# Temperature and Thermal Equilibrium

> Physics · CIE A-Level
> Source: https://www.owlsprep.com/study/cie-9702-u20-temperature-and-thermal-equilibrium/

This foundational sub-topic introduces core concepts for all thermal physics: temperature, thermal contact and thermal equilibrium. You will learn how energy transfers between bodies and when net transfer stops.

**Prerequisites:** [Basic concepts of energy and internal energy](https://www.owlsprep.com/study/cie-9702-u20-internal-energy/)

## Learning objectives

- Define temperature and thermal equilibrium correctly
- Explain energy transfer direction between bodies at different temperatures
- Distinguish between temperature and thermal energy (heat)
- Apply thermal equilibrium concepts to practical exam scenarios

## Defining Temperature and Thermal Contact

Temperature is one of the most fundamental concepts in thermal physics. It determines the direction of net thermal energy transfer between any two bodies that can exchange energy.

**Temperature** — An intensive physical quantity that indicates the direction of net thermal energy transfer between bodies in thermal contact, proportional to the average kinetic energy of particles in a substance

*Notation:* $\theta$ (Celsius), $T$ (Kelvin)

*Example:* A hot pan has a higher temperature than cold water, so net energy flows from pan to water.

> **tip**
>
> Temperature is an intensive property: it does not depend on the amount of substance. A cup and a bathtub of boiling water both have the same temperature of 100°C.

**Worked example:** A 1 kg block of copper at 60°C is placed next to a 10 kg block of copper at 30°C. In which direction does net thermal energy flow?

1. Net energy flow depends only on temperature difference, not total mass or internal energy.
2. The 1 kg block has a higher temperature ($60^\circ C > 30^\circ C$).
3. Net thermal energy flows from the 1 kg block at 60°C to the 10 kg block at 30°C.

## Thermal Equilibrium: Core Conditions

When two bodies are in thermal contact, energy will continue to transfer until a balanced state is reached. This balanced state is called thermal equilibrium.

**Thermal Equilibrium** — A steady state where two bodies in thermal contact have no net transfer of thermal energy between them, which occurs when their temperatures are equal

*Example:* A thermometer left in a patient's mouth reaches thermal equilibrium when it stops changing temperature.

**Exam command terms**

When CIE asks you to 'explain why the thermometer is left for several minutes before reading', the answer always refers to thermal equilibrium:

- **Explain why we wait to read a thermometer** — Require thermal equilibrium between thermometer and object *(State that energy transfers until temperatures are equal, so reading is accurate.)*

**Worked example:** Explain when a mercury thermometer placed in hot water reaches thermal equilibrium with the water.

1. Initially, the thermometer is cooler than the water, so net energy flows from water to the thermometer.
2. Energy transfer causes the mercury to expand and its temperature to rise.
3. When the mercury temperature equals the water temperature, there is no net energy transfer. This is thermal equilibrium, so we can take an accurate reading.

> **Exam tip:** This is a common 2-3 mark explanation question in CIE Paper 2, always mention both equal temperature and zero net energy transfer.

## Key Distinction: Temperature vs Thermal Energy

One of the most common mistakes in A-level Physics is confusing temperature and thermal energy (heat). These are completely different quantities, with key differences:

- Temperature is *intensive*: it does not depend on the amount of substance
- Thermal energy (heat) is *extensive*: it depends on the amount of substance
- Temperature measures *average* kinetic energy per particle; thermal energy measures *total* energy transferred

**Worked example:** Explain why a 10 kg block of ice at 0°C has more internal energy than a 1 kg block of ice at 0°C, even though their temperatures are equal.

1. Temperature depends on average kinetic energy per particle, which is identical for both blocks at 0°C.
2. Internal energy is the total kinetic and potential energy of all particles in the block.
3. The 10 kg block has 10 times more particles than the 1 kg block, so total internal energy is higher.
4. There would be no net energy transfer between the two blocks because their temperatures are equal.

## Common pitfalls

- **Wrong:** Claiming bodies in thermal equilibrium have equal internal energy
  - Why it fails: Internal energy depends on mass, substance and state, as well as temperature. Only temperature is guaranteed equal at equilibrium
  - Correct: State that thermal equilibrium means equal temperature and zero net thermal energy transfer between bodies in contact
- **Wrong:** Claiming net energy flows from higher internal energy to lower internal energy
  - Why it fails: Energy flow direction depends on temperature difference, not total internal energy difference
  - Correct: State that net thermal energy always flows from higher temperature to lower temperature, regardless of total internal energy
- **Wrong:** Thinking thermal equilibrium requires physical contact between bodies
  - Why it fails: Bodies only need to be able to exchange energy (thermal contact), which can happen via radiation across a vacuum
  - Correct: Define thermal equilibrium by equal temperature and zero net energy transfer, regardless of physical contact
- **Wrong:** Claiming temperature is a measure of total heat in a body
  - Why it fails: Temperature measures average kinetic energy per particle, not total energy
  - Correct: Define temperature as a quantity that determines the direction of net thermal energy transfer, proportional to average particle kinetic energy

## Cheatsheet

| Concept | Core Definition | Key Property |
| --- | --- | --- |
| Temperature | Determines direction of energy transfer | Intensive (independent of mass) |
| Thermal Contact | Allows energy exchange between bodies | Does not require physical contact |
| Thermal Equilibrium | Zero net energy transfer in thermal contact | Equal temperature |
| Thermal Energy (Heat) | Total energy transferred between bodies | Extensive (depends on mass) |

## What's next

Temperature and thermal equilibrium are the foundation of all thermal physics topics for CIE A-Level. These concepts underpin every calculation and explanation you will do in this unit, from measuring specific heat capacity to analysing ideal gas behaviour. Mastering the distinction between temperature and energy now will help you avoid common mistakes in later calculation questions. Next, you will learn how to construct temperature scales and define absolute zero, then move on to calculation-based topics for thermal processes. The concept of thermal equilibrium will also be central when you study heat transfer and thermal processes in engines.

- [Specific Heat Capacity](https://www.owlsprep.com/study/cie-9702-u20-specific-heat-capacity/)
- [Specific latent heat](https://www.owlsprep.com/study/cie-9702-u20-specific-latent-heat/)
- [First Law of Thermodynamics](https://www.owlsprep.com/study/cie-9702-u20-first-law-of-thermodynamics/)

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