This document discusses state functions and path functions in thermodynamics. It defines a state function as a property that depends only on the initial and final states of a system and not on the path between them. Examples given are changes in internal energy, enthalpy, pressure, temperature and volume. In contrast, a path function depends on the specific path or process taken between the initial and final states, with work and heat given as examples. The document provides an overview to distinguish state functions from path functions in thermodynamics.

1. Thermodynamics:
State versus Path Functions
By Shawn P. Shields, Ph.D.
This work is licensed by Shawn P. Shields-Maxwell under a
Creative Commons Attribution-NonCommercial-ShareAlike

2. Overview
When we talk about a given system, we say
it is in a particular “thermodynamic state.”
A particular thermodynamic state is
characterized by a few “macroscopic
observables,” such as
Pressure, temperature, volume, color,
altitude, etc.

3. Differences (Changes) in Macroscopic
Observables
Changes in Pressure (P), Volume (V), and
Temperature (T):
What can we say about all of these?
It doesn’t matter how the system arrived at the
final state from the initial state, the difference
(or change) is the same.


4. A Thermodynamic “State Function”
State Functions only depend on the current
(thermodynamic) state of the system.
How the system attained that state does not
matter!
Example: Compression of a gas inside a piston.
Vi Vf

5. A Thermodynamic “State Function”
A State Function is
defined as a
property of a system
that only depends on
the initial and final
state of the system,
and is independent of
the path followed in
getting from one to
the other.Ti
Tf
∆T
T
Ti
Tf
∆T
T

6. Examples of State Functions
∆U is a state function.
Some other state functions…
∆H (Enthalpy, coming soon…)
∆P ∆T ∆V
Altitude Mass
chemical composition

7. Path Functions
A path function
does depend on
the path followed
in getting from
the initial to the
final state.
"Path near Clonmass Bay - geograph.org.uk - 899872" by Ross - From geograph.org.uk. Licensed under Creative Commons Attribution-Share Alike 2.0
via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Path_near_Clonmass_Bay_-_geograph.org.uk_-
_899872.jpg#mediaviewer/File:Path_near_Clonmass_Bay_-_geograph.org.uk_-_899872.jpg

8. Path Functions
Work (w) and heat (q) are path
functions.
Two rock climbers of equal mass
scale the same cliff. One climbs
straight up while the other
backslides numerous times on the
way up…
who did more work?
Cliffs along the Atlantic coastline of County Mayo, near
Ballycastle, Ireland by Phil Armitage (public domain)

9. What You Should Be Able to Do (so
far)
Define a state function
Recognize state functions from
examples given.
Define a path function.
Recognize examples of path functions.

10. What You Should Be Able to Do (so
far)
Define a state function
Recognize state functions from
examples given.
Define a path function.
Recognize examples of path functions.