## Free Energy in Thermodynamics

**Free energy** like Gibbs free energy or thermodynamic potential and Helmholtz’s work function is very helpful in various physical or chemical calculations and studies in thermodynamics. Therefore, the free energy in thermodynamics is an energy term of the system and a state function in a thermodynamic equilibrium reaction. The entropy formula measure the unavailable energy for doing useful work but free energy is the calculation of internal energy or enthalpy change that available for doing useful work.

In learning chemistry, the property measures in two forms in thermodynamics reaction, first are Helmholtz work function (A), and the second is Gibbs free energy (G).

### Definition of Gibbs Free Energy

Gibbs free energy is a thermodynamics property defined as, G = H – TS. Since H and TS are energy terms, G is also energy terms, further specific heat or enthalpy of reaction, temperature, and entropy are all state functions and perfectly differential quantities. Therefore, G also a state function and perfectly differential quantity.

### Work Done by Thermodynamic System

Let us consider a reversible isothermal and isobaric change of the system, ΔG = ΔH – TΔS. But, ΔH = ΔU + PdV, for isobaric process. Therefore, ΔG = ΔU + PdV – TΔS. Again, TΔS = q (heat) = ΔU + w, and the work may be partially mechanical and partially non-mechanical or fully mechanical or fully non-mechanical.

∴ ΔG = ΔU + PΔV – ΔU – w

or, – ΔG = w – PΔV = w_{non-mechanical}

This formula signifies that decreases of G equal to the non-mechanical work done by the system in the reversible isothermal isobaric process in chemistry or physics.

### Calculation of Gibbs Free Energy Change

We have by the definition of Gibbs free energy, G = H – TS = U + PV – TS. For a small change of the thermodynamic system, dG = dU + PdV + VdP – TdS – SdT. But TdS = q = dU + PdV, when the work is mechanical work only. Therefore, dG = VdP – SdT. This is another basic thermodynamic chemical equation. Two cases of this equation may be considered when the process is reversible isothermal free energy change, dG = VdP because of the heat change in the isothermal process zero. But for reversible isobaric process, dP = 0, and dG = – SdT.

### Definition of Helmholtz Free Energy

Helmholtz free energy is a thermodynamic property defined as, A = U – TS, where U = internal energy and TS also an energy terms. Therefore A is also an energy term. Further internal energy, temperature, and entropy are all state functions and perfectly differential quantities. Therefore, A also a state function and perfectly differential quantity.

### How to Measure of Work Function?

Let us consider an isothermal reversible change of the system, the work function, ΔA = ΔU – TΔS. Where TΔS = q = ΔU + w_{max}. Because of reversible isothermal process yields maximum work. Therefore, ΔA = ΔU – (ΔU + w_{max}) or, – ΔA = w_{max}. This formula signifies that decreases of work function equal to the maximum work done by the system. Therefore, the work function measures the thermodynamic property of the system that decreases to give the maximum amount of work available during an isothermal transformation of the system. This work may be purely or partially mechanical work.

- If the system isothermal reversible, its value will be equated with w
_{max}. - If the same change is not isothermal and reversible, then A will decreases to the same extent as the system works but – ΔA ≠ w
_{max}. - When the process is irreversible, there will be some drop of A but it will exceed the output work.

### Change of Helmholtz Work Function

We have from the definition of Helmholtz wor function formula, A = U – TS. For a small change of the system, dA = dU – TdS – SdT. But TdS = q (heat) = dU + PdV, when the work is mechanical work only. Therefore, dA = – PdV – SdT. This is the basic thermodynamic equation. Two cases of this free energy equation may be considered, for the reversible isothermal process, and dA = – PdV and for the reversible isochoric system, dA = – SdT.

### Standard free energy of Formation

The standard free energy of formation is defined as the energy change that occurs when one mole of a molecule from its chemical elements in the standard state. The formation of the water molecule process spontaneously. But if we mixing hydrogen and oxygen at 25°C. The hydrogen and oxygen molecule does not react appreciably due to the extremely slow rate of reaction, which is no concern of thermodynamics. If the reaction rate is accelerated by a chemical catalyst or electric spark, the equilibrium is established easily and we can calculate the thermodynamics standard free energy.