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 · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

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

Model answer (4 marks)

In an isothermal process the temperature is constant, so the average kinetic energy of the gas molecules remains unchanged.

When the volume is halved the molecules are confined to a smaller space, increasing the number density.

A higher number density means that, for a given speed, molecules collide with the walls more often per unit area per unit time.

Because each collision delivers the same impulse (speed unchanged), the increased collision frequency raises the force per unit area, i.e. the pressure rises.

Examiner tips

Use the phrase "isothermal process" to show you know temperature is constant.
Explain that the kinetic energy per molecule stays the same but the collision rate increases.
Show the link between collision rate and pressure.
Mention the volume halving explicitly to justify the density increase.

Common mistakes

Saying the kinetic energy increases, which is wrong for isothermal.
Confusing volume decrease with temperature increase.
Failing to connect collision frequency to pressure.

Mark scheme (4 marks)

In an isothermal process the temperature remains constant, so the average kinetic energy of the molecules remains constant.
Reducing the volume means the molecules are confined to a smaller space, so the number of molecules per unit volume (number density) increases.
Molecules collide with the container walls more frequently per unit area per unit time.
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 in this question

isothermal · ideal gas · pressure