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Everything about Thermodynamic Potential totally explained

A thermodynamic potential is a scalar potential function used to represent the thermodynamic state of a system. One main thermodynamic potential which has a physical interpretation is the internal energy, U. It is the energy of configuration of a given system of conservative forces (that is why it's a potential) and only has meaning with respect to a defined set of references (or datums). Expressions for all other thermodynamic energy potentials are derivable via Legendre transforms from an expression for U. In thermodynamics, certain forces, such as gravity, are typically disregarded when formulating expressions for potentials. For example, while all the working fluid in a steam engine may have higher energy due to gravity while sitting on top of Mt. Everest than it would at the bottom of the Mariana trench, the gravitational potential energy term in the formula for the internal energy would usually be ignored because changes in gravitational potential within the engine during operation would be negligible. Five common thermodynamic energy potentials are:
Name Symbol Formula Natural variables
Internal energy U, T S - p V + sum_i mu_i N_i + cdots ~~~~~S,V,p ,

The Gibbs-Duhem is a relationship among the intensive parameters of the system. It follows that for a simple system with I components, there will be I+1 independent parameters, or degrees of freedom. For example, a simple system with a single component will have two degrees of freedom, and may be specified by only two parameters, such as pressure and volume for example. The law is named after Josiah Willard Gibbs and Pierre Duhem.

Chemical reactions

Changes in these quantities are useful for assessing the degree to which a chemical reaction will proceed. The relevant quantity depends on the reaction conditions, as shown in the following table. Δ denotes the change in the potential and at equilibrium the change will be zero.
Constant V Constant p
Constant S ΔU ΔH
Constant T ΔF ΔG
Most commonly one considers reactions at constant p and T, so the Gibbs free energy is the most useful potential in studies of chemical reactions.

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