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# State and Path function in Thermodynamics

The state of a system is determined with the help of some measurable quantities like volume, temperature, density, pressure, etc. These quantities that can identify the state of a function are called properties. State and path functions both are ** thermodynamics terms** that are used to name these properties.

### State function in Thermodynamics

A ** thermodynamic property that depends only on the initial and final state** and does not depend on the path taken to reach the final state or value is

**or point function.**

*known as the state function*Properties that depend on state include pressure, temperature, amount of substance, etc. For example, density is a state function, it does not depend on how a substance is obtained. Similarly, the thermodynamics properties like internal energy (U), enthalpy (H), entropy (S), etc., are state functions. A change in their values depends on their initial and final state.

The state functions depend on the values of different parameters at a particular time, it does not depend on how these values are obtained or irrespective of the path taken.

Let us take a *simple example to understand state function;*

A person standing on the first floor of a building. His potential energy is mgh where m is the mass of the person, g is gravity and h1 is the height of the first floor from the ground. Now he reaches the top floor by lift then his potential energy becomes mgh2 where m (mass) and gravity (g) are the same only height changes. Now if he takes a different route to reach the top floor such as stairs even then the potential energy will be mgh2 as he reaches the same height in this case. So, the potential energy depends on the initial and final heights irrespective of the path followed to reach the top floor. So, potential energy is a state function, not a path function.

### Path function in Thermodynamics

A ** thermodynamic property that depends on the path between the initial and final state is known as the path function.** The path functions depend on the path taken or covered between two (initial and final) states. For example, work and heat. If different paths are chosen to reach from one point to another point, the work done will be different however you reach the same point in each case. So, work is not a state function as we cannot say that a system will have a specific amount of work at a specific state.

Let us take a *simple example to understand path function;*

Path function is a thermodynamic property whose value depends on the path followed to attain that value. For example, a person carries a 10kg weight from point A to point B after travelling a distance of 2 km and the work done by him is W. In this second case, he takes the same weight from point A to point B but this time he travels 3 km, so in this case, the work done by him will be more, however, he takes the weight to the same destination. So, we can see the work done by him depends on the path followed, so, work is a path function. A path function has variable values based on the route.

### Difference between state function and path function

State Function | Path Function |
---|---|

It refers to a property whose value does not depend on the path followed to reach that value. | It is a property whose value depends on the path followed to reach that value. |

They are also called point functions. | They are also called process functions. |

It can be integrated using values of the initial and final state of a system. | They need multiple integrals and limits of integration for integrating the property of the system. |

Value of state function remains the same regardless of the path or steps involved to reach that value. | Value of the path function will be different if a different path is taken to reach the final state. |

Different paths give the same value | Different paths give different values |

For example; entropy, mass, temperature, volume, etc. | Example; heat and mechanical work. |