Quantization Of Time And Energy

[Jokodo]

And anyway, in a perfect vacuum, the water drops would instantly vaporize. Your scenario requires air to work at all but requires a perfect vacuum (plus a few more unrealistic assumptions) to show what you want it to show. Who's contradicting themselves now?

I think and reason in images supported by math. When I think about a tank of gas I see a 3D picture of the molecules colliding with each other and the tank. The best people I worked with had the ability to communicate by analogy and metaphor. Wrote theory alone is insufficient. The ability can be developed.

Analogies and metaphors are good to visualise stuff otherwise hard to wrap your head around. They don't serve as proofs.

If you do not see the analogy of rain to a gas in a tank hitting the wall then you are inexperienced, narrow minded, or just being stubborn.

I see the analogy and I'm telling you it doesn't show what you want it to show (even if analogies could prove stuff).

One last time. If you accept quantization of matter as atoms which have finite mass and finite thermal energy for fuels thne the total energy of a bucket of gas is the sum of the finite energy of each molecule. Reject that then nothing more to say.

Energy is finite, but not quantized. And if it were, pressure is still momentum transferred per unit of time per unit of area. You'd have to show that time and space are quantized too.

 

[Jokodo]

For a finite change in energy dE there is a finite change in velocity dv. If you claim dE is infinitely divisible then site an energy source that is not quantized, compared to coal and gasoline.

...assuming a 100% efficient engine? What are you doing debating on this forum, you should be writing up a patent application!

 

[steve_bank]

Got it. A block of aluminum comprised of discrete atoms is infinitley divisble. The weight of the block can chnage other than by multiples of atoms. The weight can be more or less than the sum of the quantized mass of atoms.

The energy in a gas comprised of atoms can change by any amount, not limited by the discrete energy of the individual atoms.. The total energy of the gas can be more or less than the sum of the discrete energy of the atoms.

Ol. You win.Arithmetic, addition and subtraction, does not apply to atoms....

How then do I calculate the total mass of a block of aluminum given the number of atoms and how do I calculate the total klinetic energy energy of a sas in a tank?

The chemical equation for cburing hydrogen will show a balnce of atoms and energy, discrte atoms and discrete energy.

You are looking at it as ca continuum. It works as long as there are many partcles. We treat variables as continuous because quantizatrion effects are insignificant with large numbers of partcles. When I work with pressure it is as a continuous variable that can take on any value.



https://en.wikipedia.org/wiki/Continuum_mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century.

Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. Fundamental physical laws such as the conservation of mass, the conservation of momentum, and the conservation of energy may be applied to such models to derive differential equations describing the behavior of such objects, and some information about the particular material studied is added through constitutive relations.

https://en.wikipedia.org/wiki/Statistical_mechanics

Statistical mechanics is one of the pillars of modern physics. It is necessary for the fundamental study of any physical system that has a large degree of freedom. The approach is based on statistical methods, probability theory and the microscopic physical laws. [1][2][3][note 1]

The primary goal of statistical thermodynamics (also known as equilibrium statistical mechanics) is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles and the interactions between them. In other words, statistical thermodynamics provides a connection between the macroscopic properties of materials in thermodynamic equilibrium, and the microscopic behaviours and motions occurring inside the material

 

[Juma]

Back to basics.

The derivative of the velocity with respect to energy of a particle is

dv = [(2/m)^1/2] * [1(2*x^1/2)] dE where v is velocity and E energy.


For a finite change in energy dE there is a finite change in velocity dv. If you claim dE is infinitely divisible then site an energy source that is not quantized, compared to coal and gasoline.

No. It is you that states that energy is quantizied so you have the burden of proof.

 

[Juma]

Got it. A block of aluminum comprised of discrete atoms is infinitley divisble. The weight of the block can chnage other than by multiples of atoms. The weight can be more or less than the sum of the quantized mass of atoms.

The energy in a gas comprised of atoms can change by any amount, not limited by the discrete energy of the individual atoms.. The total energy of the gas can be more or less than the sum of the discrete energy of the atoms.

Ol. You win.Arithmetic, addition and subtraction, does not apply to atoms....

How then do I calculate the total mass of a block of aluminum given the number of atoms and how do I calculate the total klinetic energy energy of a sas in a tank?

The chemical equation for cburing hydrogen will show a balnce of atoms and energy, discrte atoms and discrete energy.

You are looking at it as ca continuum. It works as long as there are many partcles. We treat variables as continuous because quantizatrion effects are insignificant with large numbers of partcles. When I work with pressure it is as a continuous variable that can take on any value.



https://en.wikipedia.org/wiki/Continuum_mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century.

Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. Fundamental physical laws such as the conservation of mass, the conservation of momentum, and the conservation of energy may be applied to such models to derive differential equations describing the behavior of such objects, and some information about the particular material studied is added through constitutive relations.

https://en.wikipedia.org/wiki/Statistical_mechanics

Statistical mechanics is one of the pillars of modern physics. It is necessary for the fundamental study of any physical system that has a large degree of freedom. The approach is based on statistical methods, probability theory and the microscopic physical laws. [1][2][3][note 1]

The primary goal of statistical thermodynamics (also known as equilibrium statistical mechanics) is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles and the interactions between them. In other words, statistical thermodynamics provides a connection between the macroscopic properties of materials in thermodynamic equilibrium, and the microscopic behaviours and motions occurring inside the material

Nobody has said that you cannot calculate the mass by multiplicating number of atoms with their individual mass.
It was your argument that velocity isnt quantized that got shot down.
Dont muddle the water..

 

[Jokodo]

Got it. A block of aluminum comprised of discrete atoms is infinitley divisble. The weight of the block can chnage other than by multiples of atoms. The weight can be more or less than the sum of the quantized mass of atoms.

Nobody said so.

The energy in a gas comprised of atoms can change by any amount, not limited by the discrete energy of the individual atoms..

You have not provided a reason to believe that the "discrete energy of the individual atom" is a thing.

The total energy of the gas can be more or less than the sum of the discrete energy of the atoms.

The total energy of the gas is exactly the sum of the energy of the atoms, but those energies are not discrete.

Ol. You win.Arithmetic, addition and subtraction, does not apply to atoms....

How then do I calculate the total mass of a block of aluminum given the number of atoms and how do I calculate the total klinetic energy energy of a sas in a tank?

The total kinetic energy of gas in a tank is the sum of the kinetic energy of the individual molecules. Each individual atom's kinetic energy is determined by its mass and its velocity, with mass, but not velocity, being a constant determined by the type of molecule.

The chemical equation for cburing hydrogen will show a balnce of atoms and energy, discrte atoms and discrete energy.

True, the energy released in burning to molecules of hydrogen and one molecule of oxygen to produce two molecules of water is constant. But that does not imply that the kinetic energy in a tank can only vary in discrete steps. The energy of that reaction does not typically all go to accelerating one and only one molecule. The momentum gained or lost in any collision between two atoms/molecules, or between an atom and the encasing, varies not only with the atom's mass and 'absolute' velocity, but crucially with their relative velocity, thus the angle between their movement vectors in any frame in which they're both in motion. Claiming that individual atoms can only accelerate in discrete steps is claiming that angles are discrete, and you have yet to even make an attempt to argue this is the case, let alone convince anybody.

You are looking at it as ca continuum. It works as long as there are many partcles. We treat variables as continuous because quantizatrion effects are insignificant with large numbers of partcles. When I work with pressure it is as a continuous variable that can take on any value.

No. You treat it as a continuous variable because it is a continuous variable. Pressure is force per square meter, or energy per second per square meter. Even if energy were quantized, which to repeat you have provided no argument for, that still wouldn't let you conclude that pressure is.

https://en.wikipedia.org/wiki/Continuum_mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century.

Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. Fundamental physical laws such as the conservation of mass, the conservation of momentum, and the conservation of energy may be applied to such models to derive differential equations describing the behavior of such objects, and some information about the particular material studied is added through constitutive relations.

https://en.wikipedia.org/wiki/Statistical_mechanics

Statistical mechanics is one of the pillars of modern physics. It is necessary for the fundamental study of any physical system that has a large degree of freedom. The approach is based on statistical methods, probability theory and the microscopic physical laws. [1][2][3][note 1]

The primary goal of statistical thermodynamics (also known as equilibrium statistical mechanics) is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles and the interactions between them. In other words, statistical thermodynamics provides a connection between the macroscopic properties of materials in thermodynamic equilibrium, and the microscopic behaviours and motions occurring inside the material

None of that states that the motions of the particles inside the material are occuring at discrete velocitiese.

 

[steve_bank]

Got it. A block of aluminum comprised of discrete atoms is infinitley divisble. The weight of the block can chnage other than by multiples of atoms. The weight can be more or less than the sum of the quantized mass of atoms.

The energy in a gas comprised of atoms can change by any amount, not limited by the discrete energy of the individual atoms.. The total energy of the gas can be more or less than the sum of the discrete energy of the atoms.

Ol. You win.Arithmetic, addition and subtraction, does not apply to atoms....

How then do I calculate the total mass of a block of aluminum given the number of atoms and how do I calculate the total klinetic energy energy of a sas in a tank?

The chemical equation for cburing hydrogen will show a balnce of atoms and energy, discrte atoms and discrete energy.

You are looking at it as ca continuum. It works as long as there are many partcles. We treat variables as continuous because quantizatrion effects are insignificant with large numbers of partcles. When I work with pressure it is as a continuous variable that can take on any value.



https://en.wikipedia.org/wiki/Continuum_mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century.

Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. Fundamental physical laws such as the conservation of mass, the conservation of momentum, and the conservation of energy may be applied to such models to derive differential equations describing the behavior of such objects, and some information about the particular material studied is added through constitutive relations.

https://en.wikipedia.org/wiki/Statistical_mechanics

Statistical mechanics is one of the pillars of modern physics. It is necessary for the fundamental study of any physical system that has a large degree of freedom. The approach is based on statistical methods, probability theory and the microscopic physical laws. [1][2][3][note 1]

The primary goal of statistical thermodynamics (also known as equilibrium statistical mechanics) is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles and the interactions between them. In other words, statistical thermodynamics provides a connection between the macroscopic properties of materials in thermodynamic equilibrium, and the microscopic behaviours and motions occurring inside the material

Nobody has said that you cannot calculate the mass by multiplicating number of atoms with their individual mass.
It was your argument that velocity isnt quantized that got shot down.
Dont muddle the water..

If matter is quantized at the atomic level by both matter and energy then energy and mass can only incremnt in atomic multiples. Therefore energy can only be transferred in quantized steps.

 

[steve_bank]

jokodo your are tryimg to get around the obvious conclusion with not so elegant metaphysics.

You have not provided a reason to believe that the "discrete energy of the individual atom" is a thing.

Take a modern physics class or read a book, Modern Physics by Tippler is a good read, old editions are cheap. How does science prove anything? You are rejecting quantum physics, strange for someone with a masters that says since in the title.

I am not inventing anything, mostly black and white testbook .

Here it is. From statistical mechanics Newtonian pressure is the mass density, number of atoms or molecules per volume, multiplied by the average particle velocity squared. I'd forgotten equipartition of energy, total energy of a particle is distributed among degrees of freedom.

https://ocw.mit.edu/high-school/phy...deal-gases/8_01t_fall_2004_w12d1_class_29.pdf

Read the link. In a block of aluminum the total kinetic energy in the block wen moving is velocity squared times the mass of one atom times the nimber of atoms.

In a gas it is the mass density times average particle velocity squared.

Energy is quantized. Velocity can only change in discrete steps of quantized energy.

Contemplate the difference between continuum mechanics and particle statistical mechanics.

 

[Jokodo]

jokodo your are tryimg to get around the obvious conclusion with not so elegant metaphysics.

You badly wanting it to be the case doesn't make something an "obvious conclusion".

You have not provided a reason to believe that the "discrete energy of the individual atom" is a thing.

Take a modern physics class or read a book, Modern Physics by Tippler is a good read, old editions are cheap. How does science prove anything? You are rejecting quantum physics, strange for someone with a masters that says since in the title.

Please point out where I'm doing so.

I am not inventing anything, mostly black and white testbook .

Here it is. From statistical mechanics Newtonian pressure is the mass density, number of atoms or molecules per volume, multiplied by the average particle velocity squared. I'd forgotten equipartition of energy, total energy of a particle is distributed among degrees of freedom.

https://ocw.mit.edu/high-school/phy...deal-gases/8_01t_fall_2004_w12d1_class_29.pdf

Read the link.

I did. It doesn't say that individual or average velocities can only increase in discrete steps. If you think it does, would you be so kind as to point out on which page you find that claim being made?

In a block of aluminum the total kinetic energy in the block wen moving is velocity squared times the mass of one atom times the nimber of atoms.

Indeed. I never said otherwise.

In a gas it is the mass density times average particle velocity squared.

Density is not number of atoms, it's number of atoms per cubic metre. Even if you'd shown that energy is quantized (which you haven't), this doesn't show that pressure is unless you can provide evidence that space, too, is quantized.

Energy is quantized. Velocity can only change in discrete steps of quantized energy.

Now this is an unsupported claim. Velocities after an impact depend not only on the initial 'absolute' velocities (if such a pre-relativistic concept had any merit), but specifically on their relative velocities and thus the angle at which they're meeting. So even in a purely Newtonian universe, angles would have to be quantized for velocities to be. In a relativistic universe, the concept of quantized velocities doesn't even compute.

 

[Jokodo]

Got it. A block of aluminum comprised of discrete atoms is infinitley divisble. The weight of the block can chnage other than by multiples of atoms. The weight can be more or less than the sum of the quantized mass of atoms.

The energy in a gas comprised of atoms can change by any amount, not limited by the discrete energy of the individual atoms.. The total energy of the gas can be more or less than the sum of the discrete energy of the atoms.

Ol. You win.Arithmetic, addition and subtraction, does not apply to atoms....

How then do I calculate the total mass of a block of aluminum given the number of atoms and how do I calculate the total klinetic energy energy of a sas in a tank?

The chemical equation for cburing hydrogen will show a balnce of atoms and energy, discrte atoms and discrete energy.

You are looking at it as ca continuum. It works as long as there are many partcles. We treat variables as continuous because quantizatrion effects are insignificant with large numbers of partcles. When I work with pressure it is as a continuous variable that can take on any value.



https://en.wikipedia.org/wiki/Continuum_mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century.

Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. Fundamental physical laws such as the conservation of mass, the conservation of momentum, and the conservation of energy may be applied to such models to derive differential equations describing the behavior of such objects, and some information about the particular material studied is added through constitutive relations.

https://en.wikipedia.org/wiki/Statistical_mechanics

Statistical mechanics is one of the pillars of modern physics. It is necessary for the fundamental study of any physical system that has a large degree of freedom. The approach is based on statistical methods, probability theory and the microscopic physical laws. [1][2][3][note 1]

The primary goal of statistical thermodynamics (also known as equilibrium statistical mechanics) is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles and the interactions between them. In other words, statistical thermodynamics provides a connection between the macroscopic properties of materials in thermodynamic equilibrium, and the microscopic behaviours and motions occurring inside the material

Nobody has said that you cannot calculate the mass by multiplicating number of atoms with their individual mass.
It was your argument that velocity isnt quantized that got shot down.
Dont muddle the water..

If matter is quantized at the atomic level by both matter and energy then energy and mass can only incremnt in atomic multiples. Therefore energy can only be transferred in quantized steps.

If the sky is blue and the ocean is red, then the Earth's core must be pure gold. Are you denying the sky is blue?

See, two can play the game of using a trivial fact and an unwarranted premise to draw a conclusion that wouldn't follow even in the premises were true -- and then pretend that the other person is denying the trivial fact!

 

[steve_bank]

At this point you're either being a troll or you lack basic science foundations such as Newtonian/classical mechanics. Without that statistica and quantum l mechanics will seem incomprehensible.

Take the time to read and comprehend the links on continuum mechanics, statistical mechanics, and the link applying statistical
mechanics to a gas. This is mainstream engineering.The last link shows how Newton's laws of motion are derived from particles. The basis for continuum, Newtonian, mechanics is in statistical mechanics as stated in the link.

The link directly answers your request for an equation. If you can not follow the derivations then you are lacking foundation. I expect tjhat is what you Aare struggling against.

The pressure on the tank wall is based on particle average velocity and th integer number of atoms, mass density. If you can't make the leap from energy being determined by integer numbers of atoms to energy being quantized, then that is your problem.

I could work the statistical mechanics equations to show energy can only change in steps of atoms, same as I showed dv/DE before but you would just ignore it. Have you had and used differential equations undergrad

Go ahead, refute textbook statistical mechanics.?

 

[Jokodo]

At this point you're either being a troll or you lack basic science foundations such as Newtonian/classical mechanics. Without that statistica and quantum l mechanics will seem incomprehensible.

Take the time to read and comprehend the links on continuum mechanics, statistical mechanics, and the link applying statistical
mechanics to a gas. This is mainstream engineering.The last link shows how Newton's laws of motion are derived from particles. The basis for continuum, Newtonian, mechanics is in statistical mechanics as stated in the link.

The link directly answers your request for an equation. If you can not follow the derivations then you are lacking foundation. I expect tjhat is what you Aare struggling against.

The pressure on the tank wall is based on particle average velocity and th integer number of atoms, mass density. If you can't make the leap from energy being determined by integer numbers of atoms to energy being quantized, then that is your problem.

I could work the statistical mechanics equations to show energy can only change in steps of atoms, same as I showed dv/DE before but you would just ignore it. Have you had and used differential equations undergrad

Go ahead, refute textbook statistical mechanics.?

Energy is not measured in atoms. Nor is it determined by the number of atoms alone.

If you think the link answers my questions (whatever they may be), you sure can point out where it does so? I made no request for formulae, I know some of them and can look up the others alright if I feel a need to do so. I did not request an equation, I requested an argument that kinetic energy is quantized. (And, possibly, a formulation that allows kinetic energy to be quantized while still being compatible with relativity. Do you know of one?) An equation from which this follows would serve as an argument alright, but, as far as either of us can tell, your link does not contain any such equation.

I'm not the one trying to refute textbook mechanics, you are.

 

[steve_bank]

At this point you're either being a troll or you lack basic science foundations such as Newtonian/classical mechanics. Without that statistica and quantum l mechanics will seem incomprehensible.

Take the time to read and comprehend the links on continuum mechanics, statistical mechanics, and the link applying statistical
mechanics to a gas. This is mainstream engineering.The last link shows how Newton's laws of motion are derived from particles. The basis for continuum, Newtonian, mechanics is in statistical mechanics as stated in the link.

The link directly answers your request for an equation. If you can not follow the derivations then you are lacking foundation. I expect tjhat is what you Aare struggling against.

The pressure on the tank wall is based on particle average velocity and th integer number of atoms, mass density. If you can't make the leap from energy being determined by integer numbers of atoms to energy being quantized, then that is your problem.

I could work the statistical mechanics equations to show energy can only change in steps of atoms, same as I showed dv/DE before but you would just ignore it. Have you had and used differential equations undergrad

Go ahead, refute textbook statistical mechanics.?

Energy is not measured in atoms. Nor is it determined by the number of atoms alone.

If you think the link answers my questions (whatever they may be), you sure can point out where it does so? I made no request for formulae, I know some of them and can look up the others alright if I feel a need to do so. I did not request an equation, I requested an argument that kinetic energy is quantized. (And, possibly, a formulation that allows kinetic energy to be quantized while still being compatible with relativity. Do you know of one?) An equation from which this follows would serve as an argument alright, but, as far as either of us can tell, your link does not contain any such equation.

I'm not the one trying to refute textbook mechanics, you are.

The energy of a gas is the sum of individual kinetic energy of each atom. Each atom has mass, see the Periodic Table. Each atom has kinetic energy 0.5 mass x velocity squared. Each atom has a discrete individual kinetic energy.

Take a bag of ball bearings and throw ity. Ignoring the bag each ball has its individual discrete energy. The total energy is the sum of each ball. The kinetic energy in the bag can only change in increments of balls when thrown. The kinetic energy of a gas can only change in groups of atoms. Pressure is the sum of all the 'balls' in the gas. This is what you reject.

Get a book on classical mechanics and read it cover to cover. Then get a modern physics text. You do not seem to have the basic science vocabulary.

Good luck on your science journey.

Addung

The last link does answer your question about pressure.

Scroll down to where pressure = ..

As a continuum 1/2 mv^2 mass is a continuous variable, put someting on a scale and weigh it/

In statistical mechanics of particles mass becomes the sum of the individual masses of the atoms in the gas and velocity becomes the average velocity of all the atoms. At that point mass can only change in multiples of atoms, as a result total energy can only be changed in multiples of atoms. For constant mass a change in velocity caused by an increase in the temperature of the has is quantized as well, same analysis as the derivation. Heat is molecular vibration, as such quantized by atoms. Pressure is the average velocity times sum of the masses. Dimensionally it will work out to Newtons/m^2, Pascals. The average force from many atoms striking the wall.

You can try and offer an alternative analysis.

 

[Jokodo]

At this point you're either being a troll or you lack basic science foundations such as Newtonian/classical mechanics. Without that statistica and quantum l mechanics will seem incomprehensible.

Take the time to read and comprehend the links on continuum mechanics, statistical mechanics, and the link applying statistical
mechanics to a gas. This is mainstream engineering.The last link shows how Newton's laws of motion are derived from particles. The basis for continuum, Newtonian, mechanics is in statistical mechanics as stated in the link.

The link directly answers your request for an equation. If you can not follow the derivations then you are lacking foundation. I expect tjhat is what you Aare struggling against.

The pressure on the tank wall is based on particle average velocity and th integer number of atoms, mass density. If you can't make the leap from energy being determined by integer numbers of atoms to energy being quantized, then that is your problem.

I could work the statistical mechanics equations to show energy can only change in steps of atoms, same as I showed dv/DE before but you would just ignore it. Have you had and used differential equations undergrad

Go ahead, refute textbook statistical mechanics.?

Energy is not measured in atoms. Nor is it determined by the number of atoms alone.

If you think the link answers my questions (whatever they may be), you sure can point out where it does so? I made no request for formulae, I know some of them and can look up the others alright if I feel a need to do so. I did not request an equation, I requested an argument that kinetic energy is quantized. (And, possibly, a formulation that allows kinetic energy to be quantized while still being compatible with relativity. Do you know of one?) An equation from which this follows would serve as an argument alright, but, as far as either of us can tell, your link does not contain any such equation.

I'm not the one trying to refute textbook mechanics, you are.

The energy of a gas is the sum of individual kinetic energy of each atom. Each atom has mass, see the Periodic Table. Each atom has kinetic energy 0.5 mass x velocity squared. Each atom has a discrete individual kinetic energy.

Take a bag of ball bearings and throw ity. Ignoring the bag each ball has its individual discrete energy. The total energy is the sum of each ball. The kinetic energy in the bag can only change in increments of balls when thrown. The kinetic energy of a gas can only change in groups of atoms. Pressure is the sum of all the 'balls' in the gas. This is what you reject.

I reject it because it's gibberish. You switch back and forth between equating pressure with mass and equating pressure with energy. Pressure is measured in Pascals. 1 Pascal is per definition 1 kg⋅m⁻¹⋅s⁻², or 1 J⋅m⁻³. Saying that mass is quantized (or even energy is quantized, for which you have provided no argument), therefore pressure is is like saying since 2 is a natural number, 2 * pi has to be a natural number.

Get a book on classical mechanics and read it cover to cover. Then get a modern physics text. You do not seem to have the basic science vocabulary.

Good luck on your science journey.

Says the guy who seems to think that pressure is measured in kilograms...

 

[Jokodo]

In statistical mechanics of particles mass becomes the sum of the individual masses of the atoms in the gas and velocity becomes the average velocity of all the atoms.

indeed.

At that point mass can only change in multiples of atoms, as a result total energy can only be changed in multiples of atoms.

Does not follow

For constant mass a change in velocity caused by an increase in the temperature of the has is quantized as well, same analysis as the derivation.

Does not follow.

Heat is molecular vibration, as such quantized by atoms.

Does not follow.

Pressure is the average velocity times sum of the masses.

No, it isn't. It's the square of the average velocity times the sum of the masses divided by m^3.

Dimensionally it will work out to Newtons/m^2, Pascals. The average force from many atoms striking the wall.

You can try and offer an alternative analysis.

How about you just look up this stuff yourself?

 

[steve_bank]

Kinetic energy of the gas = 0.5 * ( summ of mass of atoms) * (average velocity)^2 Energy is quantized by individual atoms.

From SI the Pascal = force/area = Newtons/m^2.

The motions of the atoms are random. There is no continuous pressure on the walls. There are probabilities of number of collisions with the wall per second.

m = mass of particles
n = number of particles
p = momentum
F = force in Newtons
rho = n*m/V mass density, mas per unit volume
P = F/A pressure force per unit area F
v = average particle velocity
A = area

Newton's 2nd law

p = mv
F = dp/dt = rho * A * v^2

Newton's 3rd law equal and opposite reaction. Collision with the wal results in an equal but opposite reaction, force in Newtons on the wall.

Fwall = -Fgas = rho * A * v^2
F/A = rho * v^2

F/A = pressure = rho * v^2

rho varies in multiples of atoms, therefore pressure is quantized by atoms. Direct application of Newton's Laws.


The result of random collisions of discrete atoms each with a finite energy creates a force per unit area the Pacal Newtons/m^2

So that is what statistical mechanics is all about, learn something new every day. If you want to refute Newton, be my guest.

 

[steve_bank]

indeed.


Does not follow

For constant mass a change in velocity caused by an increase in the temperature of the has is quantized as well, same analysis as the derivation.

Does not follow.

Heat is molecular vibration, as such quantized by atoms.

Does not follow.

Pressure is the average velocity times sum of the masses.

No, it isn't. It's the square of the average velocity times the sum of the masses divided by m^3.

Dimensionally it will work out to Newtons/m^2, Pascals. The average force from many atoms striking the wall.

You can try and offer an alternative analysis.

How about you just look up this stuff yourself?

You are a real trip. Either a troll or lacking in basic physics and thermodynamics.



What is heat and how does it propagate through a sold mass? Hint... statistical mechanics.

 

[Jokodo]

indeed.


Does not follow



Does not follow.


Does not follow.

Pressure is the average velocity times sum of the masses.

No, it isn't. It's the square of the average velocity times the sum of the masses divided by m^3.

Dimensionally it will work out to Newtons/m^2, Pascals. The average force from many atoms striking the wall.

You can try and offer an alternative analysis.

How about you just look up this stuff yourself?

You are a real trip. Either a troll or lacking in basic physics and thermodynamics.



What is heat and how does it propagate through a sold mass? Hint... statistical mechanics.

That does not imply energy, much less pressure, is quantized. If you think it does, show your work and collect your Nobel.

 

[Jokodo]

Kinetic energy of the gas = 0.5 * ( summ of mass of atoms) * (average velocity)^2 Energy is quantized by individual atoms.

From SI the Pascal = force/area = Newtons/m^2.

The motions of the atoms are random. There is no continuous pressure on the walls. There are probabilities of number of collisions with the wall per second.

m = mass of particles
n = number of particles
p = momentum
F = force in Newtons
rho = n*m/V mass density, mas per unit volume
P = F/A pressure force per unit area F
v = average particle velocity
A = area

Newton's 2nd law

p = mv
F = dp/dt = rho * A * v^2

Newton's 3rd law equal and opposite reaction. Collision with the wal results in an equal but opposite reaction, force in Newtons on the wall.

Fwall = -Fgas = rho * A * v^2
F/A = rho * v^2

F/A = pressure = rho * v^2

rho varies in multiples of atoms,

You just quoted a definition as mass per unit volume! Are you forgetting V, or claiming it too varies in multiples of atoms?

therefore pressure is quantized by atoms.

... If we ignore it's also determined by velocity and volume, yes. Why should we?

Direct application of Newton's Laws.


The result of random collisions of discrete atoms each with a finite energy creates a force per unit area the Pacal Newtons/m^2

So that is what statistical mechanics is all about, learn something new every day. If you want to refute Newton, be my guest.

You're not telling me anything new. Talking about refuting Newton, are you perchance denying that the amount of momentum transferred in an elastic collision depends on relative velocity? That relative velocity depends on the angle between two vectors?

 

[steve_bank]

I know what you are saying, same issue as with electrons and current. You are back into the issue with reals and integers. Current is continuous because velocity is continuous. Multiplying a sum of discrete objects by a non integer real number does not make the result continuous,it does not make the quantized objects continuous.

1kg x 1.43218743759374 results in a continuous real number. As a continuum we treat the 1kg as continuous and infinitely divisible. In reality the kg is quantized. The quantization is undetectable at the macro continuum level. That is Newtonian mechanics.

n = number of particles.
m - atomic mass
total mass = n*m.

The total mass of a gas is m*n. Mass is quantized. Velocity is the average of all paericle velocities.

Two ways to change energy and pressure.

At constant temperature add more atoms and equilibrium is reestablished. Velocity is constant so total energy increases in multiples of atoms.

To change gas energy at constant mass , energy has to be added to the tank. Heat the tank with coal and coal is composed of atoms with thermal energy per atom. You are thinking continuum mechanics. 1 atom of carbon = x joules of heat. 2 atoms of carbon = 2x joules of heat. The step is not continuous and divisible. Heat is quantized.

Energy either organic or nuclear is per atom. Thenenergy in a waterfall driving a turbine can only chnges in multiples of molecules.



E = 1/2 mv^2
dv = [2/m]^1/2 * [1/2E^1/2] dE

A finire change in energy DE yields a finite change in velocity dv. dE is quantized unless you can cite an example of of an energy source that is not quantized.



The link shows pressure is quantized. Where is a continuous infinitely divisible energy source? No hand waving, an example. How can velocity change continuously when energy is quantized?


Energy is quantized, therefore energy transfer to a particle is quantized. The dv is so small we treat velocity as a continuum.

In combustion heat is released by breaking discrete bonds and discrete changes of state in the atoms. Combustion is quantized. Heat of combustion is KJ/mole. Quantized.

heat transfer q = mcdt Heat transfer is quantized by mass. Heat conducts from atom to atom.

https://en.wikipedia.org/wiki/Combustion