Gibbs Free Energy and the Grand Potential

In summary, Gibbs Free Energy is the appropriate potential for systems with both heat exchange and mechanical work, while the grand potential is suitable for systems with heat exchange and chemical work. However, defining a potential of the form (E-TS-μN+PV) that is conserved in some ensemble may lead to issues as it results in G=μN and g=-PV. This potential must depend on at least one extensive variable in order to specify the amount of substance in the system.
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Gibbs Free Energy is the appropriate potential when there is both heat exchange and mechanical work (G=E-TS+PV). On the other hand the grand potential is appropriate when there is heat exchange and chemical work (g=E-TS-μN).
Is there any issue in defining a potential of the form (E-TS-μN+PV) such that it is conserved in some ensemble? If there is no problem, is there a consensus on a name for such potential and its corresponding ensemble?
 
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The problem is probably that the corresponding potential vanishes identically as G=mu N and g=-PV. You need the potential to depend on at least one extensive variable. If not, you can no longer specify the amount of substance you are talking about.
 

1. What is Gibbs Free Energy and why is it important in thermodynamics?

Gibbs Free Energy, also known as the Gibbs Function, is a thermodynamic quantity that measures the amount of energy available in a chemical or physical system to do useful work at a constant temperature and pressure. It takes into account both the enthalpy (heat content) and entropy (measure of disorder) of the system. It is important because it helps determine the spontaneity and equilibrium of a reaction or process, as well as the maximum amount of work that can be extracted from a system.

2. How is Gibbs Free Energy related to the concept of chemical potential?

Chemical potential is a measure of the potential energy of a molecule in a system. It is directly related to Gibbs Free Energy through the equation: ΔG = -RT ln(K), where R is the gas constant, T is the temperature, and K is the equilibrium constant. This equation shows that the change in Gibbs Free Energy is directly proportional to the change in chemical potential, and therefore, can be used to predict the direction and spontaneity of a reaction.

3. What is the difference between Gibbs Free Energy and the Grand Potential?

Gibbs Free Energy is a measure of the energy available to do work in a system at constant pressure and temperature, while the Grand Potential is a measure of the energy available to do work in a system at constant pressure, temperature, and particle number. In other words, the Grand Potential takes into account the effects of both chemical reactions and phase transitions (changes in particle number) in a system, while Gibbs Free Energy does not.

4. How is the Grand Potential used in studying phase transitions?

The Grand Potential is used in studying phase transitions because it takes into account the effects of changes in particle number in a system, which is crucial in understanding phase transitions. By calculating the Grand Potential, scientists can determine the conditions under which a phase transition will occur, such as the critical temperature and pressure.

5. Can Gibbs Free Energy and the Grand Potential be used for non-equilibrium systems?

No, Gibbs Free Energy and the Grand Potential are only applicable to systems in equilibrium. This is because both quantities are based on the assumption that a system is at a constant temperature, pressure, and particle number, which is not true for non-equilibrium systems. For non-equilibrium systems, other thermodynamic quantities such as entropy production and chemical affinity must be used to analyze the system.

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