📚 Thermometers | 温度计
Thermometers are indispensable instruments in physics and everyday life, used to measure temperature. Temperature itself is a measure of the hotness or coldness of a body and determines the net direction of thermal energy transfer between objects. A reliable temperature measurement underpins everything from weather forecasting to industrial process control and scientific experiments at the highest level of precision.
温度计是物理学和日常生活中不可或缺的仪器，用于测量温度。温度本身衡量物体的冷热程度，并决定物体之间热能传递的净方向。可靠的温度测量是天气预报、工业过程控制乃至最高精度科学实验的基础。
1. What is Temperature? | 什么是温度？
Temperature is a physical quantity that indicates how hot or cold an object is relative to a chosen scale. Microscopically, temperature is proportional to the average random kinetic energy of the particles (atoms or molecules) in a substance. In the kinetic model of matter, a higher temperature means the particles move faster, leading to a higher internal energy for a given mass. It is temperature that dictates thermal equilibrium: when two bodies are placed in thermal contact, energy will spontaneously flow from the body at higher temperature to the body at lower temperature until both reach the same temperature.
温度是一个物理量，表示物体相对于选定标度的冷热程度。从微观上看，温度与物质中粒子（原子或分子）的平均无规动能成正比。在物质动理论模型中，温度越高意味着粒子运动越快，对于给定质量而言内能也越高。正是温度决定了热平衡：当两个物体热接触时，能量会自发地从高温物体流向低温物体，直到两者达到相同温度。
All temperature measurements rely on a thermometric property — a physical property that changes continuously and predictably with temperature. Typical thermometric properties include the volume of a liquid, the electrical resistance of a metal wire, the pressure of a gas at constant volume, and the electromotive force (e.m.f.) generated by a thermocouple. For a property to be useful, it must be reproducible, sensitive, and relatively easy to measure.
所有温度测量都依赖于一个测温属性——一种随温度连续且可预测变化的物理性质。常见的测温属性包括液体的体积、金属丝的电阻、恒容气体的压强以及热电偶产生的电动势。一个有实用价值的属性必须是可重复的、灵敏的且相对容易测量的。
2. The Concept of a Thermometer | 温度计的概念
A thermometer is any device that uses a thermometric property to assign a numerical value to temperature. The basic principle is to choose a substance whose physical property varies monotonically with temperature, and then calibrate the instrument using two or more well-defined fixed points. Once calibrated, the property can be measured, and by assuming a simple mathematical relationship between the property and the temperature, the temperature of an unknown environment can be determined.
温度计是利用测温属性给温度赋予数值的任何装置。基本原理是选择一种其物理性质随温度单调变化的物质，然后利用两个或多个定义明确的固定点对仪器进行校准。一旦校准后，通过测量该性质并假设性质与温度之间存在简单的数学关系，就可以确定未知环境的温度。
Historically, the Celsius scale was defined by the ice point (0 °C) and the steam point (100 °C) at standard atmospheric pressure. Modern precision thermometry, however, uses the triple point of water (0.01 °C, 273.16 K) as a single fixed point because it is more reproducible than the melting and boiling points. The thermodynamic Kelvin scale is founded on absolute zero and this triple point.
历史上，摄氏温标由标准大气压下的冰点（0 °C）和汽点（100 °C）定义。然而，现代精密测温使用水的三相点（0.01 °C，273.16 K）作为单一固定点，因为它比熔点和沸点更具可重复性。热力学开尔文温标正是建立在绝对零度和这一三相点之上的。
3. Fixed Points and Calibration | 固定点与校准
Calibration is the process of relating the readings of a thermometer to the internationally agreed temperature scale. For a liquid‑in‑glass thermometer, this traditionally involves marking the stem at the ice point (0 °C) and the steam point (100 °C) under atmospheric pressure of 101 325 Pa. The interval between these two marks is then divided into 100 equal divisions to give the Celsius degree. More recent standards rely on the triple point of water (273.16 K), where ice, liquid water and water vapour coexist in equilibrium.
校准是使温度计的读数与国际公认温标相关联的过程。对于液体玻璃温度计，传统方法是在标准大气压（101 325 Pa）下于冰点（0 °C）和汽点（100 °C）处标划刻度，然后将两点之间等分为100份，得到摄氏度。较新标准则依赖水的三相点（273.16 K），此时冰、液态水和水蒸汽三相共存平衡。
rate any thermometer, the sensing element is placed in good thermal contact with the fixed‑ here the constants a and b are determined from measurements at two fixed points. For a non‑ calibrated against a standard, ultimately traceable to the primary temperature standards.
校准任何温度计时，需将感温元件与固定点容器的热接触良好，并测量测温属性 X。如果假设 X 与温度 T 呈线性关系，可写作 T = aX + b，其中 a 和 b 通过两个固定点的测量确定。对于非线性温度计，则需要更复杂的插值函数。所有实用温度计都依据标准校准，最终可溯源至基准温度标准。
4. Liquid‑in‑Glass Thermometers | 液体玻璃温度计
A liquid‑in‑glass thermometer consists of a thin‑ olumn in the stem. As temperature rises, the liquid expands much more than the glass, so the column length increases. The thermometric property is the length L of the liquid column, which is assumed to increase linearly with temperature: L = L0(1 + βθ), where θ is the Celsius temperature and β is an apparent expansion coefficient.
液体玻璃温度计由一个薄壁玻璃泡和一段极细的毛细管组成，液体（通常为水银或染色的酒精）部分填充玻璃泡并在玻管中留下一段液柱。温度升高时，液体的膨胀远大于玻璃，因此液柱长度增加。测温属性是液柱长度 L，假定它与温度呈线性增长：L = L0(1 + βθ)，其中 θ 是摄氏温度，β 是视膨胀系数。
Mercury thermometers offer a wide range (approximately −39 °C to 357 °C) and respond relatively quickly, but mercury is toxic, limiting their use. Alcohol (or pentane) thermometers can reach lower temperatures (down to about −115 °C) but are less accurate at high temperatures because the dye may degrade. The main limitations are the fragility of glass, a relatively slow response for thick‑walled bulbs, and the impossibility of measuring minute temperature differences. Nevertheless, they remain common in school laboratories and for everyday use.
水银温度计量程较宽（约 −39 °C 至 357 °C）且响应较快，但水银有毒，限制了其使用。酒精（或戊烷）温度计可测更低温（低至约 −115 °C），但在高温下因染料可能降解而精度较差。其主要局限性在于玻璃易碎、厚壁玻璃泡响应较慢，且无法测量极微小的温度差异。尽管如此，它们在学校实验室和日常使用中仍然很常见。
5. Thermocouple Thermometers | 热电偶温度计
Thermocouples exploit the Seebeck effect: when two wires of different metals are joined to form two junctions and the junctions are held at different temperatures, a temperature‑dependent e.m.f. V appears in the circuit. One junction is maintained at a known reference temperature (often 0 °C, using an ice‑water bath), while the other junction acts as the temperature probe. The thermometric property is the e.m.f. V, which can be measured with a sensitive voltmeter or potentiometer.
热电偶利用塞贝克效应：当两根不同金属丝连接成两个接点，并使两接点处于不同温度时，电路中会产生与温度相关的电动势 V。一个接点保持在已知参考温度（通常使用冰水浴维持在0 °C），另一个接点则作为测温探头。测温属性为电动势 V，可用灵敏的电压表或电位差计测量。
The relationship between V and the temperature difference (θ − θref) is approximately quadratic: V = a(θ − θref) + b(θ − θref)2, where a and b are constants that depend on the pair of metals. For small temperature ranges, the quadratic term is negligible, and the response is nearly linear. Common material pairs are copper–constantan (type T) and chromel–alumel (type K).
电动势 V 与温差 (θ − θref) 之间的关系近似为二次函数：V = a(θ − θref) + b(θ − θref)2，其中 a 和 b 是取决于金属对的常数。对于小温差范围，二次项可忽略，响应近乎线性。常见的金属对包括铜‑康铜（T型）和铬镍‑铝镍（K型）。
Thermocouples are valued for their very rapid response (small thermal mass of the junction), wide operating range (from cryogenic temperatures to over 1000 °C), and robustness. However, the e.m.f. is small (tens of microvolts per kelvin), requiring careful amplification, and the slight non‑linearity must be corrected electronically for high precision.
热电偶因其极快的响应（接点热容小）、宽工作范围（从低温到超过1000 °C）以及坚固耐用而受到重视。然而，其电动势很小（每开尔文几十微伏），需要仔细放大，而且微弱的非线性需通过电路修正以获得高精度。
6. Resistance Thermometers | 电阻温度计
hly with temperature. Platinum is the preferred material because of its chemical inertness, stability, and nearly linear behaviour over a wide range. The resistance R of a platinum wire at temperature θ can be expressed as R = R0(1 + αθ + γθ2 + ...), where R0 is the resistance at 0 °C and α, γ are temperature coefficients.
电阻温度计（或电阻温度探测器，RTD）利用纯金属的电阻率随温度平稳增大的特性。铂是首选材料，因为它化学惰性、稳定且在宽范围内几乎呈线性。铂丝在温度 θ 下的电阻可表示为 R = R0(1 + αθ + γθ2 + ...)，其中 R0 是0 °C时的电阻，α、γ 是温度系数。
applications, the quadratic and higher terms are small, and the linear approximation R = R0(1 + αθ) is sufficient over a few hundred degrees Celsius. Platinum resistance thermometers can cover the range from about −200 °C to 850 °C and are widely used as secondary standards in laboratories. They offer excellent accuracy, stability, and reproducibility, but their larger size and thermal mass make them slower to respond than thermocouples.
对于许多应用，二次项及更高次项很小，在几百摄氏度范围内使用线性近似 R = R0(1 + αθ) 即已足够。铂电阻温度计可覆盖约 −200 °C 到 850 °C 的范围，并广泛用作实验室的副基准。它们具有优异的精度、稳定性和可重复性，但较大的尺寸和热容使其响应比热电偶慢。
7. Thermistors | 热敏电阻温度计
Thermistors are temperature‑ mperature coefficient (NTC): their resistance decreases sharply as temperature rises. The resistance–temperature relation is strongly non‑linear and can be modelled by an exponential equation: R = A eB/T, where T is the absolute temperature, and A and B are material constants.
热敏电阻是由半导体材料（通常是锰、镍或钴的氧化物）制成的温度敏感电阻。大多数热敏电阻呈负温度系数（NTC）：其电阻随温度升高急剧减小。电阻‑温度关系呈强烈的非线性，可用指数方程建模：R = A eB/T，其中 T 为绝对温度，A 和 B 是材料常数。
Because of the exponential dependence, thermistors possess extremely high sensitivity — a small temperature change gives a large change in resistance — making them ideal for applications requiring fine temperature resolution, such as digital clinical thermometers and electronic thermostats. Their working range is more limited (typically −50 °C to 150 °C), and the non‑linear response demands additional signal processing or a linearisation circuit. Despite this, their low cost, small size and fast response make them highly popular in consumer electronics.
由于指数关系，热敏电阻具有极高的灵敏度——微小的温度变化可导致显著的电阻变化——因此非常适用于需要精细温度分辨的场合，如数字体温计和电子恒温器。其工作范围较窄（通常 −50 °C 至 150 °C），且非线性响应需要额外的信号处理或线性化电路。尽管如此，它们成本低、体积小、响应快，在消费电子中应用极广。
8. Constant‑Volume Gas Thermometer | 恒容气体温度计
A constant‑volume gas thermometer contains a small amount of gas (often helium) sealed in a bulb connected to a manometer. The volume of the gas is kept fixed, and the pressure p is measured as the temperature of the bulb is varied. According to the ideal gas law, p/T is constant for a given amount of gas at fixed volume, provided the gas behaves ideally. The pressure therefore serves as the thermometric property.
恒容气体温度计在一个与压力计相连的玻璃泡内封存少量气体（通常为氦），保持气体容积不变，测量不同温度下气体的压强 p。根据理想气体状态方程，当气体行为接近理想气体时，对于一定量的气体，在容积不变下 p/T 为定值。因此，压强可作为测温属性。
If the pressure of the gas is measured at the triple point of water, ptr, and at an unknown temperature T, we have T = Ttr × (p / ptr), where Ttr 6 K. By using gases at very low densities and extrapolating to zero pressure, the constant‑ thermodynamic Kelvin scale independently of the gas used. It is a primary thermometer but is bulky, slow, and impractical outside standards laboratories.
测量气体在水的三相点处的压强 ptr 以及在未知温度 T 下的压强，则由 T = Ttr × (p / ptr) 可求得温度，其中 Ttr = 273.16 K。通过使用极低密度的气体并外推至零压强，恒容气体温度计可不依赖于所用气体的种类而实现热力学开尔文温标。它是一种基准温度计，但体积大、响应慢，不适用于标准实验室以外的场合。
9. Thermodynamic Kelvin Scale | 热力学开尔文温标
and by the condition that temperature is proportional to the average thermal energy of the particles in the limit of an ideal system. The zero point of the Kelvin scale is absolute zero (0 K = −273.15 °C), the theoretical lowest possible temperature where particles have minimum kinetic energy.
开尔文温标是热力学温度的国际单位制基本标度。其定义是将水的三相点赋值为精确的 273.16 K，并规定在理想系统极限下，温度与粒子的平均热能成正比。开尔文温标的零点为绝对零度（0 K = −273.15 °C），这是理论上可能的最低温度，此时粒子动能达到最小值。
ubstance. In practice, the Kelvin is realised by primary thermometers such as the constant‑volume gas thermometer, acoustic gas thermometers, or radiometric methods. For most A‑vel problems, the simple relation T(K) = θ(°C) + 273.15 is used to convert between scales.
热力学温标的主要优点在于它不依赖于任何特定测温物质的性质。实践中，开尔文通过恒容气体温度计、声学气体温度计或辐射法等基准温度计来实现。对于大多数 A‑level 问题，使用简单关系式 T(K) = θ(°C) + 273.15 即可进行温标转换。
10. Sensitivity, Range and Linearity | 灵敏度、量程与线性
When choosing a thermometer, three practical characteristics are critical: sensitivity, range and linearity. Sensitivity is the change in the thermometric property per unit change in temperature. A thermistor, for example, has a very high sensitivity because its resistance can change by hundreds of ohms per degree Celsius, while a thermocouple’s e.m.f. change is only a few tens of microvolts per kelvin. Range is the set of temperatures over which the thermometer can operate reliably. Liquid‑in‑glass thermometers might span −100 °C to 300 °C, whereas thermocouples can reach up to 1700 °C. Linearity describes how close the relationship between temperature and the measured property is to a straight line. A platinum resistance thermometer is nearly linear; a thermistor is highly non‑linear.
选择温度计时，三个实用特性至关重要：灵敏度、量程和线性度。灵敏度是指测温属性随单位温度变化的变化量。例如，热敏电阻的灵敏度极高，每摄氏度电阻可变化数百欧姆，而热电偶每开尔文仅变化数十微伏。量程是指温度计能可靠工作的
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