Seal a fixed amount of gas in a rigid tank and heat it: its temperature and its pressure climb together. Follow the gas, the gauge and the thermometer, and watch why the pressure-versus-temperature line stays straight and passes through the origin.
Take a fixed amount of gas, seal it in a container whose volume cannot change, and heat it. Its temperature goes up — and so does its pressure. The two rise together in a simple, tidy way: the pressure is directly proportional to the absolute (kelvin) temperature. Double the absolute temperature and you double the pressure.
This is one of the three gas laws, and it explains everyday warnings. A gas cylinder left in the sun, a sealed tin on a fire, or a car tyre warming on a motorway all raise their pressure as they warm, because the gas cannot expand and escape. Seeing the sealed tank next to the straight P–T line makes the proportionality obvious at a glance.
The gas is trapped in a rigid tank, so the space it can occupy never changes. Because the molecules have no room to spread out and cool by expanding, every push from a hot gas shows up as pressure instead of a change in size.
The burner adds energy Q to the gas. That energy becomes kinetic energy of the gas molecules, so they speed up. On the diagram the molecules jiggle faster as the temperature reading on the thermometer climbs.
Temperature is really a measure of how fast the molecules move on average. When they are faster, each one delivers a bigger blow when it strikes a wall, and there are more strikes every second, so the total force on the walls grows.
That growing force on the fixed wall area is a rising pressure, which the gauge shows as a bigger reading. For a fixed volume, pressure tracks absolute temperature in direct proportion — there is no threshold and no lag, just a steady rise.
Plot pressure against absolute temperature and every measured point falls on one straight line, and that line points back through the origin. So the ratio P/T is constant, giving P₁/T₁ = P₂/T₂. That is why the temperature must always be measured from absolute zero.
For a fixed amount of gas held at constant volume, pressure is directly proportional to absolute temperature. Heat the gas and its pressure rises; cool it and its pressure falls, so that the ratio of pressure to temperature stays the same.
Because the straight-line relationship passes through the origin only on an absolute scale. It is the distance above absolute zero that adds energy to the molecules, so the formula P₁/T₁ = P₂/T₂ only works when both temperatures are measured in kelvin.
Heating gives the molecules more kinetic energy, so they move faster and strike the walls of the fixed-volume container harder and more often. More forceful collisions per second mean a higher pressure on the walls.
If the volume can change, heating mostly makes the gas expand instead of raising its pressure — that is the constant-pressure behaviour described by Charles's law. The direct pressure law assumes the volume is held fixed, as in a sealed steel tank.
Anywhere a gas is sealed at constant volume: aerosol and gas cylinders, car tyres warming on a motorway, and pressurised process vessels all show pressure rising and falling with temperature. It also explains why containers carry pressure and temperature warning limits.