IBPhysicsSLRevision NotesThe Particulate Nature of MatterThermal Energy TransfersTemperature & Kinetic Energy

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First teaching 2023

First exams 2025

Temperature & Kinetic Energy (SL IB Physics)

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Katie M

Expertise

Physics

Temperature & Kinetic Energy

Particles in gases usually have a range of speeds
The average kinetic energy of the particles E_k can be calculated using the equation

$E_{k} = \frac{3}{2} k_{B} T$

Where:
- E_k = average kinetic energy of the particles in joules (J)
- k_B = 1.38 × 10^–23 J K^–1(Boltzmann's constant)
- T = absolute temperature in kelvin (K)

This tells us that the absolute temperature of a body is directly proportional to the average kinetic energy of the molecules within the body

Relationship between absolute temperature and average random kinetic energy of molecules

Graph of Absolute Temperature against Kinetic Energy of Molecules, for IB Physics Revision Notes

Worked example

The surface temperature of the Sun is 5800 K and contains mainly hydrogen atoms.

Calculate the average speed of the hydrogen atoms, in km s⁻¹, near the surface of the Sun.

Answer:

Step 1: List the known quantities

Temperature, T = 5800 K
Mass of a hydrogen atom = mass of a proton, m_p = 1.673 × 10⁻²⁷ kg
Boltzmann constant, k_B = 1.38 × 10⁻²³ J K⁻¹

Step 2: Equate the equations relating kinetic energy with temperature and speed

Average kinetic energy of a molecule: $E_{k} = \frac{3}{2} k_{B} T$
Kinetic energy: $E_{k} = \frac{1}{2} m v^{2}$

$\frac{3}{2} k_{B} T = \frac{1}{2} m_{p} v^{2}$

Step 3: Rearrange for average speed and calculate

$\frac{3 k_{B} T}{m_{p}} = v^{2}$

$v = \sqrt{\frac{3 k_{B} T}{m_{p}}} = \sqrt{\frac{3 \times (1.38 \times 10^{- 23}) \times 5800}{1.673 \times 10^{- 27}}}$

Average speed: v = 11 980 m s⁻¹ = 12 km s⁻¹

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Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.