Kinetic+potential+internal; also, Joules

[moouers]

Pardon my simple question, but I'd like some general intuition on what I'm reading in the thermochemistry section of my chemistry textbook (I'm posting the question here because it seems more related to physics, but if it needs to be moved, that's OK).

All right, I'm reading that: Total energy = kinetic energy + potential energy + internal energy.

That's great, I get that, and I get the relationship between kinetic energy and potential energy, and I understand that internal energy is the energy of the particles. But I don't see the relationship of internal to either kinetic or potential; does there have to be a relationship? Can internal energy be transformed into kinetic or potential energy of the whole system, or are they completely separate? I can't imagine a case where it can, but maybe someone here can explain it better.

In other words, if an object/substance has zero kinetic energy, and zero potential energy, and some amount of internal energy, can that internal energy be transformed into kinetic or potential energy of that object/substance? Or can kinetic and potential energy only be added to that same object through energy transfer from an outside source (my body/hand expending energy to lift it up, then dropping it, for example)? My intuition wants to say this is correct, but maybe there's some case I'm not considering where this isn't necessarily the case.

Now, about the Joules question. What does it mean to have 1 kg$\bullet$m²/s²? In plain English, what does it mean? The energy required to move one kilogram one meter squared (what?) per second squared (huh?). If my question needs clarification, let me know and I'll do my best to reword it.

Thanks in advance. Please don't be too harsh! Haven't taken any physics, and we haven't had lecture on this material yet.

 

[DennisN]

Hi moouers! I'm really lousy at chemistry , but I can provide some answers. The joule (J) is equal to the energy used when applying a force of one Newton (N) through a distance of one metre (m). So, 1 J = 1 N*m. The Newton is the force required to accelerate a mass of one kilogram at a rate of one metre per second squared. So, 1 N = 1 kg * m/s².

Joined together; 1 J = 1 N*m = 1 kg*m²/s².

So in short, the Joule is the energy used when 1 kg is moved 1 m with the acceleration 1 m/s². I will try to answer your main question too, I just have to think it through properly first.

 

[moouers]

Dennis, thank you for the explanation for joules. Very, very helpful!

 

[DennisN]

Here's the second reply; It has been a long time since I studied thermodynamics, so I had to check up on the definitions (otherwise I might confuse you if I start to talk about other physics, and I'd like to avoid that if I can ).

In thermodynamics, it seems to me the internal energy = the total energy = kinetic energy + potential energy.

So I'm confused where you got (Total energy = kinetic energy + potential energy + internal energy) from, but I don't have your book in front of me .

There is something called total energy in special relativity, but I guess that's not what you are after? (where a particle/object has a total energy = rest energy + kinetic energy).

 

[moouers]

Hi Dennis,

My book states: "The sum of the kinetic and potential energies of the particles [I read this as NOT of the system, just the particles] making up a substance is referred to as the internal energy, U, of the substance," where, "E_tot=E_k+E_p+U." It goes on to say, "Normally when you study a substance in the laboratory, the substance is at rest in a vessel. Its kinetic energy as a whole is zero. Moreover, its potential energy as a whole is constant, and you can take it to be zero. In this case, the total energy of the substance equals its internal energy, U."

Oh, and don't be afraid to bring physics into your explanations. For example, I don't use the Newton unit as of yet in chemistry, but it sure helped that you used it in your explanation!

 

[juanrga]

Pardon my simple question, but I'd like some general intuition on what I'm reading in the thermochemistry section of my chemistry textbook (I'm posting the question here because it seems more related to physics, but if it needs to be moved, that's OK).

All right, I'm reading that: Total energy = kinetic energy + potential energy + internal energy.

That's great, I get that, and I get the relationship between kinetic energy and potential energy, and I understand that internal energy is the energy of the particles. But I don't see the relationship of internal to either kinetic or potential; does there have to be a relationship? Can internal energy be transformed into kinetic or potential energy of the whole system, or are they completely separate? I can't imagine a case where it can, but maybe someone here can explain it better.

In other words, if an object/substance has zero kinetic energy, and zero potential energy, and some amount of internal energy, can that internal energy be transformed into kinetic or potential energy of that object/substance? Or can kinetic and potential energy only be added to that same object through energy transfer from an outside source (my body/hand expending energy to lift it up, then dropping it, for example)? My intuition wants to say this is correct, but maybe there's some case I'm not considering where this isn't necessarily the case.

Now, about the Joules question. What does it mean to have 1 kg$\bullet$m²/s²? In plain English, what does it mean? The energy required to move one kilogram one meter squared (what?) per second squared (huh?). If my question needs clarification, let me know and I'll do my best to reword it.

Thanks in advance. Please don't be too harsh! Haven't taken any physics, and we haven't had lecture on this material yet.

Yes, total energy = kinetic energy + potential energy + internal energy.

Yes internal energy can be transformed into kinetic or potential energy and back by virtue of conservation of total energy. For instance, if internal energy is produced by some process then mechanical energy (kinetic+potential) decreases by the same amount.

About Joules the [kg m²/s²] in plain English means that energy has units of mass times speed squared. I.e. a Joule is the (non-relativistic kinetic) energy that has pointlike free particle of mass 1 kg moving with a speed of 1 m/s. Remember the formula for kinetic energy!

 

[DennisN]

Well moouers, what your book states makes sense to me. I interpret it this way; for the whole substance (normally) E_tot = U ( Total energy = internal energy) since

E_k = 0 (no kinetic energy, since the substance does not move)
E_p = 0 (no potential energy, since it is at ground level "zero" (no gravitational potential to consider) and in no electrical field etc.)

So, from the view of the substance as a whole at the macroscopic level, total energy = internal energy.

For the particles in the substance (at the microscopic level): The substance is made up of particles having a total internal energy U. These individual particles all have kinetic energy and/or potential energy which added together equals U. These kinetic and potential energies are e.g.

Kinetic energies: Translational, rotational and vibrational energies of molecules.
Potential energies: Potential energy associated with the intermolecular attractive forces.

The confusion that arose seems to be from a slight mix of the macroscopic view with the microscopic view.

Descriptions from HyperPhysics (thermodynamics):
Internal Energy
Internal energy on the microscopic scale
Internal Energy Example
Internal Energy relations

Note from me: Now, there are other types of energies in Physics on the atomic/subatomic scale (e.g. electron binding energy, nuclear binding energy, rest energy etc.) but these are beyond the scope of standard thermochemistry/thermodynamics, so they don't need to be considered. If we went "superphysical", the internal energy would be the sum of all energies at all levels, but that is far beyond the scope of what we are talking about.

 

[moouers]

Dennis, I think you're right that I was just mixing up the macroscopic view with the microscopic view.

From one of your links: "If the water were tossed across the room, this microscopic energy would not necessarily be changed when we superimpose an ordered large scale motion on the water as a whole."

Thank you so much! This exactly answered my question, and combined with all the other links you provided, I feel I have a much better grasp on the happenings I originally posted about. Can't say "thank you" enough.

One thing that gets me though, and I keep reading it, is how the movement of molecules is considered random, such as in the sentence: "Internal energy is defined as the energy associated with the random, disordered motion of molecules."

It's not actually random though, correct? If we had the capacity to keep track of all particles and their properties at all times, wouldn't we be able to describe the movements of surrounding particles in a cause-and-effect manner? Does that make sense? Please correct me if I'm mistaken.

 

[moouers]

Yes internal energy can be transformed into kinetic or potential energy and back by virtue of conservation of total energy. For instance, if internal energy is produced by some process then mechanical energy (kinetic+potential) decreases by the same amount.

That would be if total energy of the system remains unchanged, right? But if energy is added into or out of the system, the internal energy doesn't necessarily HAVE to change?

Thanks for your response!

 

[DennisN]

Thanks, moouers, I'm glad I could help out . But I forgot your original question:

"In other words, if an object/substance has zero kinetic energy, and zero potential energy, and some amount of internal energy, can that internal energy be transformed into kinetic or potential energy of that object/substance?"

Yes. If a chemical reaction between two substances will produce e.g. heat/pressure, this energy can be used to e.g. move the substance (adding kinetic energy to the substance/object) or e.g. lift the substance/object (adding gravitational potential energy). Internal energy would be transformed into kinetic and/or potential energy. A rocket is a simple, good example. Just a simple physics example, sorry, I'm lousy at chemistry . I will reply to your last question to me as well soon.

 

[DennisN]

"Internal energy is defined as the energy associated with the random, disordered motion of molecules." It's not actually random though, correct? If we had the capacity to keep track of all particles and their properties at all times, wouldn't we be able to describe the movements of surrounding particles in a cause-and-effect manner?

You are theoretically correct. But there are several practical issues, which leads us to view the motion of molecules as random, e.g. the molecules in a hot gas would be very, very difficult to track. This means we have to use probability models (e.g. Brownian motion) to model the behavior. This is also somewhat related to Chaos theory, the study of dynamical systems that are highly sensitive to initial conditions. To sum it up; a small error in the estimation of the initial condition of a single molecule would, as time passes, lead to a large error in the estimation of the condition of all molecules, since molecules collide with each other. Roughly speaking, this is why we can't make perfect weather forecasts; it's a shame, but that's how nature works .

On the atomic/subatomic scale, there's another issue that's even more fundamental. Here, something called the Uncertainty Principle sets physical limits for what we can measure accurately (e.g. we can't measure position and momentum perfectly at the same time). This is related to why measurements on this scale are probabilistic. But now I'm getting quite far ahead of the subject...

 

[DennisN]

moouers, I will reply to your question to juanrga too.

That would be if total energy of the system remains unchanged, right? But if energy is added into or out of the system, the internal energy doesn't necessarily HAVE to change?

Yes it has, the energy has to go somewhere. If you add energy into the system (substance), e.g. heat it up with something, you introduce another thing, a heating system. Now, from a physical viewpoint you have a new system with the substance and a heating system. The total energy of this entire system is always conserved, due to the Conservation of Energy principle. So the energy you remove from the heating system will be transformed to kinetic energy of the substance (heat energy) (some energy will of course also be lost to the surroundings; then we have to start to view it from a larger perspective, e.g. the total energy in a room with the substance and the heater, the air etc.). If we consider a substance and a perfect lossless heating system (as a combined perfectly isolated system), the following rules will apply:

E_T = E_H + U = E_H + E_K + E_P, where

E_T = total energy of system (substance + heating system)
E_H = energy of the heating system
U = internal energy of the substance
E_K = kinetic energy of the particles in the substance
E_P = potential energy of the particles in the substance

I introduced some new variables on-the-fly here, hope I didn't confuse you .

 

[ZealScience]

The OP's notions are quite strange, since kinetic or potential determines the energy is due to motion or position. But internal refers actually to the scale of the energy. e.g Mechanical energy is on the scale of massive objects (including kinetic, gravitational potential, elastic potential, etc.); internal refers to molecular scale (molecular kinetic, potential); electrical describes energy due to electric fields (electrical potential, etc.)

In fact, into advanced physics, Schrodinger's Equation for example, simply uses the fact that total energy is kinetic plus potential (Hψ=Kψ+Vψ)

 

[juanrga]

That would be if total energy of the system remains unchanged, right? But if energy is added into or out of the system, the internal energy doesn't necessarily HAVE to change?

Thanks for your response!

No. Conservation of energy does not imply that energy remains unchanged. The balance law in the formalism of modern thermodynamics is dE = d_iE + d_eE. The first term describes production of total energy and the second flow with surrounds. Total energy conservation implies d_iE=0. That is the variation of total energy is due to flows with surrounds.

The relation with mechanical energy (K+V) and internal energy is E = U + K + V, therefore

d_iE = 0 = d_iU + d_i(K+V)

Neither internal energy nor mechanical energy are conserved (in general). Any process that changes the production of internal energy will be compensated by a change in the production of mechanical energy (kinetic plus potential).

 

[moouers]

You folks are awesome. Thank you all so much.