# 2.1 Temperature and Thermometers

F.3 Physics · Topic II Heat · Lesson 3

What temperature measures, the Celsius and Kelvin scales, how thermometers work, and how to calibrate one.

## Key points

- **Temperature** is a measure of the **degree of hotness** of an object. Microscopically it measures the **average kinetic energy** of the random motion of the molecules, not the total.
- **Absolute zero (絕對零度)**: the temperature at which an object has the lowest energy, −273.15 °C or 0 K. Kelvin scale: $T_K = T_C + 273$ ($T_C$ in °C); a change of 1 °C is a change of 1 K.
- **Fixed points (固定點)**: **ice point** 0 °C, pure melting ice (lower fixed point); **steam point** 100 °C, steam over pure boiling water (upper fixed point); both at normal atmospheric pressure.
- A **thermometric property (測溫特性)** varies with temperature (volume, colour, resistance) and must **only increase or only decrease**. Water cannot be used: its volume decreases from 0 °C to 4 °C, then increases.
- **Liquid-in-glass**: the liquid expands uniformly, so its level rises. Mercury: −39 °C to 357 °C, poisonous, more expensive. Alcohol: −114 °C to 78 °C, non-poisonous, less expensive.
- **More sensitive**: bigger bulb, narrower bore. **Faster response**: thinner bulb wall, a better conducting liquid (mercury). **Accurate**: uniform capillary tube, constant expansion per degree. A sensitive thermometer may not be accurate.
- **Clinical thermometer**: mercury; a **constriction** near the bulb stops the mercury falling back, so the highest temperature is recorded; shake before use; 35 °C to 42 °C; read to 0.1 °C.
- **Calibration**: mark the lengths at the two fixed points, then $T = (L_T - L_0)/(L_{100} - L_0) \times 100$ °C.

## Must know

| Thermometer | Thermometric property | Typical range |
|---|---|---|
| Liquid-in-glass | volume of the liquid ↑ | mercury −39 °C to 357 °C; alcohol −114 °C to 78 °C |
| Rotary | curvature of a bimetallic strip ↑ | −50 °C to 300 °C |
| Infrared | intensity of infrared radiation ↑ | very high temperatures |
| Resistance | resistance of a metal wire ↑ | −200 °C to 850 °C |
| Thermistor | resistance of a thermistor ↓ | −50 °C to 150 °C |
| Liquid crystal | colour of the liquid crystals | a narrow band per strip |

## Common mistakes

- ✗ "A big bulb makes it more accurate." ✓ Big bulb, narrow bore: **more sensitive**. Thin wall, mercury: **faster response**. Uniform bore: **accurate**.
- ✗ "A rise of 25 °C is a rise of 298 K." ✓ Add 273 to a **temperature**, not to a **change**: a rise of 25 °C is a rise of **25 K**.
- ✗ "The constriction makes the mercury move faster." ✓ It stops the mercury **flowing back** into the bulb, so the highest temperature stays; shake it down before use.
- ✗ "Water would make a cheap thermometric liquid." ✓ Its volume **decreases** from 0 °C to 4 °C, then increases, so it cannot be used.
- ✗ "Tea at 80 °C has more kinetic energy than a bath at 40 °C." ✓ Temperature is the **average** kinetic energy; the bath has far more molecules, so more **total** kinetic energy.

## Quick check

1. Convert 25 °C to kelvin. A liquid warms up by 25 °C: what is the rise in kelvin?
2. A liquid column is 5.0 cm long in pure melting ice and 25.0 cm in steam. In a liquid it is 12.0 cm long. Find the temperature of the liquid.
3. Why can water not be used as the liquid in a liquid-in-glass thermometer?
4. Give two ways to make a liquid-in-glass thermometer more sensitive.
5. Which of these can measure the temperature inside an oven at about 800 °C: an alcohol-in-glass, a mercury-in-glass or a resistance thermometer?

## Answers

1. 298 K; a rise of 25 K.
2. $T = (12.0 - 5.0)/(25.0 - 5.0) \times 100 = 35$ °C.
3. Its volume decreases from 0 °C to 4 °C and then increases, so it does not change in one direction only.
4. Use a bigger bulb; use a narrower bore (capillary tube).
5. The resistance thermometer (−200 °C to 850 °C); mercury only reaches 357 °C.

## Did you know?

Anders Celsius's original scale of 1742 was upside down: 0 for boiling water and 100 for melting ice. It was turned the other way round soon after his death.