ideal gas law PV=nRT
For an ideal gas, pressure, volume, and temperature are tied by one relation, PV = nRT. Even joining the same two points, the trace on the P-V plane differs according to whether the process is isothermal, isobaric, isochoric, or adiabatic. One equation splits into four paths.
Move the volume and the temperature and the pressure follows as P = nRTV, and the three values always satisfy PV = nRT. When a tire heats up in summer sun or on a highway the volume stays nearly the same while the temperature rises and the pressure rises with it, and that is this relation. The hotter air pushes harder in the same place.
Hold the temperature and the product of pressure and volume stays constant. Drag the volume and the point moves along an inverse curve, a hyperbola, and that is the trace of an isothermal process. Block the mouth of a syringe and push slowly until the volume is halved and the pressure doubles, and when the temperature is constant pressure and volume move opposite each other.
Look at the two processes with the buttons and the traces are simple. Isobaric holds the pressure, a horizontal line, and isochoric holds the volume, a vertical line, the two simplest traces. Throw a sealed can on a fire and the volume stays fixed while only the temperature rises and the pressure shoots up, isochoric, and heat a gas under a freely moving piston and it swells while holding the air pressure, isobaric.
Adiabatic means no heat is exchanged, so PVγ stays constant. Starting from the same point the adiabatic curve is steeper than the isothermal curve, because the temperature falls as the gas expands. Air climbing a mountain expands and cools and makes cloud and rain, and the nozzle of a spray can grows cold, both an adiabatic expansion so fast that heat has no time to cross and the temperature drops.
Last, lay the four processes on one place. Switch isothermal, isobaric, isochoric, and adiabatic with the buttons and the traces leaving the same start are each different at a glance, and since the area under the curve was the work, a different process means different work. The next chapter moves to the heat engine that works by this cycle and to the 2nd law. A real car engine or a refrigerator also runs as a cycle that joins these processes in a loop, and the area the closed loop encloses on the P-V plane is the net work exchanged in one turn.