# Explain why, when a fixed mass of ideal gas undergoes an isothermal compression, the pressure of the gas increases.

> IB DP Physics Higher Level (2023 syllabus) — B.1 Thermal energy transfers · Explain · 4 marks

> An ideal gas is compressed isothermally, reducing its volume to half its original value.

## Mark scheme (4 marks)

1. In an isothermal process the temperature remains constant, so the average kinetic energy of the molecules remains constant.
2. Reducing the volume means the molecules are confined to a smaller space, so the number of molecules per unit volume (number density) increases.
3. Molecules collide with the container walls more frequently per unit area per unit time.
4. Since each collision delivers the same impulse/momentum change (speed unchanged), the greater collision rate per unit area results in a greater force per unit area, i.e. higher pressure.

## Key terms

- [isothermal](https://www.gradenine.co.uk/glossary/isothermal)
- [ideal gas](https://www.gradenine.co.uk/glossary/ideal-gas)
- [pressure](https://www.gradenine.co.uk/glossary/pressure)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

---
Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-when-a-fixed-mass-5a600b67) · Published by Druglandscape Ltd.