A State Is a Set of Properties

You have picked a container and taken its inside as the system. Now what may pass through the boundary decides the kind of system you have. Press the buttons. A closed system lets heat in and out but holds the matter in, like water boiling in a covered pot. An open system lets matter travel too, the way steam escapes from an uncovered kettle. An isolated system lets neither heat nor matter through; think of a perfect thermos. The very same container is analyzed in completely different ways depending on what you agree the boundary allows. That is why a thermodynamics problem always starts by drawing the boundary. A car engine's cylinder is a real example: with the valves shut during compression it is a closed system, but the instant the valves open to push out exhaust and draw in fresh air, it becomes an open system.

With the system fixed, it is time to say what state it is in. Drag the temperature up. The particles jostle harder and the color glows hotter. At the same time the pressure bar beside it climbs, while the volume stays put because the container is rigid. Here is the point: one number is not enough to state a state. Temperature alone does not tell you everything about the system. Pressure and volume have to be there too before this state is determined. A state is a bundle of several properties held all at once. You cannot set these properties fully as you please, though: for a fixed amount of gas, once two like pressure and temperature are chosen, the remaining volume is already fixed to follow.

The cleanest way to gather the properties together is to make each one an axis. Put volume V on the horizontal axis and pressure P on the vertical, and the system's state becomes a single point on this plane. Drag the point around. Wherever it sits tells you the P and V of that instant. One state, one point. This picture is the map used throughout all of thermodynamics. Words you will meet later, isothermal, isobaric, adiabatic, are in the end just stories about where the point sits on this plane and how it moves. Wherever the point sits, it holds only the state at this instant and keeps no memory of how the system got there, and that history-free quality is exactly why a single point can stand for a whole state.

When the system changes from one state to another, we call it a process. On the diagram a process is the path the point takes from one place to another. Drag the slider to advance it. The point travels from state 1 to state 2, drawing a line as it goes. Having the same start and end does not make two processes the same. The route taken, the whole trace, is the process. For now there is just one path, but many different paths can join the same two points. And that the heat and work exchanged depend on which path you take is something you will meet soon. Just as the straight-line distance between two towns is fixed but the effort you spend depends on whether you cross the mountain or go around, the same start and end still leave the heat and work exchanged to be decided by which path you take.

But to describe a state with a single point, one promise is needed: the properties across the whole system must be uniform and no longer changing. This is called equilibrium. Heat just one side suddenly. At first the left is hot and the right is cold, so you cannot speak of the system with one number called temperature. Let time pass and the heat spreads, slowly settling toward one uniform temperature. Only once it reaches equilibrium does a single value like P or T stand for the whole system. The state point we drew is always a point placed on the assumption of this equilibrium. So a process drawn as a smooth curve on the P-V plane is really an idealization, one the system only approaches when the change happens slowly enough to stay nearly in equilibrium at every instant.