What you are looking at
A gas sealed in a cylinder by a sliding piston. The dots are molecules; they drum against the walls and the
piston, and that constant bombardment is the
pressure. How hard and how often they hit
depends on how fast they move (temperature), how crowded they are (volume), and how many there are (amount).
The graph on the right traces the law you've selected.
One law behind them all
Everything here follows from the
ideal gas law:
P V = N k T
Pressure P, volume V, amount N and absolute temperature T are locked together. Hold two of them fixed and the
other two must trade off — and each choice is one of the classic named laws:
Boyle's law (constant T)
Shrink the volume and the same molecules hit the walls more often, so pressure rises:
P ∝ 1 / V (T, N fixed)
The P–V graph is a hyperbola. Halve the volume, double the pressure.
Charles's law (constant P)
Heat the gas at fixed pressure and the piston is pushed out — volume grows in direct proportion to absolute
temperature:
V ∝ T (P, N fixed)
The V–T graph is a straight line through the origin. This is why a hot-air balloon rises and why a sealed bag
puffs up in the sun.
Gay-Lussac's law (constant V)
Heat the gas in a rigid container and, with nowhere to expand, the pressure climbs instead:
P ∝ T (V, N fixed)
A straight line through the origin again — the reason an aerosol can warns against heat.
Things to try
Switch laws and drag the free variable; watch the point ride along the predicted curve while the combination
PV/NT stays pinned at a constant. Change the amount N and see every
curve rescale. Notice the molecules speed up and glow hotter as T rises — temperature really is just their
average energy.