Helmholtz free Energy

The Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential in thermodynamics that estimates the useful work produced by a closed thermodynamic system at a fixed temperature (isothermal). The maximum work a system can perform in thermodynamics with constant temp. is equivalent to the change in Helmholtz energy during such a process. 

The Gibbs’ free energy is the amount of energy available in a thermodynamically closed system at constant pressure and temperature to conduct non-PV work.

At constant volume and temperature, the Helmholtz free energy is the maximum amount of “useful” (non-PV) work that can be extracted from a thermodynamically closed system.

The derivations that prove these definitions at the undergraduate level are listed below f.

When it is convenient for applications that occur at constant pressure, the Gibbs free energy or free enthalpy is most usually used as a measure of thermodynamic potential (particularly in chemistry). Helmholtz free energy is frequently employed in explosives research, for example, because explosive reactions by their very nature cause pressure changes.

We know from classical mechanics that the work done by a mechanical system equals a reduction in its mechanical energy, E. If dW denotes completed work, then

dW=-dE          (1).

It’s fascinating to look into the outcome of a thermodynamic system’s work. We’ll use a reversible, isothermal approach to figure out the solution. We know that the first law of thermodynamics can provide a wealth of information about thermodynamic processes. As a result, we begin with this law:

dQ=dU+dW              ..(2).

The heat absorbed by the system is denoted by dQ.

All additional thermodynamic parameters of a pure substance can be determined using the Helmholtz free energy function (along with its partial derivatives). See, for example, the IAPWS’s equations of state for water in their IAPWS-95 document.

In thermodynamics, free energy is an energy-like feature or state function of a system that is in thermodynamic equilibrium. Free energy has energy dimensions, and its value is decided by the current state of the system rather than its past. The amount of free energy in a system determines how it changes and how much work it can perform. The Helmholtz free energy F, also known as the work function and the Gibbs free energy G are two other ways to represent it. If U is a system’s internal energy, PV is its pressure-volume product and TS is its temperature-entropy product (T being the temperature above absolute zero), then F = U TS and G = U + PV TS are the equations to use.

Why do we use it?

Although Gibbs free energy is widely employed to calculate thermodynamic potential in chemistry, it is problematic for applications that do not occur at constant pressure. When dealing with explosives, for example. Because explosive reactions, by their very nature, cause pressure changes, Helmholtz free energy is employed there. It’s also used to express pure substance equations.

Helmholtz Free Energy Equation

F = U – TS

Where

U = Internal energy

T = Temperature

S = Entropy

The linear partial differential equation titled after Hermann von Helmholtz is known as the Helmholtz Equation. The Helmholtz equation is an eigenvalue problem that can only be calculated in coordinate systems with isolating variables.

This equation is useful in optics because it gives solutions that describe the propagation of electromagnetic waves (light) as paraboloidal waves or Gaussian beams.

The Helmholtz principle, in its more powerful version, argues that wherever there is a considerable divergence from randomness, a structure is observed. “We quickly perceive whatever could not happen by random,” it claims as a common-sense assertion.

Helmholtz Equation Applications

The Helmholtz equation has a few applications:

Seismology is the scientific study of earthquakes and the elastic waves that they produce. Tsunamis caused by environmental factors and volcanic eruptions caused by seismic sources are two of the study areas of seismology.

Seismic waves can be classified into three categories.

P-waves, which are fundamental waves, in the body

Secondary or shear waves are S-waves.

Normal waves and surface waves

The Helmholtz equation is derived from the wave equation in three dimensions in specific conditions. When we try to find a solution that separates the space and time variables, we get a classic Helmholtz form for the spatial part. This form can be solved using ordinary approaches. 

Electrostatics: The Laplace equation is a specific case of this equation’s electrostatics. The Laplace equation is the equation in which the right-hand side of the equation equals zero. Try modelling the electric field in a place with a net zero charge, for example. Physicists use actual boundary conditions to solve the equation by isolating variables during the procedure.

CONCLUSION

The Helmholtz equation is a useful equation that can be found in a variety of physics domains. Its solutions can be used in a variety of fields. It is a highly important tool in the study of waves. On a higher level, the underlying commonality in the answers aids our understanding of nature’s symmetry.