Table of Contents
Path function
A Path function is a function whose value depends on the path followed by the thermodynamic process irrespective of the initial and final states of the process.
An example of path function is the work done in a thermodynamic process. Work done in a thermodynamic process is dependent on the path followed by the process.
A path function is an inexact or imperfect differential.
In the P-V diagram given above one can easily see that for the same initial and final states of the system, work done in all the three processes is different.
For process A work done is b2A1a
For process B work done is b2B1a
For process C work done is b2C1a
Another example of path function is heat.
Point function
A Point function (also known as state function) is a function whose value depends on the final and initial states of the thermodynamic process, irrespective of the path followed by the process.
Example of point functions are density, enthalpy, internal energy, entropy etc.
A point function is a property of the system or we can say all the properties of the system are point functions.
Point functions are exact or perfect differential.
Note: Since a point function is only dependent on the initial or final state of the system, hence in a cyclic process value of a thermodynamic function is zero, or change in thermodynamic property is zero.
Difference between point function and path function
| Sr. no. | Point Function | Path Function |
| 1 | Its values are based on the state of the system (i.e. pressure, volume, temperature etc.) | Its values are based on how that particular thermodynamic state is achieved. |
| 2 | No matter by which process the state is obtained, its values will always remain the same. | Different processes to obtain a particular state will give us different values. |
| 3 | Only initial and final states of the process are sufficient | We need to know exact path followed by the process |
| 4 | Its values are independent of the path followed | Its values are dependent on the path followed |
| 5 | It is an exact or perfect differential | It is an inexact or imperfect differential. |
| 6 | Its cyclic integral is always zero | Its cyclic integral may or may not be zero |
| 7 | It is property of the system | It is not the property of the system |
| 8 | Its examples are density, enthalpy, internal energy, entropy etc. | Its examples are Heat, work etc. |