THE GAS DISTRUIBUTION ENERGY (I) 

This theme is very much important in the study of the gases in physics;  because here will change it from its probabilistic character to a determinist one.   The kinetic theory of the gases has many degree of indeterminations, and this is because a poor understanding of the behavior of the atoms or the molecules that form such gases.   It has been think that the atoms or the molecules,  have different velocities, because they continually are shocking (?. . . .) between themselves.   I have meditated in this problem, and have concluded that although these atomic particles move in all directions, and with different velocities;  it is very much problematic they can interfere in their trajectories and produce shocks  (?. . . ).   I  am in accordance that the temperature of the gases grows with the velocity with which the atoms or the molecules moves;  but this is also an incomplete argument.

In other themes I have say that the corpuscles as those of light, have equal capacity to for produce kinetic energy if they fixed (with guarder energy. . .) or moving at  (c)  velocity;  because this, and because in a gas their atoms or molecules are moving, can be consider that they emit fluids  of corpuscles, that act as propulsion jets;  there could be interchange of corpuscles between the atom or molecules of the gas;  conserving the same temperature..   Logically while more temperature has the gas, this has more free corpuscles, and its atoms or molecules move faster.   With all say here it is concluded that the temperature of the gas is produced with the movement of its atoms or molecules, as could be proved by the  Boltzmann´s formula,  and by the free corpuscles that move in the gas, and that produce heat, as do the corpuscles of light emitted by our  Sun;  and also that are absorbed by the atoms or molecules of the gas, when they get exhausted.   In the following paragraphs will be explained how are produced the movement of the atoms or molecules of the gas, and how they produce the temperature and pressure in the gas with the help of the corpuscles that are ejected when the atoms or molecules get their kinetic  movement..

In the accepted theories it is consider that in the air  (in a stable state, without wind, dust , etc,),  the atmosphere at normal temperature  (21^o C) the molecules of it, by preference (N²) are moving at an average velocity  v_a1.   Some of them could be moving in accordance with the accepted theories, at higher velocity than the fore one mentioned,  and other at less velocity;  all these due to the continuous shocks (?…)   between them.   I am not in accordance with this, for the reason say at the beginning of this theme.

Here will study the gas of the atmosphere in a clear state, without any perturbing effect, as wind, or any dust particles.   Can divide in an arbitrary and virtual way, for to simplify the explanations to the atmosphere,  by cubes spherical volumen, with diameter:  d  =  1 m.;  and with cubic volumen, with side equal to:  d  =  1.0  m by side;

phere of sphere of  diameter:  d  =  1m.;  the sphere will have:

Exterior surface:   S  =  p d²  =  3.1416 m²

Volume:   V  =  p d³ / 6  =  0.5236  m³

The atmosphere is formed  (in an average way) by molecules with  amu  =  28.9

Mass of each molecule: 

m_a  =  28.9 x 1.674 x 10^—27  =  4.8379 x 10^—26  Kg.

Temperatura  of air:  

T _a =  273^o + 21^o  =  2.94^o  K

With the fore data and  by experiment was found that the atmosphere pressure at sea level is:

f _a =  1.01 x 10.⁵  newtons /  m²

Molecular energy of the atmosphere in accordance with the  Boltzmann´s  law:

K_a  =  1,5 k T_a  =  1.5 x 1.38 x 10^—23 x 294  =  6.0858 x 10^—21  joule / molecule

K_a  =  0.5 m_a v_a²  =  0.5 x 4.8379 x 10^—26 v_a²  =  2.41885 x 10^—26 v_a²

The “average” velocity of the molecules of the air

va  =  (6.0858 x 1^0—21 / 2.41885 x 10^—26)^0.5  =  501.6  m / Sec.

In accordance with classical and modern physics  the atoms or the molecules of the gas have different velocities;  because this , for determine the pressure and temperature that produce this gas, it is consider an average velocity of the atoms or molecules of the gas.   In mechanophysics the fore solution is good in a partial way;  here we consider that beside the atoms or molecules of the gas, contribute to produce the  temperature and pressure, the liberated free corpuscles, that produce the movement of the mentioned atoms or molecules...   Considering the action of air into a cube of  1 m3.   In an average way an air molecule moving parallel  to to the lateral sides of the cube, affects a square side of the cube  (1 m²) in a  average  time:

t   =  d / v_a  =  1 / 501.6  =  0.001994  Sec. 

 An air molecule acts one time at its own cube, and at  501.6 – 1  =  500.6  I n  the adjacent cubes, in each one acts one time .   In an adjacent cube is moving a molecule toward the first one cube;  in such way that the action of one molecule is equivalent to  501.6 actions.   Similar thing could be say if the air is confined in a cubical recipient of  1 m³;  here the molecule reflects  501.6 / Sec., times in the walls of the recipient.

If now we consider that the molecule reduces its velocity at its square root:

va₁^0.5  =  501.6^0.5  =  22.396  m / Sec., each second.   Because this, the time of action vary as: 

t´   = t ^0.5  =  0.001994^0.5  =  0.04465  Sec.   With the cubic distribution of air we got the idea how act the molecules in the atmosphere.

Now will see how acts  the molecules in the cube   The air pressure in the exterior surface of the cube is:s:s:  

f_a  =  1.01 x 10.⁰⁵  newtons / m²  =  1.01 x 10^0.5 S_  =  1.01 x 100^0.5 x 6.0  =  6.06 x 10^0.5  newtons / S_    (m^{2             )}

By experiment have been obtained the pressure of air in the atmosphere  Fa,  at the sea level and at a temperature of  21^o C.   It is possible to divide in a hypothetic way the space of the atmosphere in cubes with volume of  1  m³, distributed in an isometric way; as was say before;  if it is choose one of them, into it can imagine a circumscribed sphere with diameter equal:  d  =  1.0  m.   In the sphere was determine its surface:  S_O  =  3.1416  m², and its volume:  V_O  =  0.5236  m³.   In the cube we have:  S_  =  6.0  m²;  V_  = 1.0 m²  m3.   Considering either the cube, or the sphere;  both can be circumscribed by the atmosphere, so are affected by it pressure  Fa.   The atmosphere mainly is constituted by nitrogen molecules:  N₂  =  28.9  amu.   With all the fore data it is possible to determine the quantity of molecules there are into the sphere, or into the cube.   The molecules of air move in all directions, either in the cube, as in the sphere;  in our model they have different velocities, as was say before;  but as the action  (movement) of the corpuscles grow, while the movement of the molecules decrease in opposite proportion, it result correct to consider the kinetic energy of the movement as a constant for all the velocities of the molecules;  so, in our problem will work for determine the different data we need, considering:  v_O1  =  501.6  m / Sec.   In classical and in modern physics;  in which  it is not consider the action of the corpuscles;  also have take the value:  v_O1,  as an  average one.

Some paragraphs before was seen the time of action:  t  =  t_  =  0.001994  Sec., of a molecule that moves parallel to the lateral sides of the cube;  but the molecules move in all directions,  so the fore value can not be applied to all them.   The times of action are function of the surface  S,  and of the volume  V,  beside of the change of velocity of the molecules.   With the cube or with the sphere can obtain the data we need, that are the quantity of molecules and of energy there is into the sphere or into the cube.   For the cube we have:  S_ =       6.0  m², and  V_  =  1.0 m³;  for the sphere:   S_O  =  3.1416  m²,   V_O  =  0.5236  m³;         S_ / V_  =  6.0 / 1.=  60 1.0  = S_O / V_O  =  3.1416 / 0.5236  =  6.0

In our model each molecule with the help of the complemented  corpuscles has the following impulse:   

f_a =  m_a v_a  =  4.8379 x 10^—26 x 501.6  =  2.4267 x 10^—23  Kg m / Sec.

The time of action of all the molecules affected by the surface  (S_  or  S_O);  and the volume  ( So or V_ or Vo) grows as follow:   

t´´  =  t   (S_O / V_O)  =  0.001994 x 3.1416 / 0.5236  =  0.01196  Sec.

The velocity of a molecule decrements at a rate of      v_a^0.5;  so their time of action (and of that of the corpuscles) vary in the same proportion:

 t´´´ =  (t´´)^0.5  =  0.01196^0.5  =  0.10936  Sec.

Considering the action in the surface of the sphere, that also is proportional to the action in the surfaaeofce of the cube…

t  /IV =  t´´´/ V_  =  0.10936  / 1.0  =  0.1094  Sec. xx

While the atmosphere pressure with an impulse:   f_a  =  6.06 x 105  newtons in the surface of the cube;  the molecules and the free corpuscles into the cube act in the opposite way with the same impulse, in an active time:  t_IV   =  0.1094  Sec.;  so each molecule into the cube oppose to the atmosphere pressure with an impulse / Sec.:

f_a´  =  f_a / t_V  =  2.4267 x 10^—23 / 0.1094  =  2.218 x 10^--22  newton / Sec.

The quantity of molecules  (Ñ)  that oppose the pressure  f_a, are those that are into the cube:

Ñ  =  f_a / f_a´  =  6.06 x 100^0.5 / 2.218 x 10^—22  =  2.732x 10²⁷ molecules / cube  

Weight of the molecules in a cube of 1 m².    w  =  129 Kgs./ m³       We obtain:

w  =  Ñ m_a  =  2.732 x 10²⁷ x 4.8379 x 1^0—26  =  132 Kgs / m³.  »  129  Kgs. / m³    

Considering the molecule with its average velocity:  v_a1    after a time it gets zero velocity, it remain so during a lapse of time during which it absorb some corpuscles, and gets the velocity:  va1  again, and so on.

xxxxxxxxxxxxxxxxxxxxxxxxxxx

It has been explained that an atom of a gas varies its velocity  at a rate:  van0.5  m / Sec.   If the maximum velocity of an air molecule in accordance with our theory is:  v_a1  =  501.6  m / Sec., in moving a distance  (L) it reduces its velocity:  Dv_a1  =  501.6^0.5  =  22.396  m / Sec.,  so the molecule gets the velocity:  va₂  =  v_a1 – Dv_a1  =  501.6 – 22.396  =  479.204  m / Sec.   Next, this last velocity is reduced:  Dv_a2  =  va₂^0.5  =  479.204^0.5  =21.891  m / Sec.;  so:  va₃  =  va₂ – D v_a2  =  479.204 – 21.891  =  457.313  m / Sec.  And so on.

Next will be given the reduced velocities and their decrement.

    501.6^0.5  =  .22.3.96;       479.204^0.5  =  21.891;       457.313^0.5  =  21.385;       435.928^0.5  = 20…879;

415.048^0.5  =  20.373;      394.675^0.5  =  19.855;       374.809^0.5  =  19.360;        355.048^0.5  =  18.843;

336.205^0.5  =  18.336;      317.869^0.5  =  17.829;       300.040^0.5  =  17.322;        282.718^0.5  =  16.814;

 265.904^0.5  =  16.307;      249.597^0.5  =  15.759;      233.798^0.5  =  15.290;        218.508^0.5  =  14.782;    

203.726^0.5  =  14.273:       189.453^0.5  =  13.764:      175.689^0.5  =  13.252;        162.434^0.5  =  12.745;

149.683^0.5  =  12.235;       137.448^0.5  =  11.724;        125.724^0.5  =  11.213;        114.511^0.5  =  10.701;

103.811^0.5 =  10.189;         93.622^0.5  =     9.676;         83.946^0.5  =   9.162:          74.874^0.5  =    8.648;

  66.2260^.5  =  8.138;           58.088^0.5  =   7.622;           50.466^0.5  =   7.104;          43.362^0.5  =   6.585;

 36.777^0.5  =  6.064;            30.713^0.5  =   5.542;           25.171^0.5  =   5.017;          20.154^0.5  =   4.489;

 15.665^0.5  =  3.958;            11.707^0.5  =   3.422;            8.285^0.5  =    2.875;            5.410^0.5  =   2.326;

  3.084^0.5  =   1.756;              1.327^0.5  =   1.152

Sum of decrements:          S  =  22.396 + 21.891 + 21.385 + . . .  1.756 + 1.152  =  501.014  »  501.6

In a liquid or in a solid it is easy to consider that sound can advance along the atoms or the molecules of them, because they are fixed in their places;  not so in the gases in which the atoms or the molecules are constantly moving, some at higher velocity than sound.   In the atmosphere, in accordance with the given conditions, such velocity vary  from  va  =  501.6  to  0.0  m/ Sec.   In the accepted theories it is consider that sound moves by waves.   But taking in account waves of sound in air or in a gas result too problematic, for the reason given before.   The model will be given here is taking in account that sound is manifested by some vibrations that are produced in the atoms or in the molecules;  such vibration will affect to the atoms or molecules that get in contact with the medium in which is produced the sound.   If the atoms or molecules are moving at bigger velocity than sound, they reduce their velocity to that of sound, emitting some corpuscles.   If the atoms or molecules of the air (or gas) have less velocity than sound;  when are affected by the mentioned vibrations, absorb some corpuscles, incrementing their velocity to that of sound.   In this way the sound is produced by the translation movement of the atoms or molecules of the air or gas.

                                                                                                Monterrey, Mexico, August 1, 2006

                                                                                                                               February / 2007

                                                                                                            Manuel de Hoyos Robles

.  

If I were a protected investigator of a prestige university I would win a Nobel price of physics by a work like this one.

Si fuera un protegido de una universidad de mucho prestigio ganaría el premio Nobel de física por un trabajo como este.

Si Dios me dio la capacidad de beneficiar a la humanidad con mi trabajo de investigación, con mucho gusto lo seguiré haciendo, aunque nadie me lo agradezca, y se piense mal de mi, porque no se comprenda que todo lo que diga y haga es pensando en el bien de todos, mas que en el mío;  a mi padre le sucedió lo mismo; yo no soy mas que una persona que tengo vergüenza y dignidad.   Hay muchas injusticias en todo esto, porque las personas egoístas nada mas piensan en recibir los agradecimientos  (aunque no los merezcan)  pero no en darlos.

Este tema tiene un valor muy grande, porque le da a la teoría de los gases un valor completamente determinista y tendrá que sustituir a las teorías vigentes en este terreno, caracterizadas por su carácter probabilístico; ojalá sea pronto; porque una física contradictoria y ambigua como es la física moderna se ha impuesto por un siglo con ideas que desde hace tiempo ya resultan mas perjudiciales que benéficas.