Helmholtz and Gibbs energies

Conditions for equilibrium and the definition of Helmholtz and Gibbs energies 

If the heat is transferred at constant volume and no non-expansion work is done, 

The combination of the Clausius inequality (eq. 1.30) and the first law of thermodynamics for a system at constant volume thus gives 

Correspondingly, when heat is transferred at constant pressure (pV work only), 

For convenience, two new thermodynamic functions are defined, the Helmholtz (A) and Gibbs (G) energies  

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The Helmholtz and Gibbs energies on the other hand involve constant temperature and volume and constant temperature and pressure, respectively. Most experiments are done at constant Tandp, and most simulations at constant Tand V. Thus, we have now defined two functions of great practical use. In a spontaneous process at constant p and T or constant p and V, the Gibbs or Helmholtz energies, respectively, of the system decrease. These are, however, only other measures of the second law and imply that the total entropy of the system and the surroundings increases. 

The Helmholtz and Gibbs energies are useful also in that they define the maximum work and the maximum non-expansion work a system can do, respectively. The combination of the Clausius inequality 7dS > dq and the first law of thermodynamics dU = dq + dw gives... 

In this discussion of indifferent states we have always used the entropy, energy, and volume as the possible extensive variables that must be used, in addition to the mole numbers of the components, to define the state of the system. The enthalpy or the Helmholtz energy may also be used to define the state of the system, but the Gibbs energy cannot. Each of the systems that we have considered has been a closed system in which it was possible to transfer matter between the phases at constant temperature and pressure. The differentials of the enthalpy and the Helmholtz and Gibbs energies under these conditions are... 

The differentials of the Helmholtz and Gibbs energies could be written in the usual manner. However, it is convenient to use the functions (A — EP) and (G — EP) in order to change the independent variable from P to E. When this is done we obtain... 

Helmholtz and Gibbs energies are almost indistinguishable). Upon charging, or rather charge-separation, a potential difference is created. The electrical work of withdrawing protons against this potential is... 

We use the terms Helmholtz and Gibbs energies for what has previously been referred to as Helmholtz and Gibbs free energies, respectively. 

Nitrogen is to be isothermally compressed at O C from I bar to 100 bar. Compute the work required for this compre.ssion the change in internal energy, enthalpy Helmholtz and Gibbs energies of the gas and the heat that must be removed to keep the gas at constant temperature if... 

In Chapter 4 the Helmholtz and Gibbs energies of pure components were introduced by the relations... 

These definitions are also valid for mixtures, provided the values of U, H, and 5-used are those for the mixture. That is. the Helmholtz and Gibbs energies of a mixture bear the same relation to the mixture internal energy, enthalpy, and entropy as the pure component Gibbs energies do to the pure component internal energy, enthalpy, and entropy. 

The Helmholtz and Gibbs energies are both extensive, conceptual state functions having dimensions of energy. Unfortunately, only in special cases do the changes AA and AG have physical interpretations. 

Helmholtz and Gibbs energy are derived according to their definition... 

The Helmholtz and Gibbs energies are often referred to as free energies. Both are defined using the entropy, S. In Chapter 1, we developed a molecular level definition of the absolute entropy. From that definition, it should be clear that entropy is a thermod3mamic state function, too. Therefore, A and G are state functions. 

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