---
title: "Thermodynamic State Variables and PV Diagrams"
description: "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."
canonical: https://lightmysky.com/learn/science/thermodynamic-state-variables-and-pv-diagrams-mt_G3EYx84GZK
source: https://lightmysky.com/learn/science/thermodynamic-state-variables-and-pv-diagrams-mt_G3EYx84GZK.md
retrieved: 2026-09-12
---

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# 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.

Subject: Science · Area: Thermal & Statistical Physics · Ages 18 to 19
Page: https://lightmysky.com/learn/science/thermodynamic-state-variables-and-pv-diagrams-mt_G3EYx84GZK

## Ready when they can

- 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

## Lesson: State variables and the paths on a PV diagram

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.

**Example.** 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.

**Tip.** 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.

**Recap.** State variables fix the now, paths fix the work, and loops return every state variable home.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [The Gas Laws and the Ideal Gas Equation](https://lightmysky.com/learn/science/the-gas-laws-and-the-ideal-gas-equation-mt_G7DOTVl4KM)

## Opens up

- [Equipartition and the Heat Capacities of Gases](https://lightmysky.com/learn/science/equipartition-and-the-heat-capacities-of-gases-mt_3OjJwVWlYD)
- [The First Law of Thermodynamics for Any Process](https://lightmysky.com/learn/science/the-first-law-of-thermodynamics-for-any-process-mt_LIWgeWSXHz)