Key Difference – State Function vs Path Function
Thermodynamics is a major branch of physical chemistry which indicates the thermochemical relationships with different forms of energy and work. There are four thermodynamic laws used in describing the behavior of a thermodynamic system. The state function and path function are two ways of expressing different thermodynamic properties of systems. The key difference between state function and path function is that state functions do not depend on the path or process whereas path functions depend on path or process. Therefore state function and path function are opposite of each other.
CONTENTS
1. Overview and Key Difference
2. What is State Function
3. What is Path Function
4. Similarities Between State Function and Path Function
5. Side by Side Comparison – State Function vs Path Function in Tabular Form
6. Summary
What is State Function
State function is a thermodynamic term that is used to name a property whose value does not depend on the path taken to reach that specific value. State functions are also known as point functions. A state function only depends on the current state of the thermodynamic system and its initial state (independent from the path). The state function of a thermodynamic system describes the equilibrium state of that system irrespective of how the system arrived at that state.
Examples of State Functions
 Mass
 Energy – enthalpy, internal energy, Gibbs free energy, etc.
 Entropy
 Pressure
 Temperature
 Volume
 Chemical composition
 Altitude
A state function depends on three things: the property, initial value and final value. Enthalpy is a state function. It can be given as a mathematical expression as given below.
In which, t_{1} is the final state, t_{0} is the initial state and h is the enthalpy of the system.
What is Path Function?
Path function is a thermodynamic term that is used to name a property whose value depends on the path taken to reach that specific value. In other words, a path function depends on the path taken to reach a final state from an initial state. Path function is also called a process function.
A path function gives different values for different paths. Hence path functions have variable values depending on the route. Therefore, when expressing the path function mathematically, multiple integrals and limits are required to integrate the path function.
Examples of Path Functions
 Mechanical work
 Heat
 Arc length
The internal energy is given by the following equation:
∆U = q + w
In which ∆U is the change in internal energy, q is the heat and w is the mechanical work. The internal energy is a state function, but heat and work are path functions.
What are the Similarities Between State Function and Path Function?
 Both are functions described in thermodynamics.
 Both are properties of thermodynamic systems.
What is the Difference Between State Function and Path Function?
State Function vs Path Function 

State function is a thermodynamic term that is used to name a property whose value does not depend on the path taken to reach that specific value.  Path function is a thermodynamic term that is used to name a property whose value depends on the path taken to reach that specific value. 
Other Names  
State functions are also called point functions.  Path functions are also called process functions. 
Process  
State functions do not depend on the path or process.  Path functions depend on the path or process. 
Integration  
State function can be integrated using the initial and final values of the thermodynamic property of the system.  Path function requires multiple integrals and limits of integration to integrate the property. 
Values  
The value of state function remains the same regardless of the number of steps.  The value of path function of a single step process is different from a multiple step process. 
Examples  
State functions include entropy, enthalpy, mass, volume, temperature, etc.  Path functions include heat and mechanical work. 
Summary – State Function vs Path Function
State function and path function are two forms of thermodynamic expressions that give different properties of thermodynamic systems. These terms are different from each other; the key difference between state function and path function is that state functions do not depend on the path or process whereas path functions depend on path or process.
Reference:
1. “State function.” Wikipedia, Wikimedia Foundation, 24 Feb. 2018, Available here.
2. “State vs. Path Functions.” Chemistry LibreTexts, Libretexts, 23 Jan. 2018, Available here.
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