Describe the relationship between the motion of particles and temperature, including the idea that there is a lowest possible temperature (-273°C), known as absolute zero, where the particles have least kinetic energy

2.1.2 Particle Model

Objective

Describe the relationship between the motion of particles and temperature, including the idea that there is a lowest possible temperature (‑273 °C), known as absolute zero, where the particles have the least kinetic energy.

Key Concepts

• All matter is made up of particles (atoms, molecules, ions) that are in constant motion.
• The average kinetic energy of these particles determines the temperature of the substance.
• Increasing temperature → particles move faster (greater kinetic energy).
• Decreasing temperature → particles move slower (less kinetic energy).
• Absolute zero (0 K or ‑273 °C) is the theoretical temperature at which particles have minimum possible kinetic energy.

Relationship Between Temperature and Kinetic Energy

The kinetic theory of gases gives a quantitative link between temperature and the average kinetic energy of particles:

\$\langle E{\text{k}} \rangle = \frac{3}{2}k{\mathrm{B}}T\$

where

• \(\langle E_{\text{k}} \rangle\) = average translational kinetic energy per particle (J)
• \(k_{\mathrm{B}}\) = Boltzmann constant \((1.38 \times 10^{-23}\,\text{J K}^{-1})\)
• \(T\) = absolute temperature in kelvin (K)

Temperature Scales

What Happens at Absolute Zero?

1. Particle motion slows to the minimum allowed by quantum mechanics.
2. Translational kinetic energy approaches zero, but particles retain zero‑point energy.
3. All macroscopic thermal motion ceases; no heat can be extracted from the system.
4. In practice, absolute zero cannot be reached, but temperatures within a few nanokelvin of 0 K have been achieved in laboratory settings.

Implications for Everyday Phenomena

• Heating a solid causes its particles to vibrate more vigorously, leading to expansion.
• Cooling a gas reduces the speed of its molecules, lowering pressure if volume is constant (Gay‑Lussac’s law).
• Phase changes (solid–liquid–gas) occur when particles gain or lose enough kinetic energy to overcome intermolecular forces.

Quick Revision Checklist

• Define absolute zero and give its value in both Celsius and Kelvin.
• State the equation linking average kinetic energy to temperature.
• Explain how particle motion changes when temperature rises or falls.
• Identify at least two real‑world examples where temperature affects particle motion.