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FREE AND RELATED ENERGY

Physics. Research in physics.

Doctor of technical sciences, prof., Etkin VA

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The need to distinguish the quantitative and qualitative characteristics of energy from the second law of thermodynamics was reflected in the division of energy adopted in thermodynamics into a free and bound energy (suitably suitable and unfit for performing external work under certain conditions). Such a division became possible after R. Clausius introduced the concept of entropy S, which is fundamental for thermodynamics. In accordance with its meaning, Helmholtz called the product of the absolute temperature T and entropy S "bound energy," and the remainder F = U-TS - "free energy" . Following this, J. Gibbs introduced the concept of "free enthalpy" G as the difference between the enthalpy of the system H = U + pV and the associated energy TS. It is easy to show that under conditions of constant temperature T and volume V of the system, the decrease in the Helmholtz free energy determines the maximum mechanical work (expansion work) that the system can perform under reversible character of the processes. Indeed, denoting the elementary work of the expansion by dWp and expressing the heat of the reversible process dQ in a known way through the absolute temperature T and entropy , After applying the Legendre transformation TdS = d (TS) - SdT on the basis of (2), we have for T, V = const:

Similarly, denoting by Non-mechanical operation, and applying the transformation pdV = d (pV) - Vdp, we find from (2) under the conditions T, p = const:

Therefore, the free energy of Helmholtz and Gibbs is called, respectively, isochoric-isothermal and isobaric-isothermal potential, respectively. However, the concept of "free energy" (Helmholtz and Gibbs) does not characterize the "stock" of transformable energy in the system, since Are not only due to the energy of the system itself, but also due to the energy of the environment in the process of heat exchange with it. Moreover, the associated energy TS, strictly speaking, can not be considered a part of the internal energy U or the enthalpy H, since in most cases TS is larger than themselves in most cases [5]. It should also be noted that the transfer of free energy into a bound energy does not completely describe the dissipative processes in the system. Thus, in the processes of mechanical processing of metals, the heat output coefficient (the ratio of the released heat to the work of destruction) often turns out to be less than unity, which indicates the transition of part of the energy to nonthermal forms. Finally, in open systems (exchanging matter with the environment) work Is not at all determined by the decrease of any thermodynamic potential of the system. The reason for this is not difficult to understand by considering the combined equation of the first and second principles for open systems in the form of a generalized Gibbs relation:

Where Is the mass of the kth substance and its chemical potential. If we include the work in the right-hand side of (5) And apply the transformation From (5) we find:

From the definition of the chemical potential
And the Gibbs-Duhem relation Equality of non-mechanical work follows Zero. Thus, in many cases the energy is divided into free and bound and loses its heuristic value.

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Author: Doctor of technical sciences, prof., Etkin VA
PS The material is protected.
Date of publication on August 15, 2004