Why there are two free energies? What does Helmholtz energy signify?

Summary

Are exergy and free energies the same? Yes, free energy is exergy as a concept. The difference is exergy is total available energy while Gibbs free energy is energy available in the isothermal and isobaric systems. So, the two are not the same

In simple words both Gibbs (G).and Helmholtz's ( A) free energies measure the thermodynamic potential of a system at a constant temperature. That is they measure the potential energy of a system with kinetic energy being constant at a constant temperature

Both calculate the available residual energy in a system to do work after enthalpy (H).and entropy (S) interactions.

G = H - TS applies at constant pressure

A = U - TS applies at constant volume with PV being zero ( U is internal energy)

G = A + PV

AT constant V when PV =0

Gibbs free energy = Helmholtz free energy

You don't need as much energy at constant volume to meet entropy creation at constant volume.

The Helmholtz free energy becomes a measure of the sum of energy you have to put in to generate a system once the spontaneous energy transfer of the system from the environment is taken into account.

The Gibbs free energy change?dG= dH - TdS is the?maximum?amount of non-expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but no matter) at fixed temperature and pressure. This maximum can be attained only in a completely?reversible process.

The?Gibbs free energy is most commonly used as a measure of thermodynamic potential (especially in?chemistry ) when it is convenient for applications that occur at constant?pressure.

Eventually, these two free energies would connect you to

Cp.- Cv = R.

?Detail

The crux is here.

The internal energy (U) can be said to be the amount of energy required to create a system in the non-existent changes of temperature (T) or volume (V). However, if the system is created in an environment of temperature, T, then some of the energy can be captured by spontaneous heat transfer between the environment and system. The amount of this spontaneous energy transfer is TΔS where S is the final entropy of the system. In that case, you don't have to put in as much energy. Note that if a more disordered, resulting in higher entropy, the final state is created, where less work is required to create the system. The Helmholtz free energy becomes a measure of the sum of energy you have to put in to generate a system once the spontaneous energy transfer of the system from the environment is taken into account.

What is free energy?

Free energy is a thermodynamic state function, like the internal energy, enthalpy, and entropy. Free energy is a composite function that balances the influence of energy vs. entropy. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at a constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden.

Two free energies

Gibbs Energy and Helmholtz Energy

The main difference between Gibbs Energy and Helmholtz Energy

If a system is isothermal and closed, with constant pressure, it is describable by the Gibbs Energy, known also by a plethora of nicknames such as "free energy", "Gibbs free energy", "Gibbs function", and "free enthalpy".

If a system is isothermal and closed, with constant volume, it is describable by the Helmholtz Energy.

The IUPAC (the International Union of Pure and Applied Chemistry) officially refers to the two as Gibbs Energy and Helmholtz Energy, respectively.

Gibbs Energy

The Gibbs Energy is named after a Josiah William Gibbs.

This energy can be said to be the greatest amount of work (other than expansion work) a system can do on its surroundings, when it operates at a constant pressure and temperature.

First, a modelling of the Gibbs Energy by way of equation:

G = U + PV – TS

Where:

U = Internal Energy

TS = absolute temperature x final entropy

PV = pressure x volume

Of course, we know that U+PV can also be defined as: H = U + PV

Where:

H is enthalpy

Which leads us to a form of how the Gibbs Energy is related to enthalpy:

G = H?TS

All of the members on the right side of this equation are state functions, so G is a state function as well. The change in G is simply:

ΔG = ΔH ?TΔS

?Helmholtz Free Energy

The?Helmholtz free energy?is supposed as a thermodynamic potential which calculates the “useful” work retrievable from a closed thermodynamic system at a constant temperature and volume. For such a system, the negative of the difference in the Helmholtz energy is equal to the maximum amount of work extractable from a thermodynamic process in which both temperature and volume are kept constant. In these conditions, it is minimized and held constant at equilibrium. The Helmholtz free energy was originally developed by Hermann von Helmotz and is generally denoted by the letter?A, or the letter?F.

constant volume, given by the formula:

ΔA = ΔE– TΔS

A = Helmholtz Free Energy in Joule

E = Energy of the System in Joule

T = Absolute Temperature in Kelvin

S = Entropy in Joule/ Kelvin

Summarily, the Helmholtz free energy is also the measure of an isothermal-isochoric closed system’s ability to do work. If any external field is missing , the Helmholtz free energy formula becomes:

ΔA = ΔU –TΔS

A = Helmholtz Free Energy in Joule

U = Internal Energy in Joule

T = Absolute Temperature in Kelvin

S = Entropy in Joule/Kelvin

The internal energy (U) can be said to be the amount of energy required to create a system in the non-existent changes of temperature (T) or volume (V). However, if the system is created in an environment of temperature, T, then some of the energy can be captured by spontaneous heat transfer between the environment and system. The amount of this spontaneous energy transfer is TΔS where S is the final entropy of the system. In that case, you don't have to put in as much energy. Note that if a more disordered, resulting in higher entropy, the final state is created, where less work is required to create the system. The Helmholtz free energy becomes a measure of the sum of energy you have to put in to generate a system once the spontaneous energy transfer of the system from the environment is taken into account.

Relating Helmholtz Energy to Gibbs Energy

The Helmholtz Energy is given by the equation:

A = U?TS

It is comparable to Gibbs Energy in this way:

G=A+PV

The Helmholtz Energy is used when having a constant pressure is not feasible.

Along with internal energy and enthalpy, the Helmholtz Energy and Gibbs Energy make up the quad group called the?thermodynamic potentials; these potentials are useful for describing various thermodynamic events.

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Credit: Google