A surface can disappear without the substance escaping
A sealed tube can contain liquid carbon dioxide below and vapour above. Warm it along a suitable path, and the visible boundary eventually disappears. The material is still inside the tube. Near the critical point, the liquid and vapour become alike enough that the surface separating them comes to an end. Thomas Andrews made careful measurements of this behaviour and reported them in 1869.
The familiar ideal-gas picture has no way to make such a surface. It treats molecules as moving points whose encounters with the walls produce pressure. At a fixed temperature, compression simply raises the pressure smoothly. This is useful for a dilute gas, where molecules spend most of their time far apart. It leaves out the ingredients that let a dense group of molecules stay together.
Molecules need room, and they pull on one another
In his 1873 doctoral work, Johannes Diderik van der Waals treated a gas and a liquid as two arrangements of the same molecules. He retained their thermal motion and added two effects. Molecules take up room, so the space available for their motion is smaller than the container. They also attract one another, which changes the pressure they exert on its walls.
Think of a molecule approaching a wall. Molecules behind it pull it back toward the fluid. Its impact can therefore deliver less momentum to the wall than an ideal-gas calculation would predict. In a dilute gas this reduction is small. As the molecules crowd together, attraction can substantially favour a dense state.
The finite size acts in the other direction at strong compression. Molecules cannot all occupy the same place. Reducing their available room makes further compression increasingly difficult. The competition between thermal motion, attraction and crowding gave van der Waals one approximate description that could reach both gaslike and liquidlike densities.
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Compression can change the amount of liquid
Below the critical temperature, slowly compressing a vapour can create liquid. Through the coexistence interval at fixed temperature, much of the volume reduction comes from converting vapour into denser liquid. The pressure stays at the saturation value as long as both phases remain in equilibrium. A piston can move a long way while the pressure changes very little.
A raw van der Waals curve develops a looping section in this region. Part of that loop predicts that pressure rises when the fluid expands, an unstable response for a freely equilibrating uniform fluid. The physical equilibrium follows a constant-pressure coexistence line instead. The choice of that line must make both phases equally favourable; it is commonly represented by Maxwell’s equal-area construction.
At the critical point, the difference between the coexisting densities shrinks to zero. Above its temperature, compression can make a fluid very dense without crossing a liquid–vapour phase boundary. A path around the critical endpoint can therefore connect liquidlike and gaslike states continuously.
For carbon dioxide the critical temperature is close to thirty-one degrees Celsius, a little above an ordinary warm room. Above that temperature, pressure alone cannot recover a distinct liquid–vapour surface. Cooling matters as much as compression. Andrews’s measurements made that distinction visible, and a theory of condensation had to make room for both controls.
The simple picture opened a harder question
The theory made the relation between gases and liquids intelligible, which is the contribution recognized by the 1910 Physics Prize. Its two material constants compress complicated molecular behaviour into a manageable model. That is a remarkable explanatory gain, but the approximation treats each molecule’s surroundings too uniformly to predict all the details near a real critical point.
Near that point, unusually large patches of fluid can become denser or thinner together. These density fluctuations extend over many molecular distances and may strongly scatter light. To understand why different substances can share the same critical behaviour, physicists had to study how fluctuations change when one looks at larger and larger scales. That later question leads to Kenneth Wilson’s work.