# 2.1 Revision: Temperature and Thermometers

F.3 Physics · Topic II Heat · Lesson 6

Fixed points, temperature scales, thermometer properties and calibration.

## Key points

- **Temperature** describes the degree of hotness of an object; it relates to the average kinetic energy of its particles' random motion.
- **Fixed points** must be easily and accurately reproducible: pure melting ice ($0\,{}^{\circ}\mathrm{C}$) and pure boiling water ($100\,{}^{\circ}\mathrm{C}$) at standard atmospheric pressure.
- **Calibration (校準)**: use equal divisions only when the thermometric property changes linearly with temperature.
- **Kelvin** is an absolute scale with zero at **absolute zero (絕對零度)**. Write K without a degree sign.
- **Thermometric property (測溫性質)** changes consistently with temperature over the measuring range; water's volume decreases from $0$ to $4\,{}^{\circ}\mathrm{C}$, then increases.
- **Sensitivity (靈敏度)**: for otherwise similar liquid-in-glass thermometers, a larger bulb or narrower bore gives a larger column rise per degree.
- **Response time**: a thinner bulb wall allows faster heat transfer. Accuracy depends on calibration and correct use.
- **Mercury clinical thermometer**: the constriction holds the maximum reading after removal; shake it down before use. Fine divisions aid reading, without guaranteeing accuracy.

## Must know

| Skill | Rule or working principle |
|---|---|
| Linear calibration | $T=\dfrac{X-X_0}{X_{100}-X_0}\times100\,{}^{\circ}\mathrm{C}$ |
| Celsius → kelvin | $T_{\mathrm{K}}\approx T_{\mathrm{C}}+273$ (classroom approximation) |
| Celsius → Fahrenheit | $T_{\mathrm{F}}=1.8T_{\mathrm{C}}+32$ |
| Temperature changes | A rise of $1\,{}^{\circ}\mathrm{C}$ equals $1\,\mathrm{K}$ or $1.8\,{}^{\circ}\mathrm{F}$ |
| Liquid-in-glass / rotary | Liquid expansion / bending of a bimetallic strip |
| Liquid crystal | Colour changes with temperature |
| Resistance / thermistor | Metal resistance increases / thermistor resistance can decrease as temperature rises |
| Infrared / thermocouple | Surface infrared intensity / voltage from two-metal junctions at different temperatures |

Here $T$ is the Celsius temperature; $X_0$ and $X_{100}$ are the property values at the two fixed points. $T_{\mathrm{C}}$, $T_{\mathrm{K}}$ and $T_{\mathrm{F}}$ are numerical scale readings.

## Common mistakes

- ✗ “Use the column length from zero.” ✓ Subtract the ice-point length, then divide by the fixed-point interval.
- ✗ “Sensitivity means fast response.” ✓ Sensitivity concerns a small temperature change; response time concerns how quickly the reading changes.
- ✗ “Fine divisions guarantee accuracy.” ✓ Fine divisions aid reading; accuracy depends on calibration and correct use.
- ✗ “Add 273 to a temperature rise.” ✓ Add 273 approximately to a Celsius reading. A rise of $10\,{}^{\circ}\mathrm{C}$ is $10\,\mathrm{K}$.
- ✗ “The constriction makes mercury return slowly.” ✓ It prevents the column returning to the bulb after removal, retaining the maximum reading.

## Quick check

1. For a linear thermometer, column lengths are $4\,\mathrm{cm}$ at the ice point and $24\,\mathrm{cm}$ at the steam point. What temperature gives $10\,\mathrm{cm}$?
2. Convert $20\,{}^{\circ}\mathrm{C}$ to kelvin using the classroom approximation, and to Fahrenheit.
3. A temperature rises by $5\,{}^{\circ}\mathrm{C}$. What is the rise in K and in $^{\circ}\mathrm{F}$?
4. For otherwise similar liquid-in-glass thermometers, name two ways to increase sensitivity and one to shorten response time.
5. Why can the mercury clinical thermometer be read after removal?

## Answers

1. $(10-4)/(24-4)\times100=30\,{}^{\circ}\mathrm{C}$.
2. Approximately $293\,\mathrm{K}$; $68\,{}^{\circ}\mathrm{F}$.
3. $5\,\mathrm{K}$; $9\,{}^{\circ}\mathrm{F}$.
4. Larger bulb or narrower bore; thinner bulb wall for faster response.
5. The constriction holds the mercury column at its maximum reading.

## Did you know?

Celsius and Fahrenheit have the same numerical reading at −40 degrees.