THE INSTANTANEOUS VALUES OF MAIN THERMODYNAMIC PARAMETERS AND POTENTIALS THAT ARE CHARACTERISTIC TO GIBBS THERMODYNAMIC MICROSTATES

The equations that combine the instantaneous values of main thermodynamic parameters and potentials (that are characteristic to Gibbs thermodynamic microstates) of the simplest gases and liquids were found. The maximum possible (limit) velocity of matter transfer and the four wave functions and derivatives from them, which can take with certain probability any arbitrary instantaneous values, are used as thermodynamic hidden parameters and variables in these equations. Such gases and liquids can gradually (evolutionally) quasi-equilibrium cool down with self-creation of stable gravitational fields due to electromagnetic interactions of their molecules. In those fields the local values of characteristic intensive parameter are saved in time and corresponding to it characteristic extensive parameter is the same in the whole space at the same time. The electro-magnetic nature of gravitational field in matter was justified. It was proved that hypothetical ideal matter (ideal gas, ideal liquid) in principal cannot self-create gravitational field due to the absence of electromagnetic interaction of its molecules. The dependencies of physical and other thermodynamic characteristics of matter on the hidden parameters and variables were examined.

Introduction

Internal energy U of real gases and liquids depends on many pairs of their intensive () and extensive () thermodynamic parameters. However, it can also be shown as a sum of internal energy of hypothetic ideal gas (liquid)  and output of multiplication of resulting intensive () and extensive () thermodynamic parameters: ,           ,

where: , , . For gases: ,  is virial coefficients that depend on both temperature and individual gas properties [1], while  is universal gas constant and  is spatial thermodynamic parameter of matter, that does not vary in space at conditions of quasi-equilibrium cooling down of matter (is the same on any radial distance r from the gravitational attraction center in the comoving to it frame of reference of spatial coordinates and time t). And exactly this invariability in space of  is responsible for the fact that properties of quasi-equilibrium cooling down real gases are close to properties of hypothetic ideal gas.

“Ideal” component  of internal energy is de facto identical to Helmholtz free energy , while “ideal” component  of enthalpy is identical to the Gibbs free energy G:

, , ,

This, of course, is caused by the absence of binding energy () in ideal gas and ideal liquid due to the absence of electromagnetic interaction of their molecules and atoms. Self-organization of hierarchically more complicated interactions and interconnections in matter is in the tendency of  Helmholtz and  Gibbs free energies to their minimum.  Lower  layers  of  matter, loaded by its upper layers form the extended system. The energy of such extended system [1] that consists of the whole RGTD-bonded matter is indeed equivalent to enthalpy. Moreover, as it is shown further, parameter  (in contrast to  parameter) takes the same value in the whole space filled by quasi-equilibrium cooling down homogeneous matter (. And, therefore, Gibbs energy “behaves” as it is expected: it only changes in space along the radial coordinate r together with the gravitational potential. And when Gibbs energy changes in time together with the gravitational potential, it “behaves” like multiplicative component of enthalpy (like the energy of extended system).

All thermodynamic parameters and characteristics of matter are its internal properties and, in contrast to its mechanic characteristics, can be determined only in its intrinsic time. Gravity and velocity of matter motion have an influence only on the flow of intrinsic time of matter and, thus, on the formation of correspondent to it space-time continuum (STC). Their effect on the matter is purely gauge and, therefore, only leads to the formation of spatially inhomogeneous thermodynamic states of matter and to the emergence of correspondent to them thermodynamic processes.

Mutual dependencies of instantaneous values of main thermodynamic parameters and potentials of matter

Thermodynamic processes in matter confront the intranuclear evolutionary and gravitational processes in it. While in mechanics the main role is played by the inert free energy  (equivalent to inertial mass ), in thermodynamics the main role is given to the total internal energy  of matter. Therefore, frequency of intranuclear interaction  corresponds to inversely proportional to it frequency of electromagnetic interaction of its molecules in the comoving FR:  (). This frequency is changing together with the change of velocity of light  in matter (that corresponds to radiation refractive index  at the wavelength of maximum of energy of thermal radiation) and with the change of internal scale factor  of matter [2-4]. Here: ; ;  and  are the constants of cooled down to the limit (, ) and quasi-equilibrium cooling down (, ) matter, which is not identical for different matters and for their various phase or aggregate states and not dependent both on strength of gravitational field and on matter thermodynamic parameters;  and  are maximum possible (limit) velocities of matter in any point on the phase boundary of the same matter and on the boundary of different matters correspondingly;  and  are the limit velocity of quasi-equilibrium cooling down matter in the comoving with it the non-rigid FR (so not in the metric STC, but in the inseparable from matter its own physical STC, in which the radial motion of molecules of matter, which cooling down is absent and the time is counted by the clocks coming with them);  and  are the expected Lorentz shrinkage of dimensions of matter (that moves in the process of quasi-equilibrium cooling down) in arbitrary point and on the phase boundary of the same matter or with another matter respectively;  is minimal possible distance of electromagnetic interaction between molecules of certain matter or its critical value; c is constant of the velocity of light.

In contrast to used in cosmology spatially inhomogeneous external scaling factor , which is the cause of the curvature of matter intrinsic space, internal scaling factor  takes nonsimilar values for different matters and depends on thermodynamic state of matter. This factor characterizes the distinction between average statistic value of interaction distance  in the atoms of concrete  matter  and  the  value  of  this distance    that corresponds to  critical  equilibrium values of internal energy multiplicative component , Gibbs free energy , temperature , pressure . And if parameter  characterizes the difference of real velocity of electromagnetic interaction propagation in matter from the constant of velocity of light с, then  is responsible for compensation of the influence of increase of propagation velocity of electromagnetic wave on the frequency of electromagnetic interaction  of matter microobjects. If for gases and simplest liquids the dependencies of instantaneous values of their thermodynamic parameters and potentials on  and  allow to separate these variables, then instantaneous value of their Gibbs free energy (that corresponds to their instantaneous thermodynamic microstates) can be expressed via these two parameters and via their function  in the following way:

Methods of thermodynamics allow us to analyze equilibrium states of matter even when there is no analytic dependence of thermal energy of matter on its thermodynamic parameters. With the purpose of revealing of some features let us examine analytic representation of such dependency for gases and simple liquids. According to it the instantaneous values of main thermodynamic parameters and potentials can be represented in the following way:

,

where: ,  ,  ,   are multiplicatively dependent on  and  components of instantaneous values of internal energy, enthalpy, Gibbs free energy and Helmholtz free energy of instantaneous Gibbs microstate of matter correspondingly;

 is instantaneous value of realized via negative feedback partial additive compensation of multiplicative representation of thermodynamic potentials of microstate of matter (a multiplicative decrease in its free energies over time); , ; ,

, ,  are normalized values of thermodynamic parameters (entropy, temperature, molar volume and pressure) of Gibbs microstates of matter;

, , ,

, while: n is the hidden variable that is the indicator of the magnitudes of instantaneous microfluctuations of values of pressure and molar volume when  and during not absolutely rigid retention of occupied by gas constant volume;

k, , m are the hidden variables that are indicators of the influence of parameters  and  on the parameters of thermodynamic microstates of latently coherent matter.

Variables k, , m and n characterize instantaneous collective microstates of the whole gravithermodynamically bonded matter and similarly to the wave functions of quantum mechanics can take with certain probability any arbitrary instantaneous values. The probability that Gibbs microstate of matter have instantaneous energy, the corresponding certain composition of values of these variables, obviously, is represented by canonic Gibbs distribution. The concrete mathematical expectations , , ,  of those variables (that depend on the parameter ) correspond to parameters of a thermodynamic macrostate of matter.

Normalized values of thermodynamic parameters of instantaneous microstates of matter are mutually related via the following dependencies:

,

As it was expected, all instantaneous thermodynamic potentials reach their minimum independently both on the values of variables k, ,  m,  n  and on  the value of spatial gas-related parameter : , , , . And, moreover, the change in space of available thermodynamic parameters of cooling down matter is inevitably accompanied by the change of its hidden thermodynamic parameters  and :

, ,

where:  is the increment of metric radial distance.

And the bigger the distance from matter to the gravitational attraction center the smaller is its internal energy. That is why in contrast to inert free energy (which is the greater the greater the distance from the substance to the gravitational attraction center) the thermal energy behaves like a negative mass. And this is confirmed by numerous investigations of the influence of heating of matter on its weight [5-6].

Precisely the condition of spatial homogeneity of hierarchic complexity of RGTD-bonded matter  determines the spatial distribution of the set of main thermodynamic parameters of this quasi-equilibrium cooling down matter. Since parameter:

expressed not only via constants (including also  which characterizes the quasi-equilibrium of the process of cooling down of matter throughout the whole time), but also via velocity of the light in matter , limit velocity of motion  and Lorentz shrinkage of dimensions of the matter that moves in the process of quasi-equilibriumly cooling down  (), then only via them we can in temporal form (via ) or in spatial form (via ) express instantaneous values of all main thermodynamic parameters and potentials of RGTD-bonded matter:

where: , , , ;  is the limit velocity of quasi-equilibrium cooling down matter in comoving with it FR (in its own space-time continuum (STC), in which the radial motion of molecules of cooling down matter is absent);  is instantaneous value of partial additive compensation of multiplicative representation of thermodynamic potentials of matter microstate (multiplicative increase of bound energy as we approach the gravitational attraction center);  is the instantaneous value of Gibbs energy G (that is similar to the Lagrangian, since it constantly tends to its minimum too). As we can see, due to  when homogeneous matter is quasi-equilibrium cooling down the gravitational changes in time of its Gibbs free energy and Helmholtz free energy take place similarly to the changes in space of multiplicative component of internal energy  and enthalpy  correspondingly. Precisely, if when :

,

then:    ,

where:  is the increment of metric time of cooling down matter in a comoving with it FR.

In the process of free fall of matter in gravitational field the Helmholtz and Gibbs thermodynamic free energies, as well as the Hamiltonian of inert free energy of matter, are conserved not only due to the presence of weightlessness in its FR (), but also due to the total compensation of the influence of gravitation on its thermodynamic state by the motion.  However it is possible only in hypothetical absolutely empty space.  But when  there is a resistance to motion these energies will be gradually increasing due to the matter cannot reach the required for their conservation value  and thus also due to accommodation of the matter of falling body to the new thermodynamic state of matter of the environment.

Before the appearance of spatial inhomogeneity of limit velocity of matter  the only thing that could interfere its distancing from the future gravitational attraction center (due to tending of its Gibbs thermodynamic energy to its minimum) was the electromagnetic interaction of its molecules. That is why the hypothetic ideal gas and ideal liquid in principle cannot create their gravitational field. As we see, here we have a dependency of spatial distribution of intrinsic values of these thermodynamic parameters and potentials (not the dependency of spatial distribution of other their values observed by other clocks and by other length standards) on  (and, so, also on  and ). It would be non-logical if  and  would not influence on spatial distribution of the set of intrinsic values of main thermodynamic parameters of matter. So this does not contradict to invariance of thermodynamic parameters and potentials of matter relatively to the space-time transformations [Danylchenko, 2008: 19]. On the contrary, it only confirms the fact that limit velocity of matter motion , as well as , is the internal hidden RGTD-parameter of matter and not the non-dependent on certain RGTD-state of matter external gravitational parameter.

Conclusion

The gravitational reduction of molar volume of matter when approaching the gravitational attraction center is unobservable directly in intrinsic FRs of matter. However, we still can say about its presence in Euclidean space of CFREU due to the presence of gravitational curvature of intrinsic space of matter. And we also can indirectly say about the presence of evolutionary self-contraction of matter due to the presence of the process of Universe expansion in FR of people’s world. In the equations, which combine the instantaneous values of main thermodynamic parameters and potentials (that are characteristic to Gibbs thermodynamic microstates), the maximum possible (limit) velocity of matter transfer and Lorentz shrinkage of dimensions of matter as well as four wave functions and derivatives from them, which can take with certain probability any arbitrary instantaneous values, can be used as thermodynamic hidden parameters and variables.

Gases and liquids can gradually (evolutionally) quasi-equilibrium cool down with the self-creation of stable gravitational fields due to electromagnetic interaction of their molecules. In these fields all values of extensive parameter  is the same in the whole space at the same tіme and correspondent to it intensive parameter  is conserved in time.

References

1. Bazarov, I.P.: 1964, Thermodynamics. New York: Pergamon Press, [distributed in the Western Hemisphere by Macmillan, New York] (1964).

2. Danylchenko, Pavlo: 2008, United nature of gravitational and thermodynamic properties of matter. Introduction to Relativistic Gravithermodynamics. Vinnytsia: Nova knyga, 19-59. (in Russian) https://elibrary.com.ua/m/articles//download/11187/3431.

3. Danylchenko, Pavlo: 2008a, United nature of gravitational and thermodynamic properties of matter. Abstracts of the RUSGRAV-13, June 23 – 28. Moscow: PFUR, 109 (in Russian).

4. Danylchenko, Pavlo: 2020, Foundations of Relativistic Gravithermodynamics. Foundations and consequences of Relativistic Gravithermodynamics (in Ukrainian), Vinnytsia: Nova knyga, 5-84; https://elibrary.com.ua/m/articles//download/11192/3626.

5. Einstein, Albert, Leopold Infeld: 1938, Is heat a substance? The Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta. London.

6. Chen, Y.T., Alan Cook: 1993, Gravitational Experiments in the Laboratory. Cambridge Univ. Press, (1993); https://doi.org/10.1017/CBO9780511563966 (2009).

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