Temperature, Gases, and Thermal Expansion

Temperature tracks particle motion at the microscopic level. Heating a substance usually changes how fast its particles move, how often they collide, and how far apart they sit on average.

This lesson supports Chapter 11 of High School Physics.

Temperature and thermal energy are distinct

For a classical ideal gas, absolute temperature is proportional to average translational kinetic energy per particle. For other materials, the relationship depends on their microscopic degrees of freedom. Thermal energy depends on temperature, the amount of matter, and the substance. A bathtub of warm water can contain more thermal energy than a cup of hotter water because the bathtub holds far more particles.

The ideal gas law links four variables

For an ideal gas, \[PV=nRT.\] Pressure \(P\), volume \(V\), amount \(n\), and absolute temperature \(T\) change together. Gas-law temperatures must be in kelvins. For a fixed amount of gas at fixed volume, raising the temperature increases pressure because particles strike the walls more often and with greater momentum change.

Most materials expand when heated

Linear thermal expansion can be modeled by \(\Delta L=\alpha L_0\Delta T\). Expansion joints in bridges and gaps in rails allow length to change safely. Water is unusual near its freezing point, so the simple “warmer means less dense” pattern has an important exception.

Worked example

A \(2.0\text{ m}\) metal rod has \(\alpha=12\times10^{-6}/^\circ\text{C}\) and warms by \(50^\circ\text{C}\). Its length change is \(\Delta L=\alpha L_0\Delta T=1.2\times10^{-3}\text{ m}\), or \(1.2\text{ mm}\).

Watch the idea in action

Khan Academy India – English gives a focused explanation of the chapter’s central idea. Pause before each calculation and predict the next step on paper.

Practice questions

1. How is absolute temperature related to motion in a classical ideal gas?
2. Write the ideal gas law.
3. Which temperature scale belongs in gas-law calculations?
4. For a fixed amount of gas at fixed volume, what happens to gas pressure when temperature rises?
5. Write the linear expansion formula.
6. Why do bridges need expansion joints?

Answers

1. It is proportional to average translational kinetic energy per particle.
2. \(PV=nRT\).
3. Kelvin.
4. Pressure rises.
5. \(\Delta L=\alpha L_0\Delta T\).
6. They allow safe length changes as temperature changes.

Keep studying

High School Physics includes 12 full-length practice tests: two in the book and ten online.

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