Open, closed, and isolated systems

[juanrga]

In agreement with one administrator I am posting this here. The topic is multidisciplinary but my main doubts are for physicists.

 

I have just uploaded a draft about Open, closed, and isolated systems.

 

I am using the standard terminology, although, in the discussion section, I notice that some physicists use a coarse-grained terminology. I suppose that their terminology is motivated by their lack of interest in problems of chemical or biological interest. I do not recommend the use of this coarse-grained terminology, because I do not find any reason for using it. If someone disagree, please state your views.

 

I also criticize the textbook by physicists Walter Greiner, Ludwig Neise, & Horst Stöcker. They seem to be confused about the laws of conservation of matter and energy. For instance, they claim that the particle number is conserved in closed systems, but this is clearly wrong in presence of chemical reactions. I would like to see your points, specially because it seems that a part of physics literature confounds conservation laws (i.e. zero production) with 'invariance' or 'time-independence'.

 

The part about atoms in molecules will be changed after the comments sent by Prof. Chérif F. Matta.

 

I would like to receive further review, comments, and suggestions.

Edited April 21, 2012 by juanrga

[studiot]

1) I agree that number of participating particles is not necessarilly preserved.

 

2) The idea of an isolated system is seductively attractive. But is the statement "Does not interact in any way" a bit strong? Even a complete vacuum devoid of any matter has a characteristic impedence of 377 ohms and interacts with EM radiation through this.

Edited April 21, 2012 by studiot

[juanrga]

1) I agree that number of participating particles is not necessarilly preserved.

 

Thank you.

 

2) The idea of an isolated system is seductively attractive. But is the statement "Does not interact in any way" a bit strong? Even a complete vacuum devoid of any matter has a characteristic impedence of 377 ohms and interacts with EM radiation through this.

 

If the system interact in some way, then it is not isolated, but closed or open.

 

Greiner, Neise, & Stöcker write in their textbook:

 

It is obvious that at least the isolated system is an idealization, since in reality an exchange of energy with surrounds cannot be prevented in the strict sense.

 

Initially I was ready to add their remark to the article, but finally I did not because I disagree. The universe as a whole is, by definition an isolated system. This is not an idealization.

 

Thank you very much. After reading your comment about isolated systems I think that I will add these thoughts to the article, explaining why the concept of isolated system is not an idealization and giving as example of an isolated system the universe, as a whole.

Edited April 21, 2012 by juanrga

[studiot]

Yes the practical approach of the victorian physicists and engineers who introduced and defined these ideas did not address the problem of the boundary.

 

If you divide things into the system and the environment (= that which is not the system) there must be a boundary between the two.

 

Now the nature of boundary problem is the question "Are the boundary elements part of the system or the environment?"

 

The point is they are neither wholly in either, but possess some affinity for both.

 

This is similar to the question of open v closed intervals or neighbourhoods in pure mathematics.

 

The only logical conclusion I can come to is that a truly isolated system has no boundary.

 

In many cases we can dismiss the boundary as insignificant, but the issue becomes significant if our system is all boundary as in the case of surface tension.

 

go well

 

Thank you for the friends communication. I am very new here and still trying to understand the system.

Edited April 21, 2012 by studiot

[D H]

In agreement with one administrator I am posting this here. The topic is multidisciplinary but my main doubts are for physicists.

 

I have just uploaded a draft about Open, closed, and isolated systems.

 

I disagree with your assessment of energy in open and closed systems. Energy is not conserved in such systems. You used a thermometer as an example of a closed system. The energy of the thermometer is not constant; that's the very point of a thermometer.

[juanrga]

Yes the practical approach of the victorian physicists and engineers who introduced and defined these ideas did not address the problem of the boundary.

 

If you divide things into the system and the environment (= that which is not the system) there must be a boundary between the two.

 

Now the nature of boundary problem is the question "Are the boundary elements part of the system or the environment?"

 

The point is they are neither wholly in either, but possess some affinity for both.

 

This is similar to the question of open v closed intervals or neighbourhoods in pure mathematics.

 

The only logical conclusion I can come to is that a truly isolated system has no boundary.

 

In many cases we can dismiss the boundary as insignificant, but the issue becomes significant if our system is all boundary as in the case of surface tension.

 

go well

 

Thank you for the friends communication. I am very new here and still trying to understand the system.

 

The answer to your question "Are the boundary elements part of the system or the environment?" is "it depends!"

 

If your system is a gas in a closed container, the walls are not part of the system. If your system is the gas plus the container, then the walls are part of the system. For a living cell the membrane is part of the system.

 

This is the reason which the formal definition introduced in the article does not use the concept of boundary, but the value of d_eY. This d_eY is a function of the variables of the system. This formal definition works even for systems for the which (spatial) localization fails.

 

I will add some of these remarks in the discussion section. Again thanks .

 

I disagree with your assessment of energy in open and closed systems. Energy is not conserved in such systems. You used a thermometer as an example of a closed system. The energy of the thermometer is not constant; that's the very point of a thermometer.

 

In my original post I wrote:

 

I also criticize the textbook by physicists Walter Greiner, Ludwig Neise, & Horst Stöcker. They seem to be confused about the laws of conservation of matter and energy. For instance, they claim that the particle number is conserved in closed systems, but this is clearly wrong in presence of chemical reactions. I would like to see your points, specially because it seems that a part of physics literature confounds conservation laws (i.e. zero production) with 'invariance' or 'time-independence'.

 

Your post confirms my suspicion that one part of the physics literature (I have never found this problem in chemical or biological literature) confounds conservation of a quantity with the 'invariance' or 'time-independence' of that quantity.

 

By definition, a quantity Y is conserved when its production (or destruction) is zero: d_iY=0. Otherwise the quantity is not conserved. Entropy is not a conserved quantity in a dissipative process because d_iS>0, energy is a conserved quantity because the identity d_iE=0 holds always. The statement d_iE=0, in words, is the usual "Energy can neither be created nor it is destroyed" that you can find in many textbooks.

 

Evidently d_iE=0 does not imply that E was constant. Substituting d_iE=0 into the balance law (see first equation in the knowledge article)

 

dE= d_iE + d_eE

 

we obtain the law [1]

 

dE= d_eE.

 

If the system is isolated, d_eE=0, and then E is constant. For a thermometer (not in equilibrium) d_eE /= 0 and E is not constant. But in both cases energy has been conserved because its production is zero: d_iE=0.

 

For both isolated and closed systems d_eE = dQ + dW. Substituting this back in [1] we obtain the well-known "law of conservation of energy"

 

dE = dQ + dW

 

or first law of thermodynamics.

 

Please, notice that if you insists on your viewpoint, you would be obligated to rename the first law of thermodynamics as the law of non-conservation of energy, each time that you are applying the law to a closed system for the which dE /= 0.

 

Thank you. I will add something of all this in the discussion section of the current article. Although the bulk of a detailed discussion of what is a conserved quantity and what is not will go to another specific article (maybe an article about balance laws or maybe in an article about conservation laws I do not know still)

Edited April 22, 2012 by juanrga

[D H]

Your post confirms my suspicion that one part of the physics literature (I have never found this problem in chemical or biological literature) confounds conservation of a quantity with the 'invariance' or 'time-independence' of that quantity.

 

By definition, a quantity Y is conserved when its production (or destruction) is zero: d_iY=0. Otherwise the quantity is not conserved. Entropy is not a conserved quantity in a dissipative process because d_iS>0, energy is a conserved quantity because the identity d_iE=0 holds always. The statement d_iE=0, in words, is the usual "Energy can neither be created nor it is destroyed" that you can find in many textbooks.

You are misapplying conservation of energy. It applies to an isolated system only. That the energy of a closed system can change is the difference between an isolated and a closed. Thermal and non-thermal energy can flow into or out of a closed system.

 

The problem here is that you have added a nonsense quantity, [math]d_i E[/math]. The first law of thermodynamics for a closed or isolated system can be written as [math]dU = \delta Q + \delta W[/math], where [math]dU[/math] is the change in the internal energy of the system, [math]\delta Q[/math] is the heat flow into the system, and [math]\delta W[/math] is the work done on the system. In other words, the change in the total internal energy of a system is equal to the total energy flow into or out of the system.There is no extra [math]d_i E[/math]. It is [math]dU[/math].

 

 

BTW, please stop with passive aggressive nonsense such as this:

Please, notice that if you insists on your viewpoint, you would be obligated to rename the first law of thermodynamics as the law of non-conservation of energy, each time that you are applying the law to a closed system for the which dE /= 0.

[studiot]

A

You are misapplying conservation of energy. It applies to an isolated system only. That the energy of a closed system can change is the difference between an isolated and a closed. Thermal and non-thermal energy can flow into or out of a closed system.

 

B

The problem here is that you have added a nonsense quantity, [math]d_i E[/math]. The first law of thermodynamics for a closed or isolated system can be written as [math]dU = \delta Q + \delta W[/math], where [math]dU[/math] is the change in the internal energy of the system, [math]\delta Q[/math] is the heat flow into the system, and [math]\delta W[/math] is the work done on the system. In other words, the change in the total internal energy of a system is equal to the total energy flow into or out of the system.There is no extra [math]d_i E[/math]. It is [math]dU[/math].

 

 

 

@A

I agree

 

@B

 

I don't think you really mean this. The emboldened part of B is at variance with A

 

I don't think Juan is introducing nonsense, I think this is some attempt to introduce Gibbs equation

 

 

 

However it should also be remembered that many thermo formulae only apply to homogenous systems.

 

I have tried to use LATex but it didn't work here. I would greatly appreciate advice on how to include formulae here.

I am not a code specialist so I just use Mathtype and copy/paste.

Edited April 22, 2012 by studiot

[D H]

I don't think you really mean this. The emboldened part of B is at variance with A

I was distinguishing from open systems, where the first law of thermodynamics takes on a more complex form. [math]dU = \delta Q + \delta W[/math] still holds in an isolated system; all three terms are trivially zero.

 

I have tried to use LATex but it didn't work here. I would greatly appreciate advice on how to include formulae here.

It works. You just have to use the right escape.

 

In many other forums you use [tex]...[/tex] to invoke display math mode, [itex]...[/itex] for inline math. At this forum, there is no distinction between display math mode and inline mode, and you use [ math ] LaTeX code [ /math ] (get rid of the spaces) instead of [tex] LaTeX code [/tex].

[studiot]

was distinguishing from open systems, where the first law of thermodynamics takes on a more complex form. still holds in an isolated system; all three terms are trivially zero.

 

Sorry but I have to disagree.

 

The work done is the net work done.

 

Zero net work may be done but not on/by an isolated system, which may not allow (any) energy exchange at all.

 

Similarly heat or other energy exchanged.

 

This is a case where there is a difference between a term with a zero value and a term which is disallowed.

[juanrga]

You are misapplying conservation of energy. It applies to an isolated system only. That the energy of a closed system can change is the difference between an isolated and a closed. Thermal and non-thermal energy can flow into or out of a closed system.

 

The problem here is that you have added a nonsense quantity, [math]d_i E[/math]. The first law of thermodynamics for a closed or isolated system can be written as [math]dU = \delta Q + \delta W[/math], where [math]dU[/math] is the change in the internal energy of the system, [math]\delta Q[/math] is the heat flow into the system, and [math]\delta W[/math] is the work done on the system. In other words, the change in the total internal energy of a system is equal to the total energy flow into or out of the system.There is no extra [math]d_i E[/math]. It is [math]dU[/math].

 

I am perplexed by reading that. The quantity [math]d_i E[/math] is the well-known production of energy. The law of conservation of energy states [math]d_i E = 0[/math] for isolated, closed, and open systems.

 

The first time I meet the equation [math]d_i E = 0[/math] was when I studied a well-known thermodynamics monograph by a famous Nobel Laureate, who precisely won the Nobel Prize for his extension of classical thermodynamics. Do you really need a snapshot of the page of his very famous monograph, with the equation [math]d_i E = 0[/math] being his equation (2.1), to be submitted here as image?

 

Whereas you think your response, you can also find the equation [math]d_i E = 0[/math] in this biologists textbook.

 

Contrary to your claims, it is self-evident that total energy E is conserved in both closed and open system. Again this is all well-known even at the undergrad level and I do not need to go into details. If you are interested you can check, for instance, the section "15.4 Energy conservation in open system" in the well-known textbook Modern thermodynamics by Prigogine and Kondepudi.

 

BTW, please stop with passive aggressive nonsense such as this:

Please, notice that if you insists on your viewpoint, you would be obligated to rename the first law of thermodynamics as the law of non-conservation of energy, each time that you are applying the law to a closed system for the which dE /= 0.

 

No offence was intended, of course. But the above is a natural consequence of your incorrect viewpoint! You cannot consider [math]dE = dQ + dW[/math] "the law of conservation of energy", if you still insist on that energy is not conserved when [math]dE \neq 0[/math].

 

The rest of scientific community names to [math]dE = dQ + dW[/math] the first law of thermodynamics or "the law of conservation of energy", because the conservation of energy is given by [math]d_i E = 0[/math] and not by [math]dE = 0[/math].

Edited April 23, 2012 by juanrga

[studiot]

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JRGA

 

An isolated system does not interact in any way with its surroundings and, therefore, neither matter nor energy can be transferred between system and surroundings. A closed system does not exchange matter with the exterior. An open system is one that can exchange both matter and energy with the exterior.

 

 

JRGA

 

A mercury thermometer is a closed system –since matter cannot enter or leave it– but is not isolated; precisely the net exchanges of energy compress and expand the mercury inside the thermometer

 

 

DH

 

You used a thermometer as an example of a closed system. The energy of the thermometer is not constant; that's the very point of a thermometer.

 

 

DH

 

That the energy of a closed system can change is the difference between an isolated and a closed. Thermal and non-thermal energy can flow into or out of a closed system.

 

Yes, yes, yes and yes we are all agreed here.

 

JRGA

 

Contrary to your claims, it is self-evident that total energy E is conserved in both closed and open system.

 

Is there is a terminology issue here?

 

DH correctly referred to 'internal energy' here. These days internal energy is normally given the symbol U to distinguish it from other energies. E is an old symbol for internal energy (eg Moore and Moelwyn-Hughes) but is now the general symbol for energy.

 

 

 

Internal energy of a closed system like a thermomenter is clearly not conserved if you heat it up.

 

JRGA

 

The answer to your question "Are the boundary elements part of the system or the environment?" is "it depends!"

 

One of the substantial sources of error in thermodynamics is failure to define the system appropriately.

 

 

 

It is often really helpful to consider lots of different cases.

 

 

 

In an isolated system U cannot change, but, although necessary, this is not a sufficient condition for the system to be isolated.

 

 

 

This is where I disagree with DH.

 

 

 

The first law tells us that energy and work can flow into and out of a system with a resultant zero net change in U. But only for open or closed systems, since by definition no energy can flow into or out of an isolated system.

 

 

 

However if we set delta U, q and w to zero in the first law it is still not sufficient to define an isolated system since mass may enter or leave the system whilst all terms in the first law are zero.

 

 

 

Would you like to consider examples of how all these cases might be realised?

 

 

 

 

 

Edited April 24, 2012 by studiot

[juanrga]

Is there is a terminology issue here?

 

DH correctly referred to 'internal energy' here. These days internal energy is normally given the symbol U to distinguish it from other energies. E is an old symbol for internal energy (eg Moore and Moelwyn-Hughes) but is now the general symbol for energy.

 

Internal energy of a closed system like a thermomenter is clearly not conserved if you heat it up.

 

One of the substantial sources of error in thermodynamics is failure to define the system appropriately.

 

It is often really helpful to consider lots of different cases.

 

In an isolated system U cannot change, but, although necessary, this is not a sufficient condition for the system to be isolated.

 

This is where I disagree with DH.

 

The first law tells us that energy and work can flow into and out of a system with a resultant zero net change in U. But only for open or closed systems, since by definition no energy can flow into or out of an isolated system.

 

However if we set delta U, q and w to zero in the first law it is still not sufficient to define an isolated system since mass may enter or leave the system whilst all terms in the first law are zero.

 

Would you like to consider examples of how all these cases might be realised?

 

It is not a terminology issue, DH is clearly confused about this topic and rejected the well-known equation [math]d_i E = 0[/math] because he was completely unfamiliar with the modern thermodynamic literature that I am using.

 

As stated before E denotes total energy. Total energy is always conserved [math]d_i E = 0[/math]. Internal energy is not always conserved. In fact, textbooks cited here by me explain how to compute the production of internal energy [math]d_i U[/math] for different processes where internal energy is not conserved.

 

The general thermodynamic expression for closed systems is [math]dE = dQ + dW[/math]. The common expression that DH used [math]d U = \delta Q + \delta W[/math] is an approximation which only applies to closed systems at rest, in absence of external fields, and under certain additional approximations.

 

As I already explained conservation of energy [math]d_i E = 0[/math] would not confused with constancy of energy [math]d E = 0[/math]. This same confusion is the reason for the which the physicists cited in the OP made, in his book, the silly claim that the number of particles N in a closed system are conserved. They confounded constancy of N [math]d N = 0[/math] for a closed system with the law of conservation of N [math]d_i N = 0[/math].

 

For a thermometer at rest, in absence of external fields and with zero work, the internal energy is conserved because [math]d_i U = 0[/math]. An alternative statement is [math]dU = dQ[/math] which unsurprisingly is named the law of conservation of (internal) energy. The second equation is a direct consequence of the first.

 

The law [math]dU = dQ + dW[/math] is only valid for closed systems. It is not valid for open systems.

Edited April 24, 2012 by juanrga

[studiot]

Juan it is a pity you addressed my aside, rather than my important points.

 

I simply wondered if your cited authors were developing Gibbs canonical equation, which has similar form and notation.

You complained that these authors stated mass as constant. Well this is a requirement or restriction built into the small print as the GCE applies to unit or constant mass.

 

That aside I do not see why you criticise DH for using different notation. The truth should be the same in all. He talks of the law of conservation of energy in the form:

 

"What goes in is not lost but must be somewhere within the system."

 

You have however introduced few errors.

 

1) The only system with constant energy is an isolated one. I did offer some comments for discussion about isolated systems.

 

2) If you add heat to a thermometer you increase its internal energy.

 

3) I offered to work through with you an example of how to apply the first law to open systems so it is disappointing to be told flatly it doesn't apply.

 

I am, however, glad to see that you have got rid of that stuff about differentials. Internal energy can be a total differential because depends only upon system properties.

Heat and work exchanged and total energy can be influenced by external agents. the first two are complete quantities not differences and in my view should not be written as differentials, deltas etc.

The heat added to a system is the heat added to a system. There is no such quantity as the difference of heats added - large or small.

 

As, I'm sure you know, Gibbs alleviated this by replacing q by TdeltaS in the first law in appropriate circumstances.

 

go well

Edited April 24, 2012 by studiot

[Phi for All]

It is not a terminology issue, DH is clearly confused about this topic and rejected the well-known equation [math]d_i E = 0[/math] because he was completely unfamiliar with the modern thermodynamic literature that I am using.

!

Moderator Note

Personal attacks are against the rules you agreed to when you joined this forum. Attack the ideas instead.

[juanrga]

Juan it is a pity you addressed my aside, rather than my important points.

 

I simply wondered if your cited authors were developing Gibbs canonical equation, which has similar form and notation.

You complained that these authors stated mass as constant. Well this is a requirement or restriction built into the small print as the GCE applies to unit or constant mass.

 

That aside I do not see why you criticise DH for using different notation. The truth should be the same in all. He talks of the law of conservation of energy in the form:

 

"What goes in is not lost but must be somewhere within the system."

 

You have however introduced few errors.

 

1) The only system with constant energy is an isolated one. I did offer some comments for discussion about isolated systems.

 

2) If you add heat to a thermometer you increase its internal energy.

 

3) I offered to work through with you an example of how to apply the first law to open systems so it is disappointing to be told flatly it doesn't apply.

 

I am, however, glad to see that you have got rid of that stuff about differentials. Internal energy can be a total differential because depends only upon system properties.

Heat and work exchanged and total energy can be influenced by external agents. the first two are complete quantities not differences and in my view should not be written as differentials, deltas etc.

The heat added to a system is the heat added to a system. There is no such quantity as the difference of heats added - large or small.

 

As, I'm sure you know, Gibbs alleviated this by replacing q by TdeltaS in the first law in appropriate circumstances.

 

go well

 

I think that I addressed your points.

 

The physicists cited "were not developing Gibbs canonical equation" because the Gibbs equation has nothing to see with the definition of open, closed and isolated systems. My complain was, in essence, that these authors confounded a flow term with a production term and then did the misguided claim about conservation.

 

I have not criticized "DH for using different notation".

 

About 1) and 2). An isolated system is defined as [math]d_eE= 0[/math] and, using conservation of total energy [math]d_iE= 0[/math], the balance law gives [math]dE= 0[/math] or in words "total energy E is constant".

 

A closed system is defined as [math]d_eE \neq 0[/math] and, using conservation of total energy [math]d_iE= 0[/math], the balance law gives [math]dE \neq 0[/math]. Moreover, the generalized first law of thermo for a closed system is [math]dE =dQ + dW[/math]. For a thermometer at rest and in absence of external fields effects [math]dE=dU[/math] and [math]dW=0[/math], which gives [math]dU=dQ[/math] Or in words "internal energy U of thermometer is not constant and varies with the heat". Of course, [math]dU=dQ[/math] continues being cited in textbooks as a statement the law of conservation of energy.

 

About 3) I already explained to you that [math]dU= dQ + dW[/math] is not valid for open systems. Therefore your argument

 

However if we set delta U, q and w to zero in the first law it is still not sufficient to define an isolated system since mass may enter or leave the system whilst all terms in the first law are zero.

 

which relies on applying [math]dU= dQ + dW[/math] to an open system, is not valid.

Edited April 25, 2012 by juanrga

[studiot]

I already explained to you that is not valid for open systems. Therefore your argument

 

 

Do you really call this an explanation, in support of your statement?

 

JRGA post#13

The law is only valid for closed systems. It is not valid for open systems.

 

I cannot accept your definition of a closed system since it effectively disbars the existence of equilibrium along with the establishement of the thermodynamic temperature scale.

 

I repeat the observation that the heat added and the work done are not functions of a non isolated system but may be impressed arbitrarily by the surroundings. Yes there are internal results (effects) within the system but I can heat a thermometer as little or as much as I please or even not at all.

Edited April 25, 2012 by studiot

[juanrga]

I cannot accept your definition of a closed system since it effectively disbars the existence of equilibrium along with the establishement of the thermodynamic temperature scale.

 

I do not know why you say this. The definition of closed system that I gave is the standard one (check reference [1]) and it is perfectly compatible with equilibrium and with thermodynamic scale.

 

I repeat the observation that the heat added and the work done are not functions of a non isolated system but may be impressed arbitrarily by the surroundings. Yes there are internal results (effects) within the system but I can heat a thermometer as little or as much as I please or even not at all.

 

I do not know what do you mean here. In thermodynamics, both heat and work are functions of variables on the thermodynamic space of the system (U,V,N...). For an isolated system both dQ and dW are zero.

Edited April 25, 2012 by juanrga

[Cap'n Refsmmat]

I do not know what do you mean here. In thermodynamics, both heat and work are functions of variables on the thermodynamic space of the system (U,V,N...).

What do you mean by this? Do you mean that you can express Q and W directly in terms of U, V, N and so on? Heat and work are not properties of the system.

[D H]

In thermodynamics, both heat and work are functions of variables on the thermodynamic space of the system (U,V,N...).

There is no such thing as a heat function Q(U,V,N,...) or a work function W(U,V,N,...). That is why it is better to write heat and work as δQ and δW rather than dQ and dW. Heat and work are inexact differentials. How much heat and work are transferred to/from the environment as a system moves from one point in (U,V,N,...) space to another depends not only endpoints but on the path taken between those endpoints.

 

 

For an isolated system both dQ and dW are zero.

That is something we agree on.

[studiot]

In many other forums you use [tex]...[/tex] to invoke display math mode, [itex]...[/itex] for inline math. At this forum, there is no distinction between display math mode and inline mode, and you use [ math ] LaTeX code [ /math ] (get rid of the spaces) instead of [tex] LaTeX code [/tex].

 

Thank you DH, for the helping hand; this post is by way of trying it out. I lost a considerable amount of typing yesterday after I found the sub and superscript buttons, but could not find how to exit the mode so all my subsequent typing ended in subscript mode. The return, esc ctrl keys did not help.

 

Thinking about it I now wonder if Juan is mixing up the formulations, introduced by Gibbs and later called the 'canonical equations of state' by Plank, with the total energy of an assemblage af particles as calculated by statistical mechanics.

 

 

[math]U = U(S,V,{N_1},{N_2},{N_3}........)[/math]

[math]S = S(U,V,{N_1},{N_2},{N_3}........)[/math]

 

for gibbsian classical themodynamics

 

and

 

The total energy of a system of particles in stat mech.

 

[math]E = {\varepsilon ^a} + {\varepsilon ^b} + {\varepsilon ^c}....... = \sum {{\varepsilon ^i}} [/math]

 

 

Which leads to the 'conservation' laws for number and energy

 

 

[math]N = \sum {{n_i}} [/math]

 

 

[math]E = \sum {{n_i}{\varepsilon ^i}} [/math]

 

However both systems ( and they are compatible) are constrained by their underlying conditions of validity.

 

Yeah I got formulae working.

 

Now I've solved that can anyone tell me how to resolve the times shown on posts in my view and with my clock so that SF timeand mine coincides? I have the settings option set to (my) London time.

Edited April 26, 2012 by studiot

[imatfaal]

!

Moderator Note

The ^superscript and _subscript keys are toggles - click once before typing (cursor _will ^{change once you} start typing) and once you have typed your raised or lowered text reclick the button the next letter should ^be back _to normal size and position.

I corrected my time settings (from GMT to BST - Summer, pah! it's pouring down) by going to 'my settings' top righthand corner, next to 'sign out' and under your 'username', selecting GMT as time zone and the check box marked Currently in DST (the DST auto box didnt seem to work)

[Cap'n Refsmmat]

In many other forums you use [tex]...[/tex] to invoke display math mode, [itex]...[/itex] for inline math. At this forum, there is no distinction between display math mode and inline mode, and you use [ math ] LaTeX code [ /math ] (get rid of the spaces) instead of [tex] LaTeX code [/tex].

I suppose it's worth noting that we do distinguish between inline and display math -- inline math mode is invoked with the imath tag.

[studiot]

Thanks both, I'm beginning to get the hang of this.

 

Could the Gif i had to resort to in post #8 be replaced to save memory space?

Edited April 26, 2012 by studiot

[juanrga]

What do you mean by this? Do you mean that you can express Q and W directly in terms of U, V, N and so on? Heat and work are not properties of the system.

 

I did mean that dQ and dW are given by functions of dU, dV, dN when the state is given by (U,V,N). E.g., for the thermometer cited above, the important variable is its internal energy U and heat is given by dQ=dU.

 

There is no such thing as a heat function Q(U,V,N,...) or a work function W(U,V,N,...).

 

I have not said such thing neither wrote such equations. See also my reply to Cap'n Refsmmat.

 

That is why it is better to write heat and work as δQ and δW rather than dQ and dW. Heat and work are inexact differentials.

 

I already explained before in this same thread that both heat and work are represented by inexact differentials, δQ and δW, in classical thermodynamics, due to limitations of the classical formulation.

 

Modern thermodynamics works with an extended thermodynamics space beyond the classical formulation, abandons inexact differentials, and uses well-defined dQ and dW. As I already emphasized before the classical law

 

dU = δQ + δW

 

is an approximation to the more modern and general law

 

dE = dQ + dW

 

See the textbook "Modern thermodynamics" by Prigogine and Kondepudi, cited before, for the details.

Edited April 26, 2012 by juanrga