The Gas Laws

Each gas law describes what happens to a fixed mass of gas when one quantity is held constant.

Boyle's law — at constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume.

pV = constant (constant T)

Halving the volume doubles the pressure: the same number of particles strike a smaller area more often.

Charles's law — at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature.

V / T = constant (constant p)

The pressure law — at constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature.

p / T = constant (constant V)

Example: a sealed tin left in the sun. The volume is fixed, so the pressure law applies — the temperature rise raises the pressure, which is why aerosol cans carry a warning not to leave them in a hot car.

Explaining the laws with particles — pressure arises from the rate of change of momentum of particles striking the walls. Raising the temperature makes the particles move faster, so they hit the walls harder and more often, raising the pressure. Reducing the volume gives them less distance to travel between collisions, so they strike more often, again raising the pressure.

Plotting to show proportionality — a graph of p against V for Boyle's law is a curve, which is hard to judge by eye. Plotting p against 1/V gives a straight line through the origin, and a straight line through the origin is the only convincing demonstration of proportionality. The same trick is why absolute temperature matters: a graph of p against θ in °C is a straight line that does not pass through the origin, and extrapolating it back to zero pressure gives −273 °C, which is how absolute zero can be found experimentally.