Thermodynamic State Variables and PV Diagrams
Pressure, volume and temperature describe the state of a system regardless of how it got there, and a path on a PV diagram shows a process. The area under the path is the work done.
What a learner can do afterwards
- Distinguishes state variables from path quantities such as work and heat
- Reads the work done from the area under a path on a PV diagram
- Explains why a closed cycle returns every state variable to its starting value
1 · Read
Pressure, volume, temperature, and internal energy describe the current state of a gas, however it got there. Work and heat instead describe one particular path, so they are not state variables.
On a PV diagram each path is a process, and the area under the path gives the work done. Hotter isotherms sit higher and steeper as hyperbolas that never cross. The equation of state links pressure, volume, and temperature, so any two fix the third.
Trace a closed loop and every state variable returns to its start. The work of each leg comes from its own area. A clockwise loop expands at high pressure and squeezes at low pressure, so net work flows out, and the enclosed area equals both the net work out and the net heat in.
Never read work off the endpoints alone. Two paths between the same endpoints can carry different work and heat, because work cares about the route.
State variables fix the now, paths fix the work, and loops return every state variable home.
More to read
3.1 Thermodynamic Systems
Thermodynamics starts by drawing a fence. Everything inside the fence is the system, everything outside is the surroundings, and the wall between them decides what may pass. An isolated wall passes nothing, a conducting wall passes heat but not matter, and a movable wall lets the system do work by expanding. Naming the system and its walls is the mandatory first move in every problem.
Once the fence is drawn, the state variables take over. Pressure, volume, temperature, and internal energy each describe the present condition of the system and nothing about its past. Two samples with the same pressure, volume, and temperature are thermodynamically identical, no matter how differently they arrived there. That indifference to history is exactly what makes them state variables.
3.2 Work, Heat, and Internal Energy
Work, heat, and internal energy form the energy ledger, but only one of the three is a state variable. Internal energy belongs to the state: fix the condition of the gas and you fix its internal energy. Work and heat instead describe transfers across the fence during a particular change, so they depend on the route. Take a gas from A to B along two different paths and the internal energy change matches, while the work and heat generally do not.
The PV diagram makes this visible. A process is a curve from the start point to the end point, and the work done by the gas is the area beneath that curve. A fat bulging path encloses more area and does more work than a direct one between the same endpoints.
13.3 The Ideal Gas Law
The ideal gas law is the equation of state that ties the whole diagram together. Pressure times volume equals moles times R times temperature, so on a PV plot each temperature corresponds to one hyperbola, called an isotherm. Hotter isotherms sit higher and farther out, and since one pressure and volume pair fixes exactly one temperature, two isotherms can never cross.
A closed cycle is a loop on this diagram, and loops are where engines live. Round a full loop every state variable returns to its starting value, so the net change in internal energy is zero. Whatever area the loop encloses equals the net work done, which must have entered as net heat. One glance at a loop thus tells you the engine output: bigger enclosed area, more work per cycle.
Explore more
2 · Watch
En anglaisTake it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.