📚 How Common Thermometers Work: Principles and Calibration | 常见温度计的工作原理与读数校准
Temperature is one of the most fundamental ideas in physics. A thermometer measures temperature by using a physical property, such as the length of a liquid column, the pressure of a gas, the electrical resistance of a metal, or the e.m.f. of a thermocouple, that changes in a predictable way with temperature.
温度是物理学中最基本的概念之一。温度计依靠某种随温度可预测变化的物理属性来测量温度，例如液柱的长度、气体的压强、金属的电阻或热电偶的电动势。
In this article we examine the working principles of common thermometers, their thermometric properties, and the way they are calibrated at standard fixed points.
本文将介绍常见温度计的工作原理、它们所利用的测温属性，以及在标准固定点上进行校准的方法。
1. Temperature and Heat | 温度与热量
Temperature is a measure of the average random kinetic energy of the particles in a substance. It sets the direction in which net thermal energy will flow: heat flows from a body at higher temperature to a body at lower temperature.
温度是物质内部粒子无规则平均动能的量度。它决定了净热能传递的方向：热量总是从高温物体传向低温物体。
The Zeroth Law of Thermodynamics states that if body A is in thermal equilibrium with body B, and body B is in thermal equilibrium with body C, then A and C are also in thermal equilibrium. This principle allows us to use a thermometer as a third body to compare temperatures.
热力学第零定律指出：若物体A与物体B处于热平衡，物体B与物体C处于热平衡，则物体A与物体C也必然处于热平衡。这一定律使我们能够用温度计作为“第三物体”来比较不同物体的温度。
2. Empirical Temperature Scales | 经验温标
Every thermometer is based on a thermometric property X that varies continuously with temperature. A simple linear empirical scale can be defined by assigning values at two fixed points.
每支温度计都依赖于一个随温度连续变化的测温属性X。通过在两个固定点上指定数值，可以定义一个简单的线性经验温标。
θ = [(Xθ − X₀) / (X₁₀₀ − X₀)] × 100 °C
Here X₀ is the value at the ice point, X₁₀₀ is the value at the steam point, and Xθ is the value at the temperature θ to be measured.
其中X₀是冰点时的测温属性值，X₁₀₀是汽点时的值，Xθ是待测温度θ时的值。
Different thermometers agree exactly only at the fixed points. Between the fixed points their readings may differ because the thermometric property is not perfectly linear with temperature. This is why a truly universal scale is needed.
不同温度计只会在固定点上读数完全一致。在两个固定点之间，由于测温属性与温度并非严格线性，它们的读数可能有所差异，因此需要一种普适的温标。
3. Liquid-in-Glass Thermometers | 液体温度计
The liquid-in-glass thermometer uses the expansion of a liquid, usually mercury or coloured alcohol, sealed inside a glass bulb and capillary tube. When the temperature rises, the liquid expands more than the glass, so the length of the liquid column increases.
液体温度计利用密封在玻璃泡和毛细管中的液体（通常是水银或有色酒精）的膨胀来测温。温度升高时，液体比玻璃膨胀得更明显，于是液柱的长度增大。
The thermometric property is the volume, or more practically the length, of the liquid column. A uniform capillary tube makes the scale approximately regular.
其测温属性是液体的体积，实际上常用液柱的长度。均匀的毛细管使刻度大致均匀。
Mercury thermometers are useful from about −39 °C to 350 °C because mercury freezes at −39 °C and boils at 357 °C. Alcohol thermometers can measure lower temperatures, down to about −80 °C, but they are less suitable for high temperatures.
水银温度计在约−39 °C至350 °C范围内可用，因为水银在−39 °C凝固、357 °C沸腾。酒精温度计可测量低至约−80 °C的低温，但不适合高温测量。
Liquid-in-glass thermometers are cheap, simple and portable, but they are fragile, have a relatively slow response, and require the bulb to be fully immersed in the medium being measured.
液体温度计价格低廉、结构简单且便于携带，但容易破碎、响应较慢，而且要求测温泡必须完全浸入被测介质中。
4. Constant-Volume Gas Thermometer | 定容气体温度计
A constant-volume gas thermometer measures temperature through the pressure of a fixed mass of gas kept at constant volume. As temperature increases, the average kinetic energy of the gas molecules increases, so the pressure increases.
定容气体温度计通过测量固定质量气体在体积不变时的压强变化来测量温度。温度升高时，气体分子的平均动能增大，压强随之增大。
For an ideal gas at constant volume, pressure is proportional to the kelvin temperature:
对理想气体而言，在体积不变时，压强与开尔文温度成正比：
p ∝ T so T = 273.16 K × (p / p₃)
In this expression p₃ is the pressure of the gas when the bulb is at the triple point of water (273.16 K). Because real gases at low pressure behave almost ideally, the constant-volume gas thermometer is used as a standard reference thermometer.
式中p₃是测温泡处于水的三相点（273.16 K）时气体的压强。由于低压下的真实气体几乎具有理想气体行为，定容气体温度计被用作标准参照温度计。
The gas thermometer is accurate and can define the thermodynamic scale, but it is large, slow and inconvenient for everyday use. It is mainly used in standards laboratories.
气体温度计准确且能定义热力学温标，但体积庞大、响应慢，不适合日常使用，主要用于标准实验室。
5. Thermocouple | 热电偶温度计
A thermocouple consists of two junctions made from two different metals, for example copper and constantan. When the two junctions are kept at different temperatures, a small e.m.f. is produced. This is the Seebeck effect.
热电偶由两种不同金属（例如铜和康铜）制成的两个结点组成。当两个结点处于不同温度时，会产生一个微小的电动势，这就是塞贝克效应。
The thermometric property is the e.m.f. measured between the junctions. One junction is held at a reference temperature, usually the ice point, and the other junction is placed at the temperature to be measured.
其测温属性是两结点之间测得的电动势。一个结点保持在参考温度（通常是冰点），另一个结点置于待测温度处。
For small temperature differences, the e.m.f. is approximately proportional to the temperature difference. Thermocouples are useful over a very wide range, from about −200 °C to 1500 °C, and their small junction gives fast response and allows the measurement of temperature at a point.
在温度差较小时，电动势近似与温差成正比。热电偶适用范围很广，约从−200 °C至1500 °C，且结点小、响应快，可以测量“点”温度。
However, the e.m.f. versus temperature relation is not perfectly linear, so calibration at several known temperatures is necessary.
然而，电动势与温度的关系并非严格线性，因此必须在多个已知温度下进行校准。
6. Resistance Thermometer | 电阻温度计
A platinum resistance thermometer uses the fact that the electrical resistance of pure metal increases steadily with temperature. The thermometric property is resistance.
铂电阻温度计利用纯金属的电阻随温度稳定增大的特性。其测温属性是电阻。
Platinum is used because it is chemically stable, has a high melting point, and gives a nearly linear response over a wide range. For most purposes:
之所以选用铂，是因为它化学性质稳定、熔点高，并且在大范围内具有接近线性的响应。在多数情况下：
Rθ = R₀(1 + αθ)
Here Rθ is the resistance at temperature θ, R₀ is the resistance at 0 °C, and α is the temperature coefficient of resistance, approximately 0.00385 °C⁻¹ for platinum.
式中Rθ是温度为θ时的电阻，R₀是0 °C时的电阻，α是电阻温度系数，铂约为0.00385 °C⁻¹。
Resistance thermometers are highly accurate and stable, and are used in industry and laboratories from about −200 °C to 850 °C. The resistance is usually measured with a Wheatstone bridge. Their disadvantages are cost, size and a relatively slow response.
电阻温度计准确度高、稳定性好，在实验室和工业中可用于约−200 °C至850 °C的范围。通常用惠斯通电桥测量电阻。其缺点是成本高、体积较大、响应较慢。
7. Thermistor | 热敏电阻温度计
A thermistor is a semiconductor device whose resistance changes strongly with temperature. Most thermistors have a negative temperature coefficient, so their resistance decreases rapidly as temperature rises.
热敏电阻是一种半导体器件，其电阻随温度剧烈变化。多数热敏电阻具有负温度系数，即温度升高时电阻迅速减小。
Because the change in resistance per degree is much larger than in a metal, the thermistor is extremely sensitive. It has a small size and very fast response, making it ideal for medical thermometers and digital temperature sensors.
由于每变化1 °C所引起的电阻变化远大于金属材料，热敏电阻具有极高的灵敏度。它体积小、响应快，非常适合用于医用温度计和数字温度传感器。
However, its response is highly non-linear, so the calibration curve must be stored in electronic memory. A second disadvantage is self-heating: the measuring current warms the thermistor and changes its resistance.
但它的响应高度非线性，因此校准曲线必须存储在电子存储器中。另一个缺点是自热效应：测量电流会加热热敏电阻，从而改变其电阻。
To minimise self-heating, very small currents must be used so that power dissipated in the thermistor is negligible.
为了减小自热效应，必须使用非常小的电流，使热敏电阻中耗散的功率可以忽略不计。
8. Calibration: Fixed Points | 校准：固定点
To calibrate any thermometer, certain reproducible temperatures, called fixed points, are needed. Traditionally the two fixed points used for the Celsius scale are the ice point and the steam point.
校准任何温度计都需要某些可重复实现的温度，即固定点。传统上，摄氏温标使用的两个固定点是冰点和汽点。
| Fixed Point | Temperature | Physical Condition |
| Ice point | 0 °C = 273.15 K | Pure melting ice at standard pressure |
| Steam point | 100 °C = 373.15 K | Pure boiling water at standard pressure |
| Triple point of water | 0.01 °C = 273.16 K | Ice, liquid water and water vapour in equilibrium |
To calibrate a liquid-in-glass thermometer, the bulb is first immersed in pure melting ice and the position of the liquid column is marked 0 °C. The thermometer is then placed in steam from water boiling at standard pressure, and the new position is marked 100 °C. The interval is divided into 100 equal divisions.
校准液体温度计时，先将测温泡浸入纯净的冰水混合物中，把液柱位置标记为0 °C；再将温度计放入标准大气压下沸腾的水蒸气中，把新的液柱位置标记为100 °C；然后把这段间隔等分为100格。
For more advanced calibration, the triple point of water is used because it is more reproducible and depends on pressure much less than the ice point. Modern temperature scales use several fixed points and precise interpolation equations.
更高级的校准采用水的三相点，因为三相点更易于精确复现，且受压强影响远小于冰点。现代温标使用多个固定点和精确的内插公式。
9. Choosing a Thermometer | 温度计的选择
The best thermometer for a particular situation depends on the temperature range, the required accuracy, the response time, the size of the object being measured, and cost.
选择温度计时，应考虑温度范围、所需精度、响应时间、被测物体的大小以及成本等因素。
| Type | Thermometric Property | Advantages | Disadvantages |
| Liquid-in-glass | Liquid column length | Cheap, simple, portable | Fragile, slow, limited range |
| Constant-volume gas | Gas pressure at constant volume | Very accurate, defines thermodynamic scale | Large, slow, inconvenient |
| Thermocouple | E.m.f. between junctions | Wide range, fast, small junction | Non-linear, needs cold junction |
| Platinum resistance | Electrical resistance | Accurate, stable, reproducible | Expensive, slow response |
| Thermistor | Semiconductor resistance | Very sensitive, small, fast | Non-linear, self-heating |
In an examination, you must be able to state the thermometric property for each thermometer and explain why that property is suitable for the intended range of temperatures.
在考试中，你必须能说出每种温度计的测温属性，并能解释该属性为何适合其设计的温度范围。
10. Sources of Error and Modern Calibration | 误差来源与现代校准
No thermometer is perfect. A liquid-in-glass thermometer suffers from stem emergence error because the liquid in the exposed stem is at a different temperature from the bulb. Reading errors are also caused by parallax if the observer looks at the scale from an angle.
任何温度计都不是完美无缺的。液体温度计存在“露茎误差”，因为露在测温环境外的液柱部分温度与测温泡不同。若观察者斜视刻度，还会产生视差误差。
Resistance thermometers and thermistors experience self-heating when the measuring current passes through them. Gas thermometers can lose or gain heat through the walls of the bulb, and the gas may not behave exactly as an ideal gas.
电阻温度计和热敏电阻在测量电流通过时会产生自热。气体温度计的管壁可能发生热量散失或吸收，而且气体行为也不完全等同于理想气体。
For accurate practical measurements, modern instruments are calibrated against an international standard, now known as ITS-90. This scale is defined by specified fixed points, such as the triple point of water, the freezing point of indium, tin and zinc, and by the use of standard platinum resistance thermometers or radiation thermometers.
为了获得准确的实用测量，现代仪器需按照国际标准温标ITS-90进行校准。该温标由规定的固定点定义，例如水的三相点、铟、锡、锌的凝固点，并使用标准铂电阻温度计或辐射温度计。
Digital thermometers store calibration data in a microprocessor and apply a mathematical correction, so a non-linear sensor can still produce a highly linear and accurate temperature reading.
数字温度计将校准数据存储于微处理器中并进行数学修正，因此即使传感器本身是非线性的，也能得到高度线性和准确的温度读数。
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