 # Helmholtz Free Energy

In thermodynamics, the Helmholtz free energy refers to a thermodynamic potential that facilitates the measurement of the useful work that is obtainable from a closed thermodynamic system at a constant volume and temperature. Hermann von Helmholtz, a German physicist, first developed and presented the concept of free energy in 1882 in a lecture called “On the thermodynamics of chemical processes”. From the German word Arbeit (work), the recommendation of the International Union of Pure and Applied Chemistry (IUPAC) is to use the symbol A and the name Helmholtz energy.

## Introduction to Helmholtz Free Energy

Helmholtz free energy, simply speaking, is a thermodynamics concept. In this energy, the thermodynamic potential facilitates the measurement of the work of a closed system with constant temperature and volume.

The change’s negative in the Helmholtz energy during a process turns out to be equal to the maximum amount of work whose performance can take place by the system in a thermodynamic process in which the quantity of volume is held constant. Furthermore, if the volume were not held constant, the performance of part of this work would take place as boundary work. This makes the Helmholtz energy useful for systems held at constant volume because if the volume were not held constant, the part performance of this work would take place as boundary work.

### Differences Present Between Gibbs Free Energy and Helmholtz Free Energy

1)Experts define Helmholtz free energy as the useful work that is obtainable from a particular system. In contrast, Gibbs free energy is the maximum reversible work that is possible to obtain from a particular system.

2)Helmholtz energy is the energy needed to produce a system at constant volume and temperature. In contrast, Gibbs free energy is the energy needed to produce a system at constant temperature and pressure.

3)Helmholtz energy has a lesser application as the requirement of the volume of the system is that it must be constant. In contrast, Gibbs free energy finds more application as the system’s pressure is constant.

### Application of Helmholtz Free Energy

1)In equation of state

The representation of the pure fluids with high accuracy (like industrial refrigerants) takes place by using Helmholtz function as a sum of ideal gas and residual terms.

2)In auto-encoder:

Auto-encoder is an artificial neural network that experts make use of to encode efficient data. Moreover, the experts here use Helmholtz energy to determine the sum of code cost and reconstructed code.

### Formula of Helmholtz Free Energy

There are four quantities that experts call as “thermodynamic potentials”. Also, these quantities play an essential role in the chemical thermodynamics of reactions and non-cyclic processes. Furthermore, they are Gibbs free energy, internal energy, enthalpy and Helmholtz free energy.

Experts can define Helmholtz energy in the form of the following Helmholtz free energy formula:

F = U – TS

Where,

• F is the Helmholtz free energy in Joules
• U is the system’s internal energy in Joules
• T represents, in Kelvin, the absolute temperature of the surroundings
• S represents the entropy of the system in joules per Kelvin

Formula development for laws of thermodynamics:

• dU = δQ + δWwhich is from the first law of thermodynamics for a closed system
• also, dU = TdS − pdV(𝜹Q = TdS and 𝜹W = pdV)
• so, dU = d(TS) – SdT − pdV(product rule ie; d(TS) = TdS + SdT)
• d(U − TS) = −SdT − pdVdF = −SdT − pdV (from F=U – TS)

## FAQs For Helmholtz Free Energy

Question 1: Explain the Helmholtz Free Energy?

Answer 1: Helmholtz free energy refers to a thermodynamic potential that facilitates the measurement of the useful work that is obtainable from a closed thermodynamic system at a constant volume and temperature. Furthermore, Helmholtz free energy plays an essential role in the chemical thermodynamics of reactions and non-cyclic processes

Question 2: Give one difference between Helmholtz free energy and Gibbs free energy?

Answer 2:  Helmholtz free energy is the energy whose requirement is to produce a system at constant volume and temperature. In contrast, Gibbs free energy is the energy for which the requirement is to produce a system at constant temperature and pressure.

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