The Relation between Thermodynamics and Gravitational Constant ( G )

Although many centuries have elapsed since Newton set forth his gravitational law, physics has been unable so far to create an exact theoretical value for the universal gravitational constant (G). Through a simple thought experience (i.e. it may not be possible to perform it), it can be concluded a mathematical formula which links three different physical sciences with each other: mechanics, electromagnetism and thermodynamics in a simple form, it is possible to find an exact value for the gravitational constant using this form. In fact, the importance of this research is that it also tells us more in-formation about the electromagnetic and gravitomagnetic origin of masses, the negative and positive masses (i.e. matter and dark matter), and the smallest possible distance in the universe, which equals 1.0252 × 10 −56 m.


Introduction
My first paper about the concept of "Precise Ideal Value of the Universal Gravitational Constant G" was introduced in 2017 [1], I have created a new law in physics without mathematical proof, through this law we can obtain a precise ideal value of G, and we find it equivalent to 6.674010551359 × 10 −11 m 3 •kg −1 •s −2 , and a relativistic value of G which equals 6.674365970388 × 10 −11 m 3 •kg −1 •s −2 .
In this paper we will proof our new law of Gravitational Constant through a simple thought experience in which the electromagnetic force is equivalent with the gravitational force, to do this we will introduce a concept close to the electromagnetic mass that is the "radiation mass", which is considered as a dynamical explanation of inertial mass, relativistic and gravitational mass, knowing that there are two types of radiation mass, which are electromagnetic radiation mass m r and gravitomagnetic radiation mass m r '.
Through the discussion, we calculated an exact value for the gravitational constant G", it is possible to compare the value we had got by theoretical means with the documented experimental values in CODATA gravitational tables and we will find that the values are close in both cases as shown in my first paper.
Next, we will look at the relationship between Gravitational Constant G and quantum mechanics, which takes the form, 10 11 1 10 6.674398 10 3 where g e is the electron g-Factor which equals 2.00231930436256.

The Electromagnetic Field Notions
In the case of an orbital electric charge q has been under the influence of the central electric charge field Q as in the classical atomic model [2]. Two harmonic magnetic poles q m and Q m , are generated around each other as if they represent a magnetic atomic model accompanying the electric atomic model as shown in Figure 1. By assuming that 1 , , n ⊥ r r r are orthogonal unit vectors representing right-handed system, the values of orbital and central magnetic pole can be calculated as follows: where q m : The orbital harmonic magnetic pole. Q m : The central magnetic pole.
As a result of this new situation, magnetic forces are generated between these two harmonic poles, in addition to the emergence of new magnetic potential energy among them.
Consequently, the magnitude of these forces and potential energies will work with each other in the system, affecting the movement of the orbital and central charge.

A. K. Abou Layla
Meaning that the classical atomic model actually became two overlapping atomic models that exchange interaction with each other in the system and affect the movement of objects in it according to the following equations:

The Ĝravitomagnetic Field Notions
There is a match in shape between equations of the atomic and the astronomical models [3], the difference is in the constants of these fields, so by letting, we obtain the Ĝravitomagnetic field laws.
For example, we conclude from this there is ĝravitomagnetic forces between two masses according to the following equation: Gravitational and magnetic force equations can be reformulated as follows: where , ε  : are the two energy of masses, 2 2 , , p P : are the two momentum of masses,

Charges as Origin of Mass
For each orbital charge q moving under the influence of central charge Q, acquires an additional quantity of electromagnetic momentum P em [4].
As a result of this new situation, an additional mass is generated that can be known as an electromagnetic radiation mass m r , so it can be concluded that the moving electrical charge is a massless charge q that contains an radiation mass m r that is considered as the nucleus of this charge, as it is clarified in Figure 2.
In short, the moving electric charge q is a mechanically kahromatic charge q k .

The Concept of Electromagnetic Radiation Mass
We can prove that the electromagnetic radiation mass m r is a mass which is equivalent to the potential energy between two electric charges ε e according to the following equation:

Radiation Momentum P r
The electromagnetic momentum equation takes the following form The radiation momentum can be writing on the following form where: P r : radiation momentum equals the magnetic potential momentum P em . m r : The radiation mass. A: The magnetic vector potential. Q m : The central magnetic pole.

The Radiation Force F r
The forces of attraction or repulsion between two radiation masses can be calculated by law of universal gravitation where F r : is the Radiation force, it is attractive if the radiation masses have like-signed (i.e., F is negative) and repulsive if opposite signs (i.e., F is positive) m r , M r : are the two radiation masses, r: is the distance between masses, G: is the gravitational constant.

The Kahromatic Particles
The kahromatic particles contains from two single kahromatic charges which possible to be positive or negative charges, bound to each other by the Coulomb force and Radiation force in the case equivalent as shown in Figure 3.

Velocity of Kahromatic Particle
The kahromatic particle looks like a massless hydrogen atom, has constant, one direction velocity which equals the orbital speed of electron in Bohr's Hydrogen Atom.

Condition of Mechanical Equilibrium
For a particle to be in mechanical equilibrium, the net force must be zero, in the form of an equation, this condition is: As it is the first condition of getting the kahromatic particles in mechanical equilibrium.
Where δ : is the kahromatic equilibrium constant and its unit is a kilogram/colum. r z : is defined as the critical distance between kahromatic charges.
( ) r z m : is the critical radiation mass.
In this case, the kahromatic particles act as free-floating neutral particles whose collisions are subject to the laws and assumptions of the ideal gas theory.

The Relation between Kahromatic Gas and Thermodynamics
Suppose that we have a piston contains within it kahromatic particles gas has constant, one direction motion (i.e., without spin or vibrations), which can be represented by the classical ideal gas, as shown in Figure 4.
Assuming that N is the number molecules of theparticles gas, and that the weight of the molecule of this gas is m 0 , therefore the number of moles of this gas n is given or expressed by the equation:

A. K. Abou Layla
In this case, the general law of gases can be applied to the piston as the following: where n: is the number of gas molecules.
r total ε : is the total kinetic energy of kahromatic gas. R: is the gas constant J•K −1 •mol −1 . T z : is the temperature of gas in equivalent case K.
On the other hand, the total energy of gas r total ε is given by the equation: where r ε is the radiation kinetic energy of one particle, which can be formulated as follows:  ∝ : is the proportionality value.

The Critical Distance r z between Two Kahromatic Charges
From (5.3) we get: As the system is within kahromatic equilibrium state, so The last equation represents the relationship between three different physical sciences: gravitational, electromagnetism and thermodynamics, which explains that the Boltzmann constant is origin of electric charge.

General Gravitational Constant
There are many values of gravitational constant, including the exact and the relativistic value for gravitational constant.

The Absolute Value for General Gravitational Constant
The absolute value is a the exact value of the gravitational constant without relativity, which can be found as follows: By squaring the two sides of the Equation (5.7), we get the following: The last equation can be reformulated in terms of the elementary charge e and speed of light c to have the following form: