A group of properties/measurables that have the success of reproducing the given condition(s) of a system on re-attainment of their value(s) each time are termed state functions. This means that whenever the values of measurable properties are reproduced, the state of the system is regenerated.

## Microscopic and Macroscopic states

The state of a system can be observed at both microscopic and macroscopic levels. The state function at a microscopic level is the wavefunction (ψ), however, at a macroscopic level, the state is defined as a set of measurable properties which include temperature, pressure, volume, density, viscosity, etc. A change in any single value will result in a change in the macroscopic state of a system.

The microscopic state ad macroscopic states are interlinked through statistical mechanics where the combinations/permutations of microscopic states lead to the generation of macroscopic properties through well-defined formulas e.g. number of microscopic states W defines entropy as S=klnW where k is the Boltzmann constant.

## Microscopic vs Macroscopic State Functions

The microscopic and macroscopic state functions can be compared as:

Macroscopic states | Microscopic states |

They are defined by set of state functions | Only one state function carries all the information |

State functions include mass (m), number of particles (ni), Pressure (P), Temperature (T), Volume (V), Chemical composition (Xi), Entropy (S), all energy terms such as enthalpy (H), internal energy (U), Gibbs free energy (G), Helmholtz free energy (A) | The only state function is psi (Ψ) |

Change in any of above mentioned property can result in change in state of the system | Change in (Ψ) means the change in state of the system |

Microscopic state function (Ψ) can not be calculated from macroscopic state functions | Macroscopic state functions of the system can be calculated by applying the operator on (Ψ) |

They describe classical mechanics | They describe quantum mechanics |

These are numerical values which may have mathematical correlations | These are mathematical functions |

They do not tell us about microscopic properties | They give probability functions |

No operators are required to operate on macroscopic states |
Quantum mechanical operators are involved in microscopic states |

They only yield macroscopic information | They yield both macroscopic and microscopic information |

## Changes in States

A change in state can be brought about by nuclear, chemical, or physical processes. These processes are accompanied by certain changes and effects, which differ them from one another.

### Nuclear processes

Nuclear processes bring changes in the nuclear states of atoms leading to nuclear reactions. The atomic composition/nature of atoms changes, as in the following aspects.

Examples of nuclear processes are fission and fusion reactions.

### Chemical processes

The chemical processes bring the change in electronic composition around the nucleus leading to the formation of new molecules. Orbitals’ realignment and changes in primary bonds also take place.

Examples of chemical processes are all chemical reactions such as; gaseous hydrogen+oxygen.

### Physical processes

Physical processes correspond to non-compositional changes leading to changes in intermolecular parameters such as bond lengths, bond angles, and vibrational rotational energy of the intact composition. This may lead to some visual change of state e.g. Temperature rise changes ice to water followed by vapor formation.

Such changes can lead to phase change or phase transitions. (Solid→Liquid→Gas) phase transitions are physical processes.

## Concepts Berg

**How is internal energy a state function?**

Internal energy is a combination of all attractive and repulsive forces existing in any substance. The net effect of all primary interactions (bonds) and secondary interactions (intermolecular forces) defines the internal energy of a system. During any reaction, the combinational values of these parameters change which results in a change in the state of that system. It depends on the nature and strength of bonding/interaction, not on the route through which the change has occurred. So, the internal energy is a state function, not a path function.

**Is enthalpy a state function?**

Enthalpy is a state function just like internal energy as its effective (change) value depends on the state of the system, not the path used to bring that change.

**What is the difference between state and state function?**

A state is a set of defined state functions (properties). Each contributing property is termed a state function.

**Is heat capacity a state function?**

Heat capacity is a state function.

**Is energy a state function?**

Energy is a state function because its value depends on the current state of a system.

**Is work a path function or a state function?**

Work is a path function because the frictional and other losses associated with the path also define the work being done to bring the change. Therefore, the value of work depends on the initial and final states as well as on the path/route adopted to bring that change.