Mini Physics
Part of Mini EducationSwitch subject
Search

Thermometry & Thermometric Property

Key idea: Understand thermometric properties and thermal equilibrium, and learn what makes a good thermometer for accurate temperature measurement (O Level).

  • G3 Physics topic extensions
On this page

Learning objectives

  • Explain how a thermometric property defines a temperature scale and calibrate the scale from two fixed points

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.
Fixed points for thermometer calibrationA liquid-in-glass thermometer calibrated at 0 degrees Celsius in melting ice and 100 degrees Celsius in steam at standard pressure.Ice point0 °CSteam point100 °C0 mark100 markMelting ice + waterSteamEqual divisions between 0 °C and 100 °C
Two reference states are melting ice (0 °C) and steam above boiling water (100 °C) at standard atmospheric pressure.
Practical link

For “how to take a reading” and error reduction, see Laboratory Thermometer.

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 0°C and x₁₀₀ at 100°C. 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.

Link to thermal equilibrium

A thermometer must reach thermal equilibrium with the object. Otherwise, the reading is still changing.

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

Modelled example 1

Identifying a thermometric property

Core

Problem

In a liquid-in-glass laboratory thermometer, what is the thermometric property?
Study the worked solution

  1. Identify what is observed

    Method

    The scale reading follows the top of the liquid column in the capillary.

    Reason

    This is the directly measurable feature that changes as the liquid expands or contracts.

    Working

    x = liquid-column length

  2. Connect it to temperature

    Method

    The column length changes continuously with temperature over the working range.

    Reason

    A known relation between x and temperature lets the scale assign a temperature.

    Working

    T changes ⇒ x changes

  3. Name the property

    Method

    The thermometric property is the length of the liquid column.

    Reason

    It is the measurable physical property used to infer temperature.

    Working

    x = length of liquid column

Guided practice 2

“Continuous” and “unique”

About 4 min

Problem

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

Try this before viewing the solution

Why continuous?
Why unique?

Hints

Hint 1: test a small change and a repeated value
Ask what happens if the property jumps over values, or if one property value matches two temperatures.
View solution step by step

  1. Explain continuous response

    Method

    Small temperature changes should produce corresponding measurable property changes.

    Reason

    A discontinuous response could skip temperatures or fail to track gradual changes.

    Working

    Δ T small ⇒ Δ x measurable

  2. Explain unique response

    Method

    Each property value should correspond to one temperature over the working range.

    Reason

    If the same value represented two temperatures, the reading would be ambiguous.

    Working

    x₁ = x₂ ⇒ T₁ = T₂

Common misconception 3

Reaching thermal equilibrium

Find and correct the mistake

Learner claim

A student reads a thermometer immediately after placing it in hot water and says the low value must be a calibration error. Diagnose the claim.

Try this before viewing the solution

Most direct cause

View solution step by step

  1. Identify the transient

    Method

    The thermometer is initially cooler than the hot water.

    Reason

    It has only just been inserted.

    Working

    Tₜₕₑᵣₘₒₘₑₜₑᵣ < T_water

  2. Follow energy transfer

    Method

    Energy transfers into the thermometer and its liquid column continues rising.

    Reason

    The instrument has not yet reached the water’s temperature.

    Working

    E: water → thermometer

  3. Correct the diagnosis

    Method

    The immediate reading is low because thermal equilibrium has not been reached, not necessarily because calibration is wrong.

    Reason

    A valid reading is taken only after the column becomes steady.

    Working

    wait until steady ⇒ Tₜₕₑᵣₘₒₘₑₜₑᵣ = T_water

Examiner practice 4

Another thermometric property

2 marks

Examination question

State one thermometric property other than liquid-column length, including any condition needed to define it clearly. [2 marks]

Try this before viewing the solution

View solution step by step

  1. State a measurable property

    1 mark

    Method

    One valid answer is the pressure of a gas.

    Reason

    Gas pressure can vary reproducibly with temperature.

    Working

    p varies with T

  2. Fix the defining conditions

    1 mark

    Method

    Use a fixed mass of gas at constant volume.

    Reason

    Holding these variables fixed makes the pressure-temperature relation interpretable.

    Working

    m = constant; V = constant

Challenge 5

What makes a good thermometric property?

Minimal support

Independent transfer

An engineer proposes using a sensor’s electrical resistance to measure temperature. State three conditions the resistance-temperature behavior should satisfy to be a good thermometric property over its working range.

Try this before viewing the solution

Hints

Hint 1: think about changes, ambiguity and observation
Could the sensor track small changes, could one reading mean two temperatures, and can the property be measured practically?
View solution step by step

  1. Require continuous variation

    Method

    Resistance should change continuously with temperature.

    Reason

    Small temperature changes should not fall into gaps in the response.

    Working

    R(T) continuous

  2. Require a unique relation

    Method

    Each resistance value should correspond to one temperature in the working range.

    Reason

    This prevents an ambiguous temperature reading.

    Working

    R₁ = R₂ ⇒ T₁ = T₂

  3. Require measurability

    Method

    The resistance and its changes should be easy to measure reliably.

    Reason

    A property is not useful for an instrument if its response cannot be resolved in practice.

    Working

    Δ R must be measurable

7. Mind Stretchers

Mind stretcher 1: Choosing between two thermometersExtension

Two thermometers both measure up to 100°C. 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.

Continue with the next resource in this course.

Course and syllabus information
Course
G3 Physics topic extensions
Syllabus scope
Beyond the syllabus
Edition
G3 Physics topic extensions