thermodynamic system and state
Thermodynamics always starts by deciding how far to look. Pick one tank in front of you and call its inside the system, everything outside is the surroundings, and the line that splits the two is the boundary. First change what crosses that boundary. Let only heat cross, let matter cross too, or let nothing cross, and how you draw the boundary is how you set the scope of the analysis. Once the system is chosen you have to say what state it is in now, and a state does not end in a single number. Pressure and volume and temperature have to be there together before the state of the system is fixed, so a state is one bundle of properties gathered like this.
Pick one tank and take its inside as the system, and what can cross the boundary now decides the kind of system. Press the button and a closed system lets heat cross but not matter, like water boiling in a pot with the lid on. An open system lets matter cross too, the way steam leaves a kettle with the lid off, and an isolated system lets neither heat nor matter through, the picture of a perfect thermos. The same tank gives a completely different analysis according to how you agree on the boundary, so a thermodynamics problem always starts by drawing that line. A car engine cylinder is a closed system in the instant of compression with the valves shut, when matter cannot cross, and it becomes an open system the instant a valve opens and exhaust leaves while fresh air comes in.
With the system chosen, it is time to say what state it is in now. Raise the temperature and the particles strike harder and the color glows hot, and even though the tank is rigid so the volume stays the same, the pressure bar beside it fills up together. The point is that one number is not enough to name a state. Saying only the temperature does not tell you everything about the system, and pressure and volume have to be there too before this state is fixed, so a state is a bundle of several properties gathered at once. You cannot set those properties each as you please, and for a fixed amount of gas, once two of them such as pressure and temperature are fixed, the remaining volume is already fixed along with them.
The cleanest way to gather the properties is to make each one an axis. Put volume V on the horizontal axis and pressure on the vertical, and the state of the system is one point on this plane, and dragging the point makes that place tell the pressure and the volume of that instant. One point for one state is the map thermodynamics uses all the way through. Words that come later, isothermal or isobaric or adiabatic, are in the end a story of where the point sits on this plane and how it moves. Wherever the point is, it remembers nothing of how the system got there and holds only the state of this instant, so one state can be shown whole as one point.
A change of the system from one state to another is called a process, and on the diagram a process is the path the point travels from one place to another. Drag the slider forward and the point moves from state 1 to state 2, drawing a line. The same start and the same end do not make the process the same, and the whole trace of which path was taken is the process. For now there is only one path, but several paths can join the same two points, and which path you take changes the heat and the work exchanged, which you will meet soon. The straight distance between two towns is fixed, yet the effort differs if you cross the mountain or go around, and in the same way the same start and end still change the heat and the work according to the path.
To name a state with one point, one agreement is needed. The properties of the whole system have to be even and no longer changing, and this is called equilibrium. Heat only one side suddenly and at first the left is hot and the right is cold, so you cannot name the system with one number called temperature, and as time passes the heat spreads and settles toward one even temperature. Only once equilibrium is reached does one value such as T stand for the whole system, and the state point we draw is always a point taken on the premise of that equilibrium. So a process drawn as a smooth curve on the P-V plane is really an ideal, and it comes close to that curve only when the change is very slow and the system stays nearly in equilibrium at every instant.