Giving Thermodynamics an Equation similiar to V = C*B*E of EM theory--AP's 211+x book of science. Incorporating Vector Cross-Product and Dot-Product in Faraday law and New Ohm's law V = C*B*E.

Yesterday I saw that Harmonic Motion yields Potential and Kinetic Energy in giving sine^2 and cosine^2 for Thermodynamics. I conjecture that the K and U are the B magnetic field and E electric field in New Ohm's law. This leaves me the further speculation that Coulomb current C in Voltage = C*B*E must be the entropy term of 2nd law of thermodynamics which so much terribly confused all the physicists of the past bygone eras.

AP's 211+x book of science. Incorporating Vector Cross-Product and Dot Product in Faraday law and New Ohm's law V = C*B*E.
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I have put this off for extremely long time now. And now is the time to finally do this.

Up to now I have made New Ohm's Law without vector product. I just did not want to get wrapped in details. But now I need to detail this.

New Ohm's Law is Voltage = current C times magnetic field B times electric field E.

Now the times can be a vector product. And it must be a form of trigonometry to account for the thrusting into a coil to produce electricity.

For example, if the thrusting bar magnet is not at a perpendicular to the coil, then a trigonometry needs to be in the formula for the thrust to yield the "perpendicular component of thrust".

But this book is more than the details of the multiplication in V=C*B*E.

I want to discuss the Speed of Light as a closed loop pencil ellipse. And I want to bring in the Pythagorean theorem. And tie together the Decimal Grid System of Numbers of mathematics.

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Yes, I should not forget Dot Product along with Vector Product. So far in my writings I have kept it "General" in C*B*E, but now I need to fine tune it, to incorporate the trigonometry needed in vectors.

And already I see a clarity for speed of light as constant and maximum constant in a closed loop pencil ellipse.

But I see even much much more in a possible direct link up with Decimal Grid Systems being the true numbers of mathematics, and not that crumby, lousy degenerate Reals of Old Math. What I mean by this is say the bar magnet in Faraday's law is 3meters long thrusting through the coil. And so the smallest pencil ellipse in Decimal 10 Grid is 3 by 0.8 by 2.9. Now we double that and have a rectangle instead of right triangle. And the doubling would be the kinetic energy 1/2mv^2.
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Now I need to do this especially, for once again, I am making slow progress into Reincarnation science, I need to connect up the whole of mathematics Decimal Grid Numbers with Geometry of Pythagorean theorem.

It is a wonderful wonderful piece of evidence that electricity is always perpendicular to magnetism.

That astounding fact and idea, needs to be explained in more detail.

Of course the mathematics has the Pythagorean theorem. But the Pythagorean theorem is not the whole of mathematics. Yet in Physics, the perpendicularity of electricity to magnetism is far too much encompassing. This means that mathematics is missing something, missing something big as to why the Pythagorean theorem is not larger in the body knowledge of mathematics.

There is something I am missing in the understanding of Mathematics for the physics is quite clear--- All is Atom and Atoms are nothing but electricity and magnetism. Yet in math, the Pythagorean theorem is too small of importance. While in physics, perpendicular is at the heart of physics. So there is some more to fill in mathematics.

And perhaps it is this Vector and Dot product that rely on a angle for trigonometry. We generally do not like to think of angles as numbers, but the connection of angles to numbers is the science of trigonometry.

And of course, in my recent book proving dimensions can be 3 and only 3 dimensions. Trigonometry is 2 dimensional. An added support of the idea dimensions exist to only 3rd dimension.

I believe the solution to all this pondering will be the idea that Decimal Grid Numbers is the missing piece of mathematics that ties together math with physics and makes the Pythagorean theorem much larger. Much larger than what the Pythagorean theorem was in Old Math with their Reals and continuum..

Perhaps the continuum of Old Math Reals destroyed the Pythagorean theorem, destroying it so that it could not "show itself in full bloom and glory".

As my example earlier of a bar magnet thrusting 3meters, then the right triangle is 0.8 with 2.9 as right triangle and doubling it to a pencil ellipse for a Light Wave. That connects speed of light with kinetic energy. In a system of Reals with continuum, none of that makes sense. In a system of Discrete numbers, it makes perfect sense.

AP, King of Science, especially Physics
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Years back when I was doing TEACHING TRUE PHYSICS textbooks, I knew I had to have dot product and vector product in New Ohm's law of V=C*B*E with V voltage, C coulomb current, B magnetic field, E electric field. I knew the multiply was either a dot product or vector product. But rather than wade through details and take up time, I decided it best to just make the general math formula of V=CBE and leave the details of multiplication for a later date.

And I see that such was a wise decision, years back. To leave the details of the multiplication in Voltage in generalized form. For it may turn out that Vector Product and Dot Product are natural parts of physics mathematics or it may turn out that Vector Product and Dot Product were "crude remedies" that fixed the wrong numbers of Reals and the continuum of Old Math. In other words, there is the possibility that physics and mathematics never needed the vector and dot product if mathematics used only the Decimal Grid Numbers and a Discrete mathematics. I love that to be the case for vector and dot products for if anything AP loves more, is to throw out junk in science that only is confusing, not simple and easy.

But I suspect, beforehand that the vector and dot products are needed despite the fact that Decimal Grid Numbers are discrete and far different from Reals and continuum. And so my hunch is that vector and dot products are vital for physics and math.

So let me dive into Old Physics Old Ohm's Law of V= iR where V is voltage, i is current and R is resistance. Can we see that V= C*B*E that the B*E is either a form of vector product or dot product? Can we see that? For, can we see that as we thrust a bar magnet through a coil at a angle, that we have to compensate for that angle in the Lines of Force of Magnetism? With either the trigonometry of sine as in vector product or the cosine in dot product? Same question for Resistence in electromagnetism. Can we see that a current through a resistor is the same as a current through -- as the bar magnet thrust needs compensation of what is thrusting perpendicular. So in a current flowing through a resistance some compensation to the current as _non_perpendicular. So here we conceptually make out what Resistance is in Old Physics-- as the compensation from non-perpendicular. That a current flowing in a conductor, almost all the current is perpendicular and gets through easily , but in a resistor, much of the current is non-perpendicular and little gets through--- now I likely have that conceptual picture turned around backwards, but the reader can understand what I am driving at. In thrusting in Faraday Law, only the Perpendicular component counts in making electricity. In New Ohms Law, the V= C*B*E, the B*E is a measure of how easy or how difficult it is to have current flow through, due to perpendicularity. And the way that physicists mathematically account for that perpendicularity is via the vector product or the dot product. Resistance in electricity and magnetism is where a material absorbs the Lines of Force rather than let them go through. And it is either the vector or dot product that describes how much gets through.

AP
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Alright, I am not going to make this a separate book but incorporate it into all my TEACHING TRUE PHYSICS books. The idea is simple, that AP-EM Equations govern all math of physics. And their most General form is V= C*B*E where the * stands for multiplication, the V is voltage, the C is Coulomb electric current, the B is magnetic field and E is electric field.

The multiplication * is a multiplication in general and can be sometimes specifically a Dot product or sometimes a Vector product, utilizing cosine or sine given the specific physics of the experiment. Or the multiplication can be just straightforward scalar multiplication, without and fancy multiplication of vectors.

When I wrote TEACHING TRUE PHYSICS textbooks I was not going to specify the multiplication for it can vary. But now is the time to go back in those books and make specification loud and clear.

Well this certainly deserves a whole brand new book of science, for what I am doing is piecing together the unification of Thermodynamics with EM theory. And in the end I give Thermodynamics its own pinnacle peak equation similar to Voltage = C*B*E. This deserves a whole new book outright for it is the history of how I attained that equation-- and from all places, attained it from trigonometry functions sine and cosine. Who would have thought of that??? The fact that Harmonic motion has sine^2 and cosine^2 for Potential and Kinetic Energy, and thermodynamics is all, all about potential and kinetic energy. So Thermodynamics must have a equation of form V = C*B*E.

And the 2nd law of thermodynamics becomes nothing more than Heat flows from Hot to Cold, never the reverse. Is just the Right-Hand Rule of current flowing in a conductor. Entropy is the Coulomb current, and Potential and Kinetic Energy are merely magnetic and electric fields, or vice versa. Resistance in Old Ohms law V = iR, is not the full equation of V = i*B*E where B*E is a more general Resistance. But it is well known that resistance is Heat, and heat is thermodynamics.

So, yes, this deserves a book of its own-- the history of the discovery that thermodynamic equation A=i*B*E, similar to V=C*B*E.

> Giving Thermodynamics an Equation similiar to V = C*B*E of EM theory--AP's 211+x book of science. Incorporating Vector Cross-Product and Dot-Product in Faraday law and New Ohm's law V = C*B*E.
>
> Yesterday I saw that Harmonic Motion yields Potential and Kinetic Energy in giving sine^2 and cosine^2 for Thermodynamics. I conjecture that the K and U are the B magnetic field and E electric field in New Ohm's law. This leaves me the further speculation that Coulomb current C in Voltage = C*B*E must be the entropy term of 2nd law of thermodynamics which so much terribly confused all the physicists of the past bygone eras.
>
>
>
>
>
> AP's 211+x book of science. Incorporating Vector Cross-Product and Dot Product in Faraday law and New Ohm's law V = C*B*E.
> Archimedes Plutonium's profile photo
> Archimedes Plutonium<plutonium....@gmail.com>
> Oct 11, 2022, 4:57:20 PM (7 days ago)
> 
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> to Plutonium Atom Universe
>
> I have put this off for extremely long time now. And now is the time to finally do this.
>
> Up to now I have made New Ohm's Law without vector product. I just did not want to get wrapped in details. But now I need to detail this.
>
> New Ohm's Law is Voltage = current C times magnetic field B times electric field E.
>
> Now the times can be a vector product. And it must be a form of trigonometry to account for the thrusting into a coil to produce electricity.
>
> For example, if the thrusting bar magnet is not at a perpendicular to the coil, then a trigonometry needs to be in the formula for the thrust to yield the "perpendicular component of thrust".
>
> But this book is more than the details of the multiplication in V=C*B*E..
>
> I want to discuss the Speed of Light as a closed loop pencil ellipse. And I want to bring in the Pythagorean theorem. And tie together the Decimal Grid System of Numbers of mathematics.
>
>
> Archimedes Plutonium's profile photo
> Archimedes Plutonium<plutonium....@gmail.com>
> Oct 11, 2022, 5:13:23 PM (7 days ago)
> 
> 
> 
> to Plutonium Atom Universe
> Yes, I should not forget Dot Product along with Vector Product. So far in my writings I have kept it "General" in C*B*E, but now I need to fine tune it, to incorporate the trigonometry needed in vectors.
>
> And already I see a clarity for speed of light as constant and maximum constant in a closed loop pencil ellipse.
>
> But I see even much much more in a possible direct link up with Decimal Grid Systems being the true numbers of mathematics, and not that crumby, lousy degenerate Reals of Old Math. What I mean by this is say the bar magnet in Faraday's law is 3meters long thrusting through the coil. And so the smallest pencil ellipse in Decimal 10 Grid is 3 by 0.8 by 2.9. Now we double that and have a rectangle instead of right triangle. And the doubling would be the kinetic energy 1/2mv^2.
> Archimedes Plutonium's profile photo
> Archimedes Plutonium<plutonium....@gmail.com>
> Oct 11, 2022, 5:38:13 PM (7 days ago)
> 
> 
> 
> to Plutonium Atom Universe
> Now I need to do this especially, for once again, I am making slow progress into Reincarnation science, I need to connect up the whole of mathematics Decimal Grid Numbers with Geometry of Pythagorean theorem.
>
> It is a wonderful wonderful piece of evidence that electricity is always perpendicular to magnetism.
>
> That astounding fact and idea, needs to be explained in more detail.
>
> Of course the mathematics has the Pythagorean theorem. But the Pythagorean theorem is not the whole of mathematics. Yet in Physics, the perpendicularity of electricity to magnetism is far too much encompassing. This means that mathematics is missing something, missing something big as to why the Pythagorean theorem is not larger in the body knowledge of mathematics.
>
> There is something I am missing in the understanding of Mathematics for the physics is quite clear--- All is Atom and Atoms are nothing but electricity and magnetism. Yet in math, the Pythagorean theorem is too small of importance. While in physics, perpendicular is at the heart of physics. So there is some more to fill in mathematics.
>
> And perhaps it is this Vector and Dot product that rely on a angle for trigonometry. We generally do not like to think of angles as numbers, but the connection of angles to numbers is the science of trigonometry.
>
> And of course, in my recent book proving dimensions can be 3 and only 3 dimensions. Trigonometry is 2 dimensional. An added support of the idea dimensions exist to only 3rd dimension.
>
> I believe the solution to all this pondering will be the idea that Decimal Grid Numbers is the missing piece of mathematics that ties together math with physics and makes the Pythagorean theorem much larger. Much larger than what the Pythagorean theorem was in Old Math with their Reals and continuum.
>
> Perhaps the continuum of Old Math Reals destroyed the Pythagorean theorem, destroying it so that it could not "show itself in full bloom and glory".
>
> As my example earlier of a bar magnet thrusting 3meters, then the right triangle is 0.8 with 2.9 as right triangle and doubling it to a pencil ellipse for a Light Wave. That connects speed of light with kinetic energy. In a system of Reals with continuum, none of that makes sense. In a system of Discrete numbers, it makes perfect sense.
>
> AP, King of Science, especially Physics
> Archimedes Plutonium's profile photo
> Archimedes Plutonium<plutonium....@gmail.com>
> Oct 11, 2022, 8:57:11 PM (7 days ago)
> 
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> Years back when I was doing TEACHING TRUE PHYSICS textbooks, I knew I had to have dot product and vector product in New Ohm's law of V=C*B*E with V voltage, C coulomb current, B magnetic field, E electric field. I knew the multiply was either a dot product or vector product. But rather than wade through details and take up time, I decided it best to just make the general math formula of V=CBE and leave the details of multiplication for a later date.
>
> And I see that such was a wise decision, years back. To leave the details of the multiplication in Voltage in generalized form. For it may turn out that Vector Product and Dot Product are natural parts of physics mathematics or it may turn out that Vector Product and Dot Product were "crude remedies" that fixed the wrong numbers of Reals and the continuum of Old Math. In other words, there is the possibility that physics and mathematics never needed the vector and dot product if mathematics used only the Decimal Grid Numbers and a Discrete mathematics. I love that to be the case for vector and dot products for if anything AP loves more, is to throw out junk in science that only is confusing, not simple and easy.
>
> But I suspect, beforehand that the vector and dot products are needed despite the fact that Decimal Grid Numbers are discrete and far different from Reals and continuum. And so my hunch is that vector and dot products are vital for physics and math.
>
> So let me dive into Old Physics Old Ohm's Law of V= iR where V is voltage, i is current and R is resistance. Can we see that V= C*B*E that the B*E is either a form of vector product or dot product? Can we see that? For, can we see that as we thrust a bar magnet through a coil at a angle, that we have to compensate for that angle in the Lines of Force of Magnetism? With either the trigonometry of sine as in vector product or the cosine in dot product? Same question for Resistence in electromagnetism. Can we see that a current through a resistor is the same as a current through -- as the bar magnet thrust needs compensation of what is thrusting perpendicular. So in a current flowing through a resistance some compensation to the current as _non_perpendicular. So here we conceptually make out what Resistance is in Old Physics-- as the compensation from non-perpendicular. That a current flowing in a conductor, almost all the current is perpendicular and gets through easily , but in a resistor, much of the current is non-perpendicular and little gets through--- now I likely have that conceptual picture turned around backwards, but the reader can understand what I am driving at. In thrusting in Faraday Law, only the Perpendicular component counts in making electricity. In New Ohms Law, the V= C*B*E, the B*E is a measure of how easy or how difficult it is to have current flow through, due to perpendicularity. And the way that physicists mathematically account for that perpendicularity is via the vector product or the dot product. Resistance in electricity and magnetism is where a material absorbs the Lines of Force rather than let them go through. And it is either the vector or dot product that describes how much gets through.
>
> AP
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> Oct 18, 2022, 4:37:12 PM (24 hours ago)
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> Alright, I am not going to make this a separate book but incorporate it into all my TEACHING TRUE PHYSICS books. The idea is simple, that AP-EM Equations govern all math of physics. And their most General form is V= C*B*E where the * stands for multiplication, the V is voltage, the C is Coulomb electric current, the B is magnetic field and E is electric field.
>
> The multiplication * is a multiplication in general and can be sometimes specifically a Dot product or sometimes a Vector product, utilizing cosine or sine given the specific physics of the experiment. Or the multiplication can be just straightforward scalar multiplication, without and fancy multiplication of vectors.
>
> When I wrote TEACHING TRUE PHYSICS textbooks I was not going to specify the multiplication for it can vary. But now is the time to go back in those books and make specification loud and clear.
>
> AP
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> Oct 18, 2022, 7:47:42 PM (21 hours ago)
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> +AP's 211+x book of science. Incorporating Vector Product and Dot Product in Faraday law and New Ohm's law V = C*B*E. Incorporate that into the General Multiplication of V = C*B*E as specialized multiplication in TEACHING TRUE PHYSICS.
>
>
> AP's 211+x book of science. Incorporating Vector Product and Dot Product in Faraday law and New Ohm's law V = C*B*E.
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> AP's 211+x book of science. Incorporating Vector Product and Dot Product in Faraday law and New Ohm's law V = C*B*E.
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> Yes, I should not forget Dot Product along with Vector Product. So far in my writings I have kept it "General" in C*B*E, but now I need to fine tune it, to incorporate the trigonometry needed in vectors.
>
> And already I see a clarity for speed of light as constant and maximum constant in a closed loop pencil ellipse.
>
> But I see even much much more in a possible direct link up with Decimal Grid Systems being the true numbers of mathematics, and not that crumby, lousy degenerate Reals of Old Math. What I mean by this is say the bar magnet in Faraday's law is 3meters long thrusting through the coil. And so the smallest pencil ellipse in Decimal 10 Grid is 3 by 0.8 by 2.9. Now we double that and have a rectangle instead of right triangle. And the doubling would be the kinetic energy 1/2mv^2.
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> So during the years I initially wrote the textbook series TEACHING TRUE PHYSICS, I kept it a Generalized Multiplicaton of New Ohm's Law as V = C*B*E where the asterisk multiplication can mean normal scalar multiplication or it could mean Vector Dot Product with its use of cosine as in a*b = ab(cos theta), or Vector Cross Product with its use of sine as in axb = ab(sin theta)n.
>
> Examples abound in physics. The Faraday law if the thrusting bar magnet is thrust at an angle, we remember trigonometry as sine is opposite/hypotenuse while cosine is adjacent/hypotenuse.
>
> Throughout physics math, we need the perpendicular amount in electromagnetism.
>
> So we need the amount of magnetism that is perpendicular to the coils and that is got from cosine.
>
> Now in physics optics we have Snell's law of optics refraction as n_1(sin theta_1) = n_2 (sin theta_2).
>
> Throughout physics, the trigonometry of sine and cosine enter into the mathematics because electricity is perpendicular to magnetism, and we must adjust our values for the **perpendicular component**.
>
> So the Primal Axiom or Principle over all of Physics is --- All is Atom and Atoms are nothing but electricity and magnetism.
>
> All of our laws of physics reduce down to the EM equations and those EM equations are basically Voltage = C*B*E. Which is a Generalized multiplication.
>
> If in the Faraday law we are using, we need the dot product using cosine and angle of thrust. If in optics we are doing refraction math, we need the trigonometry of sine and angle.
>
> The trigonometry in physics laws is a aid of getting the perpendicular component of electricity and magnetism. It is sad and bad that Old Physics treats these products as fundamental, when rather, they are corrections to the physical forces going on.
>
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> In Harmonic motion we have the Potential Energy with cos^2 as (1/2)kx^2 while the Kinetic Energy 1/2(mv^2) is sin^2.
>
> All is Atom, and Atoms are nothing but electricity and magnetism. And in any phenomenon there is a perpendicular of Electricity to that of Magnetism, and we are constantly having to use trigonometry to compute the perpendicular component.
>
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> On Tuesday, October 18, 2022 at 9:01:50 PM UTC-5 Archimedes Plutonium wrote:
> In Harmonic motion we have the Potential Energy with cos^2 as (1/2)kx^2 while the Kinetic Energy 1/2(mv^2) is sin^2.
>
> All is Atom, and Atoms are nothing but electricity and magnetism. And in any phenomenon there is a perpendicular of Electricity to that of Magnetism, and we are constantly having to use trigonometry to compute the perpendicular component.
>
> Now I bring up potential and kinetic energy especially as harmonic motion, because in thermodynamics I do not recall trigonometric functions ever coming into play. I remember the Logarithmic and exponential functions by not sine or cosine. Does this mean there is no perpendicularity in thermodynamics? And thus no link to electromagnetism? I say no, because, well Potential Energy and Kinetic Energy is what thermodynamics is all about, and those have cosine^2 and sine^2.
>
> Now if thermodynamics never had any sine or cosine at all, then we could argue, thermodynamics cannot be unified to electromagnetism. But since all the sciences involve potential and kinetic energy we can say EM is the unification force.
>
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> And this brings up a most interesting question. Is the B and E fields in V = C*B*E, are those interchangeable as Potential Energy and the other as Kinetic Energy? So that one can say the B field is kinetic energy while the Electric field is potential energy or vice versa?
>
> And in all my study of physics, I have never encountered the idea that potential energy is somehow, a perpendicular of kinetic energy.
>
> But of course, now, Simple Harmonic motion is periodic as in trigonometry functions and that U + K = constant.
>
> AP

Thermodynamics already had equations of form A = B*C*D although they did not know it.

--- quoting from Wikipedia ---
Potential Differential
Internal energy

dU\left(S,V,{N_{i}}\right) = TdS - pdV + \sum_{i} \mu_{i} dN_i
Enthalpy

dH\left(S,p,{N_{i}}\right) = TdS + Vdp + \sum_{i} \mu_{i} dN_{i}
Helmholtz free energy

dF\left(T,V,{N_{i}}\right) = -SdT - pdV + \sum_{i} \mu_{i} dN_{i}
Gibbs free energy

dG\left(T,p,{N_{i}}\right) = -SdT + Vdp + \sum_{i} \mu_{i} dN_{i}

The first and second law of thermodynamics are the most fundamental equations of thermodynamics. They may be combined into what is known as fundamental thermodynamic relation which describes all of the changes of thermodynamic state functions of a system of uniform temperature and pressure. As a simple example, consider a system composed of a number of k  different types of particles and has the volume as its only external variable. The fundamental thermodynamic relation may then be expressed in terms of the internal energy as:

{\displaystyle dU=TdS-pdV+\sum _{i=1}^{k}\mu _{i}dN_{i}}

Physical situation Nomenclature Equations
Ideal gas law
p = pressure
V = volume of container
T = temperature
n = number of moles
R = Gas constant
N = number of molecules
k = Boltzmann's constant

pV = nRT = kTN\,\!

\frac{p_1 V_1}{p_2 V_2} = \frac{n_1 T_1}{n_2 T_2} = \frac{N_1 T_1}{N_2 T_2} \,\!

Pressure of an ideal gas
m = mass of one molecule
Mm = molar mass

p = \frac{Nm \langle v^2 \rangle}{3V} = \frac{nM_m \langle v^2 \rangle}{3V} = \frac{1}{3}\rho \langle v^2 \rangle \,\!
--- end quoting from Wikipedia ---

On Thursday, October 20, 2022 at 2:58:35 AM UTC-5, Archimedes Plutonium wrote:
> Thermodynamics already had equations of form A = B*C*D although they did not know it.
>
> --- quoting from Wikipedia ---
> Potential Differential

> Internal energy as dU(S,V,{N_{i}} = TdS - pdV + sum_{i} mu_{i} dN_i
> Enthalpy as dH(S,p,{N_{i}} = TdS + Vdp + sum_{i} mu_{i} dN_{i}
> Helmholtz free energy as dF(T,V,{N_{i}} = -SdT - pdV + sum_{i} mu_{i} dN_{i}
> Gibbs free energy as dG(T,p,{N_{i}} = -SdT + Vdp + sum_{i} mu_{i} dN_{i}
>
>
> The first and second law of thermodynamics are the most fundamental equations of thermodynamics. They may be combined into what is known as fundamental thermodynamic relation which describes all of the changes of thermodynamic state functions of a system of uniform temperature and pressure. As a simple example, consider a system composed of a number of k different types of particles and has the volume as its only external variable. The fundamental thermodynamic relation may then be expressed in terms of the internal energy as:
>
> dU=TdS-pdV+sum _{i=1}^{k} mu _{i}dN_{i}}
>
> Physical situation Nomenclature Equations
> Ideal gas law
> p = pressure
> V = volume of container
> T = temperature
> n = number of moles
> R = Gas constant
> N = number of molecules
> k = Boltzmann's constant
>
> pV = nRT = kTN
>
> {p_1 V_1}/{p_2 V_2} = {n_1 T_1}/{n_2 T_2} = {N_1 T_1}/{N_2 T_2}
>
> --- end quoting from Wikipedia ---

Compare the AP-EM Equations with thermodynamics of dU, dH, dF, dG

C' = (V/(BE))' = V'BE/(BE)^2 - VB'E/(BE)^2 - VBE'/(BE)^2 which is Faraday's law.
1st term as current production  -- 2nd term as Lenz law  -- 3rd term as DC, AC direction

B' = (V/(CE))' = V'CE/(CE)^2 - VC'E/(CE)^2 - VCE')/(CE)^2 which is Ampere-Maxwell law.
1st term as B production -- 2nd term as Displacement current -- 3rd term as parallel attract

E' = (V/(CB))' = V'CB/(CB)^2 - VC'B/(CB)^2 - VCB'/(CB)^2 which is Coulomb-gravity law.
1st term as E production -- 2nd term as inverse square of distance -- 3rd term as spin and orbit synchronicity

V' = (CBE)' = C'BE + CB'E + CBE' which is Transformer law
1st term as V production in a transformer  -- 2nd term as inverse square root -- 3rd term as DC, AC synchronicity

The two sets are almost exact duplicates. The only thing out of place is an extra subtraction in Helmholtz free energy dF. The enthalpy dH is all addition, as well as Voltage' is all addition.

Could it be that thermodynamics has a mistake of an extra subtraction, when it should not be subtraction in the -SdT???? Helmholtz free energy as dF(T,V,{N_{i}} = -SdT - pdV + sum_{i} mu_{i} dN_{i}.

Could it be a orientation in space problem of Old Physics that the SdT should be +SdT?????

AP, King of Science, especially Physics

On Friday, October 21, 2022 at 2:07:00 AM UTC-5, Archimedes Plutonium wrote:
> On Thursday, October 20, 2022 at 2:58:35 AM UTC-5, Archimedes Plutonium wrote:
> > Thermodynamics already had equations of form A = B*C*D although they did not know it.
> >
> > --- quoting from Wikipedia ---
> > Potential Differential
> > Internal energy as dU(S,V,{N_{i}} = TdS - pdV + sum_{i} mu_{i} dN_i
> > Enthalpy as dH(S,p,{N_{i}} = TdS + Vdp + sum_{i} mu_{i} dN_{i}
> > Helmholtz free energy as dF(T,V,{N_{i}} = -SdT - pdV + sum_{i} mu_{i} dN_{i}
> > Gibbs free energy as dG(T,p,{N_{i}} = -SdT + Vdp + sum_{i} mu_{i} dN_{i}
> >
> >
> > The first and second law of thermodynamics are the most fundamental equations of thermodynamics. They may be combined into what is known as fundamental thermodynamic relation which describes all of the changes of thermodynamic state functions of a system of uniform temperature and pressure. As a simple example, consider a system composed of a number of k different types of particles and has the volume as its only external variable. The fundamental thermodynamic relation may then be expressed in terms of the internal energy as:
> >
> > dU=TdS-pdV+sum _{i=1}^{k} mu _{i}dN_{i}}
> >
> > Physical situation Nomenclature Equations
> > Ideal gas law
> > p = pressure
> > V = volume of container
> > T = temperature
> > n = number of moles
> > R = Gas constant
> > N = number of molecules
> > k = Boltzmann's constant
> >
> > pV = nRT = kTN
> >

Over the years, I maintained that the equation as basis for all of Thermodynamics was PV = nRT, the ideal gas law. For we can generalize that to liquids and solids, not just stuck to gases. For it has a equation form of A = B*C*D the same as New Ohm's Law is A = B*C*D and more specifically Voltage = Coulomb*magnetic field * electric field.

So all we need do for PV = nRT is somehow, put Pressure on the rightside or put Volume on the rightside and we have A = B*C*D.

Over the years I was wavering as to whether Pressure is the analog of Voltage, for many do believe that is the case. And then some years I thought Volume is the analog of Voltage. Maybe it is both, and that you use one in certain circumstances and use the other in a different circumstance.

But as we move Pressure or Volume to the other side, it becomes a reciprocal. The 1/volume or the 1/pressure. And then the question arises, which makes more "physical sense", physical commonsense. For as far as I know, there is no natural physical reciprocal of either pressure or volume. What I mean is that there is a natural reciprocal of time and that is frequency as 1/time. There is a natural physical reciprocal of acceleration meters/sec^2 and that be angular momentum meters^2/sec. A reciprocal of pressure is vague, for it would be Volume/Work since pressure is Work/Volume.

AP

On Friday, October 21, 2022 at 2:07:00 AM UTC-5, Archimedes Plutonium wrote:
> On Thursday, October 20, 2022 at 2:58:35 AM UTC-5, Archimedes Plutonium wrote:
> > Thermodynamics already had equations of form A = B*C*D although they did not know it.
> >
> > --- quoting from Wikipedia ---
> > Potential Differential
> > Internal energy as dU(S,V,{N_{i}} = TdS - pdV + sum_{i} mu_{i} dN_i
> > Enthalpy as dH(S,p,{N_{i}} = TdS + Vdp + sum_{i} mu_{i} dN_{i}
> > Helmholtz free energy as dF(T,V,{N_{i}} = -SdT - pdV + sum_{i} mu_{i} dN_{i}
> > Gibbs free energy as dG(T,p,{N_{i}} = -SdT + Vdp + sum_{i} mu_{i} dN_{i}
> >
> >
> > The first and second law of thermodynamics are the most fundamental equations of thermodynamics. They may be combined into what is known as fundamental thermodynamic relation which describes all of the changes of thermodynamic state functions of a system of uniform temperature and pressure. As a simple example, consider a system composed of a number of k different types of particles and has the volume as its only external variable. The fundamental thermodynamic relation may then be expressed in terms of the internal energy as:
> >
> > dU=TdS-pdV+sum _{i=1}^{k} mu _{i}dN_{i}}
> >
> > Physical situation Nomenclature Equations
> > Ideal gas law
> > p = pressure
> > V = volume of container
> > T = temperature
> > n = number of moles
> > R = Gas constant
> > N = number of molecules
> > k = Boltzmann's constant
> >
> > pV = nRT = kTN
> >
> > {p_1 V_1}/{p_2 V_2} = {n_1 T_1}/{n_2 T_2} = {N_1 T_1}/{N_2 T_2}
> >
> > --- end quoting from Wikipedia ---
> Compare the AP-EM Equations with thermodynamics of dU, dH, dF, dG
>
> C' = (V/(BE))' = V'BE/(BE)^2 - VB'E/(BE)^2 - VBE'/(BE)^2 which is Faraday's law.
> 1st term as current production -- 2nd term as Lenz law -- 3rd term as DC, AC direction
>
> B' = (V/(CE))' = V'CE/(CE)^2 - VC'E/(CE)^2 - VCE')/(CE)^2 which is Ampere-Maxwell law.
> 1st term as B production -- 2nd term as Displacement current -- 3rd term as parallel attract
>
> E' = (V/(CB))' = V'CB/(CB)^2 - VC'B/(CB)^2 - VCB'/(CB)^2 which is Coulomb-gravity law.
> 1st term as E production -- 2nd term as inverse square of distance -- 3rd term as spin and orbit synchronicity
>
> V' = (CBE)' = C'BE + CB'E + CBE' which is Transformer law
> 1st term as V production in a transformer -- 2nd term as inverse square root -- 3rd term as DC, AC synchronicity
>
> The two sets are almost exact duplicates. The only thing out of place is an extra subtraction in Helmholtz free energy dF. The enthalpy dH is all addition, as well as Voltage' is all addition.
>
> Could it be that thermodynamics has a mistake of an extra subtraction, when it should not be subtraction in the -SdT???? Helmholtz free energy as dF(T,V,{N_{i}} = -SdT - pdV + sum_{i} mu_{i} dN_{i}.
>
> Could it be a orientation in space problem of Old Physics that the SdT should be +SdT?????

No, my mistake, all 4 Thermodynamics differential equations have similar signage to the AP-EM equations. As long as one of them has all the same signage -- all + signage. Then the other three equations has two of one sign and one of the opposite sign, then they agree. And so there is no discrepancy.