Why are only five out of eight possible thermodynamic potentials important?

In summary, the conversation discusses the derivation of 8 thermodynamic potentials and the question of why only 5 of them (entropy, Helmholtz free energy, enthalpy, Gibbs free energy, and grand potential) are considered important. The participant mentions that systems with constant entropy or chemical potential are less familiar, but potentials are still defined for them. The conversation also mentions a relevant study on the 8 physical systems of thermodynamics.
  • #1
ati
1
0
Starting from the equation

dE=tdS-PdV+[tex]\mu[/tex] dN

It is straightforward to derive all 8 possible thermodynamic potentials. My question is the following: Why are the only important potentials

Entropy
Helmholtz free energy
Enthalpy
Gibbs free energy
Grand potential ?

Why aren't the other three as relevant as these?

Thanks for your help
-Ati
 
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  • #2
Hi ati, welcome to PF. Systems with constant entropy or constant chemical potential are somewhat less familiar to us than systems with constant temperature or constant particle number. Potentials are still defined and used for the more exotic systems even though they aren't mentioned in most thermodynamics texts. Also, note that one of the potentials (E-TS+PV-[itex]\mu[/itex]N) is identically zero!

You may be interested in reading Graben and Ray's "Eight physical systems of thermodynamics, statistical mechanics, and computer simulations" Molecular Physics 80(5) (1993).
 
Last edited:

1. Why are there only five important thermodynamic potentials?

The five important thermodynamic potentials, also known as state functions, are the internal energy (U), enthalpy (H), Helmholtz free energy (A), Gibbs free energy (G), and the grand potential (Ω). These state functions are important because they describe the thermodynamic state of a system and are the key variables in solving thermodynamic problems. They are derived from the fundamental laws of thermodynamics and are based on the assumptions of a closed system, constant temperature and pressure, and the absence of non-mechanical forces.

2. What are the other three possible thermodynamic potentials?

The other three possible thermodynamic potentials are the internal energy (U), enthalpy (H), and Helmholtz free energy (A). These potentials are not as commonly used as the five important ones because they are only applicable in specific situations. For example, the internal energy (U) is only useful for a system with constant volume, the enthalpy (H) is only useful for a system with constant pressure, and the Helmholtz free energy (A) is only useful for a system with constant temperature.

3. What determines which thermodynamic potentials are important?

The importance of a thermodynamic potential is determined by its usefulness in describing a particular system or process. The five important thermodynamic potentials are applicable to a wide range of systems and processes, making them more versatile and commonly used. The other three potentials are limited in their applicability and are therefore less important.

4. Can a system have more than one important thermodynamic potential?

Yes, a system can have more than one important thermodynamic potential. In fact, in most cases, multiple potentials are used to fully describe a system. For example, the internal energy (U) and the enthalpy (H) are often used together to describe a system with both constant volume and pressure. Additionally, the Gibbs free energy (G) and the grand potential (Ω) are often used together to describe a system with both constant temperature and chemical potential.

5. Why are the grand potential (Ω) and Helmholtz free energy (A) important for open systems?

The grand potential (Ω) and Helmholtz free energy (A) are important for open systems because they take into account the effects of non-mechanical forces, such as surface tension, and the ability to exchange particles with the surroundings. In open systems, the number of particles can change, so these potentials are necessary to accurately describe the system's thermodynamic state. Additionally, the grand potential (Ω) is useful for systems with variable temperature and chemical potential, while the Helmholtz free energy (A) is useful for systems with variable temperature and volume.

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