One of the most important concepts in thermodynamics is that of **state functions** , which describe the state of a system in terms of macroscopic variables.

These functions do not depend on how the system got to its current state, but only on the state itself.

Next, we will explore in depth what state functions are, their importance, and the main functions used in thermodynamics, such as internal energy, enthalpy, entropy, and Gibbs free energy.

## What are state functions?

A **state function** is any macroscopic property or variable of a system that depends only on the current state of the system, without regard to the path or process by which that state was reached.

This implies that if the initial state and the final state of a system are known, changes in the state functions can be determined simply by comparing the two states, regardless of how the transformation occurred.

For example, if a gas in a container changes from state A to state B, the state functions only depend on the values of the macroscopic variables (such as pressure, volume, and temperature) in states A and B.

It does not matter whether the gas expanded rapidly or slowly, or whether it was first heated and then expanded, the change in state functions will be the same.

Some of the most important state functions in thermodynamics are **internal energy (U)** , **enthalpy (H)** , **entropy (S)** , and **free energies** such as the **Helmholtz free energy (A)** and the **Gibbs free energy (G)** .

## Differences between state functions and process functions

It is important to differentiate state functions from **process functions** . While state functions depend only on the initial and final states, process functions depend on the path or process the system takes to get from one state to another.

Examples of process functions are **work** and **heat** , since their value varies depending on how the transformation between states is performed.

For example, in the case of mechanical work done by an expanding gas, the value of the work depends on the process, that is, whether the expansion is isobaric (at constant pressure), isothermal (at constant temperature), or adiabatic (without heat exchange).

## Main state functions in thermodynamics

### Internal energy (U)

Internal energy ** **is the sum of all kinetic and potential energies of the molecules composing a system. For an ideal gas, internal energy is related only to the kinetic energy of the molecules due to their thermal motion, while in more complex systems, it also includes molecular interactions, vibration energies, rotation, etc.

In a closed system where only heat and work are exchanged with the surroundings, the change in internal energy, ΔU, can be expressed by the first law of thermodynamics:

ΔU=Q−W

Where Q is the heat added to the system and W is the work done by the system. Internal energy is a state function because it only depends on the current state of the system (pressure, volume, temperature), and not on the specific process that brought the system to that state.

### Enthalpy (H)

Enthalpy is another very important state function, defined as:

H=U+PV

Where P is the pressure of the system and V is the volume. Enthalpy is useful when dealing with processes that occur at constant pressure, such as chemical reactions in open vessels. Under such conditions, the change in enthalpy, ΔH, represents the heat absorbed or released by the system.

For example, when an exothermic reaction occurs in a constant pressure environment, the heat released is equal to the decrease in enthalpy of the system. In contrast, in an endothermic reaction, the heat absorbed corresponds to an increase in enthalpy.

### Entropy (S)

Entropy is a state function that measures the degree of disorder or randomness in a system. It is often associated with the Second Law of Thermodynamics, which states that in any natural process, the total entropy of the universe tends to increase.

Entropy is defined in terms of the heat exchanged in a reversible process and the temperature at which the process occurs:

ΔS=Qrev / T

Where Qrev is the heat exchanged in a reversible process and T is the temperature at which the heat exchange occurs. If the system evolves towards greater disorder (such as the expansion of a gas into a larger volume), the entropy increases.

Entropy is a state function because its value depends only on the current state of the system, not on the path taken to reach it.

The importance of entropy lies in the fact that it not only determines the direction in which natural processes occur, but also sets limits on the amount of useful work that can be extracted from a system. In an irreversible adiabatic process, for example, entropy increases, meaning that some of the useful energy is degraded.

### Helmholtz free energy (A)

Helmholtz free energy is defined as:

A=U−TS

Where T is the temperature of the system and S is its entropy. Helmholtz free energy is particularly useful in closed systems that are at constant temperature and that exchange heat with the surroundings.

The criterion for spontaneity of a process at constant temperature and volume is that the Helmholtz free energy decreases. In other words, for a process to be spontaneous, the Helmholtz free energy must decrease, which implies an increased tendency towards stability.

### Gibbs free energy (G)

The **Gibbs free energy** is a state function that combines the enthalpy, entropy, and temperature of the system:

G=H−TS=U+PV−TS

Gibbs free energy is extremely important in systems at constant pressure and temperature, such as in most biological and chemical processes occurring on Earth. The change in Gibbs free energy, ΔG, determines whether a reaction or process is spontaneous.

If ΔG is negative, the process occurs spontaneously. If ΔG is positive, the process is not spontaneous and will require an external energy input to be carried out.

Gibbs free energy is also crucial to understanding chemical equilibrium. Under equilibrium conditions, ΔG is equal to zero, meaning there is no net tendency for changes to occur in the system. Chemical reactions tend to proceed in the direction in which the Gibbs free energy decreases, and equilibrium is reached when ΔG=0.

## Importance of state functions

State functions allow the thermodynamic state of a system to be fully described. Since they are not process-dependent, they provide a powerful tool for analyzing changes in complex systems without having to study every intermediate step.

These functions are also essential in analyzing the efficiency of thermal machines, such as motors and refrigerators.

For example, in a Carnot cycle, which is an ideal thermodynamic cycle that represents the maximum efficiency limit for a heat engine, state functions allow the theoretical efficiency of the cycle to be determined by calculating changes in internal energy, entropy, and other properties.

In engineering, state functions such as enthalpy and Gibbs free energy are fundamental to the design of energy exchange processes, such as in power plants and refrigeration systems, as well as to the analysis of chemical reactions in terms of heat released or absorbed.

## Relationships between state functions

State functions are not independent of each other, and there are numerous relationships between them. For example, from the fundamental equations of thermodynamics, one can obtain auxiliary equations such as Maxwell's equations, which are a set of relationships that connect variables such as entropy, temperature, volume and pressure.

Furthermore, knowledge of one state function can lead to information about others. For example, knowing the Gibbs free energy of a system, it is possible to deduce entropy, heat exchange, and other aspects related to the spontaneity of processes.

These interrelationships make state functions key tools for solving complex thermodynamic problems.