# Temperature and thermal energy

> IB Physics SL · IB DP Physics SL
> Source: https://www.owlsprep.com/study/ib-physics-sl-u2-temperature-and-thermal-energy/

This foundational thermal physics sub-topic clarifies common misconceptions between core quantities, covers temperature scales, thermal energy transfer and thermal equilibrium, all required for subsequent IB SL thermal physics topics.

**Prerequisites:** [Particulate nature of matter](https://www.owlsprep.com/study/ib-physics-sl-u1-particulate-nature-of-matter/)

## Learning objectives

- Distinguish between temperature, thermal energy and internal energy
- Convert between Celsius and Kelvin temperature scales
- Explain thermal energy transfer in terms of particle interactions
- Apply the concept of thermal equilibrium to physical systems

## Core Definitions: Key Distinctions

The most common mistake in IB thermal physics is confusing temperature, thermal energy and internal energy: each describes a different property of a system of particles.

**Internal energy** — The total sum of the random kinetic and potential energies of all particles in a system

*Notation:* U

*Example:* A 1 kg block of iron at 50°C has more internal energy than a 0.1 kg block at the same temperature

**Temperature** — A measure of the average random kinetic energy of particles in a system, defines the direction of thermal energy transfer

*Notation:* T (K), θ (°C)

*Example:* Two objects at the same temperature have particles with the same average kinetic energy, regardless of mass

**Thermal energy** — Non-mechanical energy transferred between a system and surroundings due to a temperature difference

*Notation:* Q

*Example:* Thermal energy flows from a hot coffee cup to cool surrounding air

**Worked example:** A student claims a bucket of boiling water has the same temperature and same thermal energy as a cup of boiling water. Evaluate this claim.

1. First compare temperature: both are boiling at standard pressure, so they are at 100°C, so their temperature is equal.
2. Next compare thermal energy: the bucket holds far more water molecules than the cup. Total energy of all molecules is much larger for the bucket.
3. Conclusion: the claim is incorrect. Temperature is the same, but thermal energy of the bucket is much greater.

> **tip**
>
> Always check which quantity the question asks for: exam markers award zero marks for mixing up these terms.

> **Exam tip:** Examiners frequently test the distinction between these three quantities in both Paper 1 and Paper 2.

## Temperature Scales: Celsius and Kelvin

IB Physics requires conversion between the Celsius (°C) and absolute thermodynamic Kelvin (K) temperature scales. Absolute zero, the lowest theoretical temperature where particles have minimum kinetic energy, is defined as 0 K = -273.15°C.

$$T = \theta + 273$$

For almost all IB exam calculations, rounding to 273 instead of 273.15 is fully acceptable.

**Worked example:** Convert normal body temperature (37°C) to Kelvin, and convert the boiling point of liquid nitrogen (77 K) to degrees Celsius.

1. Step 1: Convert 37°C to Kelvin:
2. $$T = 37 + 273 = 310\ \text{K}$$
3. Step 2: Rearrange to convert 77 K to °C:
4. $$\theta = 77 - 273 = -196^\circ \text{C}$$

**Check your understanding**

Check your understanding:

1. What is 0 K in degrees Celsius?

   - 0°C
   - -273°C
   - 273°C
   - 100°C

   *Answer:* -273°C

   *Why:* Correct! Absolute zero is defined as 0 K, equal to -273°C.

## Thermal Energy Transfer and Equilibrium

Net thermal energy is only transferred when there is a temperature difference between two systems in thermal contact. Transfer always flows from higher temperature to lower temperature, until thermal equilibrium is reached.

**Thermal equilibrium** — A state where two systems in thermal contact have no net transfer of thermal energy, meaning they are at the same temperature

**Worked example:** An 80°C iron block is placed in contact with a 20°C copper block. Describe energy transfer and the final state.

1. Step 1: Identify the temperature difference: iron has a higher temperature than copper.
2. Step 2: State the direction of net transfer: net thermal energy flows from iron to copper.
3. Step 3: Temperature changes: iron cools down, copper warms up.
4. Step 4: Final state: when both blocks reach the same temperature, net transfer stops, they are in thermal equilibrium.

> **note**
>
> Small random energy exchanges still occur at equilibrium, but there is no net transfer, which is what IB exam questions require you to state.

## Particle Model Explanation

We can explain all thermal processes using the particulate nature of matter, the core foundation of thermal physics:

- Faster moving (higher kinetic energy) particles collide with slower moving particles.
- Collisions transfer kinetic energy from faster to slower particles.
- Over time, average kinetic energy equalizes across the combined system, resulting in equal temperature and thermal equilibrium.

> **info**
>
> This explains why conduction is faster in solids than gases: particles are closer together in solids, so collisions transfer energy more quickly.

## Common pitfalls

- **Wrong:** Confusing temperature with thermal or internal energy
  - Why it fails: Temperature measures average kinetic energy, so mass does not change it; total energy depends on mass
  - Correct: Always check which quantity the question asks for: same temperature does not mean same total energy for different masses.
- **Wrong:** Using Celsius instead of Kelvin in thermal formulas
  - Why it fails: Most thermal physics formulas (e.g. ideal gas law) require absolute temperature, so using Celsius gives wrong results
  - Correct: Always convert Celsius to Kelvin before substituting into formulas, except for temperature changes (ΔT is the same in both scales).
- **Wrong:** Claiming no energy transfer at all at thermal equilibrium
  - Why it fails: Examiners mark this wrong because small random energy exchanges still occur
  - Correct: State that there is no net thermal energy transfer between systems at equilibrium.
- **Wrong:** Overcomplicating temperature conversion with 273.15
  - Why it fails: Unnecessary precision leads to arithmetic errors in exams
  - Correct: Use T = θ + 273 for all standard IB calculations, unless explicitly asked for higher precision.

## Cheatsheet

| Quantity | Symbol | Definition | Unit |
| --- | --- | --- | --- |
| Temperature | T (K), θ (°C) | Average random KE of particles | K / °C |
| Thermal energy | Q | Energy transferred due to ΔT | Joule (J) |
| Internal energy | U | Total KE + PE of all particles | Joule (J) |
| Temperature conversion | n/a | $T = \theta + 273$ | n/a |
| Thermal equilibrium | n/a | No net transfer, equal $T$ | n/a |

## What's next

This sub-topic provides the foundational definitions for all thermal physics in IB SL Physics. Mastering the distinction between temperature, thermal energy and internal energy will help you avoid common costly exam mistakes and correctly solve problems involving heat transfer, phase changes and ideal gases. These core concepts are also revisited in higher level topics if you continue studying physics beyond IB SL.

- [Gases](https://www.owlsprep.com/study/ib-physics-sl-u2-gases/)
- [Thermal properties of matter](https://www.owlsprep.com/study/ib-physics-sl-u2-thermal-properties-of-matter/)

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