Thermometry & Thermometric Property

1. Definition

A. Thermometry

Thermometry is the measurement of temperature using a thermometer.

B. Thermometric property

A thermometric property is a physical property that changes continuously with temperature and can be used to measure temperature.

2. Key Ideas

• A thermometer measures temperature by using a thermometric property (something measurable that changes with temperature).
• A good thermometric property should:
  • vary continuously with temperature
  • vary uniquely (one value corresponds to one temperature over the range)
  • be easy to measure
• A thermometer gives the correct reading only when it reaches thermal equilibrium with the object.
• In a laboratory thermometer, the thermometric property is the length of the liquid column.

3. Detailed Explanations

A. Why do we need a thermometric property?

We cannot “see” temperature directly. A thermometer converts a temperature change into a measurable change in a physical property, such as a change in length, pressure, or electrical resistance.

B. Examples of thermometric properties (O Level-friendly)

Common examples include:

• Length of a liquid column in a liquid-in-glass thermometer (laboratory thermometer)
• Electrical resistance of a conductor or thermistor
• Pressure of a fixed mass of gas at constant volume

The property need not increase with temperature over every possible range. What matters is that the instrument has a known, repeatable relationship between the property and temperature over its working range.

C. Calibration between two fixed points

Suppose a liquid-column length is x₀ at 0circC and x₁₀₀ at 100circC. If the scale is linear, a measured length x_θ corresponds to

θ = 100(x_θ-x₀/x₁₀₀-x₀).

This is an interpolation between the two fixed points. A two-point calibration does not prove that a real thermometric property is perfectly linear; it defines the scale under the stated linear assumption.

D. Why should a thermometer be small compared with the object?

When you place a thermometer in contact with an object, energy is transferred between them until they reach thermal equilibrium. If the thermometer is large, it can change the object’s temperature noticeably, making the measurement inaccurate.

4. Common Mistakes

• Treating “thermometric property” as a type of thermometer (it is a measurable property used by a thermometer).
• Recording a temperature before the reading becomes steady (not at thermal equilibrium).
• Thinking temperature measures “total energy” (it is related to average kinetic energy of particles, not total energy).
• Assuming every thermometric property is automatically linear with temperature.

5. Exam Tips

• Definition keywords:
  • thermometric property: changes continuously with temperature
  • equilibrium: reading steady
• If asked “what makes a good thermometric property?”, list: continuous, unique, measurable.
• For a calibration calculation, subtract the lower fixed-point reading before taking the fraction of the full fixed-point interval.
• In practical questions, always state at least one method to reduce error:
  • wait until steady, read at eye level, good contact, avoid parallax.

6. Worked Examples

Example 1: Identifying a thermometric propertyCore

In a laboratory thermometer, what is the thermometric property?

Show Answer

The length of the liquid column in the capillary tube.

Example 2: “Continuous” and “unique”Core

Why must a thermometric property change continuously and uniquely with temperature?

Show Answer

It must change continuously so small temperature changes produce measurable changes. It must be unique so the same property value does not correspond to two different temperatures (otherwise the reading would be ambiguous).

Example 3: Reaching thermal equilibriumCore

A student puts a thermometer into hot water and reads the scale immediately. The reading is too low. Explain why.

Show Answer

The thermometer has not reached thermal equilibrium with the hot water yet, so the liquid column has not finished rising. The reading will increase until it becomes steady.

Example 4: Another thermometric propertyCore

State one thermometric property (other than length of a liquid column) that can be used to measure temperature.

Show Answer

Examples include:

• the electrical resistance of a metal wire (resistance thermometer),
• the pressure of a fixed mass of gas at constant volume (gas thermometer),
• the volume of a liquid.

Example 5: What makes a good thermometric property?Core

Give three properties of a good thermometric property.

Show Answer

A good thermometric property should:

• change continuously with temperature,
• change uniquely (one value corresponds to one temperature over the range),
• be easy to measure.

7. Mind Stretchers

Mind stretcher 1: Choosing between two thermometersExtension

Two thermometers both measure up to 100circC. One has a thicker tube and the other has a narrower tube. Which gives a more sensitive reading, and why?

Show Answer

The narrower tube gives a more sensitive reading because the same volume expansion produces a larger change in the length of the liquid column.

Mind stretcher 2: Thermometer changes the objectExtension

Why might placing a large thermometer in a small beaker of water change the water’s temperature noticeably?

Show Answer

Energy is transferred between the thermometer and the water until equilibrium. If the thermometer has a large thermal mass, it can absorb or release enough energy to change the water’s temperature significantly.

8. Practice and next step

Use the interpolation method only when a question supplies a linear thermometric property. Then return to laboratory thermometer technique or the core Thermal Physics syllabus path.