State And Path Functions

As we know that the properties of the system describe its state when the system is in thermodynamic equilibrium (thermodynamics equilibrium means system is in thermal, chemical and mechanical equilibrium simultaneously). 
The thermodynamic properties of systems are classified into two types based on their dependence on system's state and process path. These two types are;
 !!!State Function Properties And Path Functions Properties!!!

In this article, we will learn about the state function and path functions of thermodynamics in detail with the help of various examples.


Let Us Now Understand Them In Detail
State Functions/ State Variable
The properties whose value depends only on the initial and final state of the system and is independent of the path by which the state passes from the initial to the final state, are called State Functions. 
These are sometimes called "Point Functions". And the change in state functions is directly measured by finding the difference between their values in the final state and the initial state. 
In the case of a cyclic process (where the initial and final states are the same), the change in state functions is zero. Or we can say that "There Is No Change In The State Properties In Case Of Cyclic Process". 

Example Of State Functions Are- 
Temperature, Pressure, Density, Internal energy, Mass, Entropy, Enthalpy, Volume, Gibb's free energy, Etc.

Let Us Take An Example Of Coffee To Understand It More Clearly;
If you take a cup of coffee and you heat it to say 70 degrees. On leaving it to cool, it will reach the room temperature of 30 degrees. But if you heated it again from 70 degrees to 100 degrees and if you allowed it to cool, the coffee will again return to the room temperature of 30 degrees but it took a different path. So, Temperature is a state variable.
An Example Of Density 
☛ Density is a state function and if the density is ρ₁ at initial state and the density is ρ₂ at final state then the change in density is directly obtained by subtracting these values. 
               ➩ ∆ρ ＝ ( ρ₁ - ρ₂ )


Path Functions/ Path Variables
Those properties whose value depends only on the path through which the state passes from the initial to the final state, are called Path Functions. It is independent of the initial and final state of the system. There are two most common types of path functions namely "Heat And Work". 
These two functions are dependent on how the thermodynamic system changes from the initial state to final state. 
Change in path functions can not be measured directly. A path function is an inexact or imperfect differential.
........"Path Functions And State Functions Are Introduced To Identify Variables Of Thermodynamics"..........


Difference Between State Functions And Path Functions
  1. The properties whose value depend only on the initial and final state of the system irrespective of their path are called State functions While the properties whose value depend on the path followed by the process irrespective of their states are called Path functions.
  2. State function is an exact or perfect differential while Path function is an in-exact or imperfect differential.
  3. For state functions, only initial and final states of the process are sufficient While in path functions, we need to know the exact path followed by the process.
  4. State functions are the properties of the system While path functions are not the properties of the system.
  5. For a cyclic integral, the value of state function is always zero but the value of path functions may or may not be zero.



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