\ \mathrm{N/m^2}$——此量相當小，因為單是大氣壓即約 101 325 Pa。因此工程上慣用 kPa、MPa 與 bar，而氣壓量測與美制工業實務則各自沿用其單位。

Gage, absolute & vacuum pressure表壓、絕對壓力與真空壓力

Every pressure number needs its zero declared. There are only two sensible choices — absolute vacuum, or the local atmosphere — and each names a different quantity.每個壓力數值都必須說明其零點。合理的選擇只有兩種——絕對真空，或當地大氣——而兩者對應不同的物理量。

• Absolute pressure $P_{abs}$ — the actual pressure at a point, measured from absolute vacuum (absolute zero pressure). It can never be negative.絕對壓力 $P_{abs}$——某點的實際壓力，以絕對真空（絕對零壓）為基準量測。其值不可能為負。
• Atmospheric pressure $P_{atm}$ — the local ambient pressure, read from a barometer (hence barometric pressure). It varies with altitude and weather; the fixed 101.325 kPa standard atmosphere above is only a reference value.大氣壓 $P_{atm}$——當地環境壓力，由氣壓計讀取（故又稱氣壓計壓力）。它隨海拔與天氣變化；上節固定的 101.325 kPa 標準大氣壓僅為參考值。
• Gage pressure $P_{gage}$ — the amount by which absolute pressure exceeds the local atmosphere. Most instruments are calibrated to read zero in open air, so they report gage pressure.表壓 $P_{gage}$——絕對壓力超出當地大氣壓的量。多數儀器校正為在敞露大氣中讀零，故其顯示值即為表壓。
• Vacuum pressure $P_{vac}$ — the amount by which absolute pressure falls below the local atmosphere. It is reported as a positive number, i.e. a negative gage pressure quoted with its sign removed.真空壓力 $P_{vac}$——絕對壓力低於當地大氣壓的量。習慣以正值表示，亦即將負表壓去掉負號後的數值。

How the reference gets written down depends on the unit system:基準的標示方式依單位系統而異：

Gauge to absolute pressure表壓換算絕對壓力

Key terms & equations關鍵術語與重要公式

Systems, properties, states, and processes are the grammar of everything that follows. If you can name the system, list its independent properties, and say what is held fixed during a process, you have the chapter.系統、性質、狀態與過程是後續一切的文法。若能指出系統、列出其獨立性質、並說明過程中什麼被固定，本章便已掌握。

Key terms關鍵術語