Intermediate Topic 332 of 1102 Thermodynamics & Energetics
Path Function
A quantity such as heat or work that depends on the route taken between states.
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In-depth explanation of Path Function
A path function is a quantity whose value depends on the route followed between two states. Heat and work are the standard examples, and they describe energy in transit rather than stored properties of a system. The same change from state A to state B can be achieved by a reversible or an irreversible path, and the heat and work exchanged will differ between them even though the change in internal energy is identical. Since the sum of q and w is fixed by the first law, any difference in work between routes must be matched by a difference in heat. This distinction is why reversible processes serve as idealized references for maximum work.
Going deeper: Path Function
Key ideas: Heat and work are path functions, so they are written as q and w rather than delta q and delta w, because they are amounts transferred and not changes in a property. For a fixed change of state, the path chosen decides how the fixed delta U is divided between q and w. A reversible path gives the maximum work and so the maximum heat released or absorbed.
Common mistakes and connections: A common error is to compute work with a formula for the wrong path, for example using a reversible expression for a sudden expansion against constant pressure. Remember that identical start and end points do not mean identical heat and work. It links to the contrast between reversible and irreversible processes later in this area.
Visualization of Path Function
The area under each route is the work done. Both go from 1 to 3 L ending at 1 atm, but the isothermal path gives much more work, so work (and heat) depend on path. The interactive lesson shows this as a live animation or chart.
Worked example and use case
A gas expanding freely into a vacuum does no work, while the same gas expanding slowly against a piston does measurable work.
Frequently asked questions about Path Function
What is Path Function?
A quantity such as heat or work that depends on the route taken between states.
Is Path Function a beginner, intermediate or advanced topic?
Path Function is a intermediate topic in Thermodynamics & Energetics. It builds on the vocabulary of beginner topics in this area.
What should I learn before Path Function?
Study these earlier topics in Thermodynamics & Energetics first: System and Surroundings, Open Closed Isolated Systems, State Function.
What comes after Path Function?
The next topics in Thermodynamics & Energetics are Energy and Heat.
Can I practise Path Function with quizzes?
Yes. The interactive lesson includes a self-check question on Path Function, and the Thermodynamics & Energetics quiz draws on every topic in this area.
Where Path Function fits in Thermodynamics & Energetics
Path Function is topic 4 of 91 in Thermodynamics & Energetics.