Ideal Gases

Pressure and volume at constant temperature

• Squeezing a fixed amount of gas into a smaller box (at the same temperature) makes the pressure rise:
  • the molecules still move at the same average speed
  • but they have less distance to travel between collisions with the wall
  • so they hit the walls more often per second, and more frequent collisions mean higher pressure
• Letting the gas expand makes the pressure fall by the reverse logic

Pressure and temperature at constant volume

• Heating a sealed container of gas (volume fixed) makes the pressure rise:
  • the molecules gain kinetic energy and move faster
  • they hit the walls more often and each impact carries more force
  • both effects raise the pressure
• Cooling the gas reverses the effect, giving slower molecules, fewer and softer collisions, lower pressure

Volume and temperature at constant pressure

• Heating a gas in a container that can change shape (a balloon, a piston that can slide) makes the volume rise:
  • the molecules push harder on every wall
  • if a wall is free to move, it moves outward until the pressure rebalances against whatever is pushing back from outside
• The volume of a gas is proportional to its Kelvin temperature at fixed pressure