Kinetic theory of gases: temperature and pressure in a fixed volume
The kinetic theory of gases pictures gas molecules moving randomly; their collisions with the walls generate pressure, which rises on warming in a fixed volume.
Remember
When a gas is warmed in a fixed volume, its molecules move faster, strike the walls more frequently and with more force, and so the pressure goes up.
Picture a gas as a huge number of molecules in random motion, moving at high speed. A molecule that hits the wall bounces back, and the change in its momentum (its mass multiplied by its velocity) gives the wall a small push. Billions of impacts every second together make a steady force on the wall. Divide that force by the area of the wall and you have the pressure.
Temperature reflects the average kinetic energy of the molecules, which is the energy of their movement. When the gas is warmed, the molecules move faster, so they reach the walls more frequently, and each collision transfers more momentum and pushes with more force.
In a fixed volume, as in a sealed and rigid container, the gas cannot expand, and the number of molecules stays the same, so the only change is that the same molecules hit the wall with more energy. The pressure rises straight away.
Molecules do not grow when heated, and kinetic theory treats the volume of the molecules themselves as negligible compared with the volume of the container. Attractions between molecules are treated as negligible too. And gas pressure acts in every direction, because it comes from molecules striking the walls, not from the weight of the gas.
The same picture explains Boyle's law in the lungs: at a given temperature, shrink the volume of a gas and the pressure rises, because the molecules reach the walls more often.
Key facts
- Source of pressure
- random collisions of gas molecules with the container wall.
- Definition of pressure
- the force of those collisions divided by the area of the wall.
- Temperature
- a higher temperature means a higher average kinetic energy and faster molecules.
- Fixed volume
- warming raises the pressure, because the gas cannot expand.
- Not the cause
- attraction between molecules, the size of the molecules or the weight of the gas.
- To raise pressure
- raise the average kinetic energy (temperature), add molecules, or reduce the volume.
Exam traps
- Warming a gas does not make its molecules bigger, and kinetic theory treats the volume of the molecules themselves as negligible; in a fixed volume the pressure rises because the molecules move faster and hit the walls more often and harder.
- Fixing the volume of a gas does not fix its pressure, because pressure depends on the collisions of the molecules with the walls, and warming makes those collisions more frequent and more forceful.
- Molecules at higher temperature are less likely to stay stuck to the walls, not more likely, because with more energy they bounce off; stuck molecules would be removed from the gas and the pressure would be lower.
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