## Few Fundamental Thermodynamics Questions

Hi

I had a few thermodynamics questions on a thread that was locked. The link is here and my questions are directed at the last post.

 Quasistatic irreversible processes can always be realized in a completely reversible way. E.g. in the above case where the entropy of the gas increases due to absorbing heat, the heat can be supplied to the gas by a heat bath and the temperature difference between the heat bath and the gas can be made arbitrarily small. The entropy increase of the heat bath plus the entropy increase of the heat bath is then zero. The entire process is then reversible.
1. Does the author mean that all quasistatic irreversble processes are reversible or if for a quasistatic irreversible process that goes from state 1 to 2, there is actually another way to get from state 1 to 2 reversibly? Is there some kind of proof that this generalization is true as I can't find it in any books?

2. With regards to the proof for work for non-quasistatic systems, does the proof apply to quasistatic irreversible process as well? On page 17 of Anderson's modern compressible flow, he states that only for reversible process does W = integral of pdV. In addition, I thought that equation (5) that T dS >= dQ used to prove W < integral pdv also applies for any irreversible process quasistatic or not?

 An exteme example is free expansion of a gas in avacuum. In that case no work at all is performed, but this process is so violent that you can object by saying that the pressure of the gas is not well defined. But we can perform a free expansion in small steps by moving a piston very fast from one position to a slighly different position, faster than the gas can expand and then fixing the piston in that position. Then what happens is that the gas expands and bumps into the piston in that new position. The P dV term is then equal to the increase in kinetic energy of the gas which comes at the expense of the internal energy, but this kinetic energy gets dissipated after a while, so the internal energy stays the same.
3. I'm a bit confused here because I always thought that internal energy was a measure of all the microscopic energies which includes kinetic energy (and that kinetic energy directly correlates to the temperature of gas)?

4. I was also wondering for a real gas (intermolecular forces important) or a chemically reacting system, why is internal energy also a function of specific volume and enthalpy a function of pressure while this isn't the case for ideal gas and non-chemical reacting system?

5. How are irreversibilities accounted for in terms of energy balance for closed or open systems? For a closed and insulated piston cylinder and W < integral PdV, does energy balance become something like:

W = U2 - U1 = integral PdV - loss

So for closed systems do losses get accounted for in the internal energy of the final state and for steady state open systems does losses get accounted for in the enthalpy terms (assuming adiabatic processes)?

6. Is there an example that shows how heat is process dependent, in all the books I looked through they only give examples for work but just simply state this for heat without examples?

7. What is the difference between equilibrium and steady state in a general thermodynamics sense?

Thanks very much
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 Recognitions: Homework Help 1. Quasistatic irreversible processes can always be realized in a completely reversible way. ... that would be: that there is a reversible process to get you between any two states. For proof - just see if you can find two states that can only be moved between irreversibly. Put simply: there is more than one way to skin a cat. 2. I think you need to be more careful about what people are saying when they write stuff in text books. Work is not always pV work. 3. it's badly explained - in incremental free expansion described the gas also gains a bulk KE. It's the randomized KE that relates to temperature. 4. because the ideal gas is a simplified model and the real gasses have to obey real physics. 5. the irreversable processes are accounted in all cases by the statistics of the setup. 6. The questions does not mean anything: heat, for example, is another name for energy. Similarly: work is not process dependent - thermodynamic work is a process. Work is not always path dependent either. eg. for a reversible adiabatic process. 7. same as in any sense - one can oscillate (for eg.) about an equilibrium but must remain at a steady state.

Hi

Thanks very much for the response.

 Quote by Simon Bridge 2. I think you need to be more careful about what people are saying when they write stuff in text books. Work is not always pV work.
With regards to work I should have said thermodynamic work to make things more clear. So with regards to my original question, does W = ∫pdV only apply for quasi-static reversible processes only and not for quasi-static irreversible as the original author had stated since TdS > δQ?

 Quote by Simon Bridge 4. because the ideal gas is a simplified model and the real gasses have to obey real physics.
I'm not really familiar with gas interactions at a molecular level, is there a simple explanation on what real world effects that pressure and specific volume cause or reflect which in turn affect internal energy?

 Quote by Simon Bridge 5. the irreversable processes are accounted in all cases by the statistics of the setup.
So was my original reasoning correct that all irreversibility and loses are accounted for by one of the variables in the energy balance (either ΔQ, ΔU, ΔH etc.)?

 Quote by Simon Bridge 6. The questions does not mean anything: heat, for example, is another name for energy. Similarly: work is not process dependent - thermodynamic work is a process. Work is not always path dependent either. eg. for a reversible adiabatic process.
With regards to the path dependent nature of thermodynamic work and heat (in this case I'm more referring to the heat as a process of adding energy to a system or δQ as in the first law) between two states, since thermodynamic work is not path dependent for reversible adiabatic process, does this mean that heat is also not path dependent for a reversible process with no work input?

Is the path dependent nature of thermodynamic work and heat between the two states solely because there are two "source" of energy (work and heat for closed system) and one can play with different ratios of the two to get the same energy change of the system?

Thanks very much

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## Few Fundamental Thermodynamics Questions

 Quote by Red_CCF With regards to the path dependent nature of thermodynamic work and heat (in this case I'm more referring to the heat as a process of adding energy to a system
The process of adding energy to a system is called "doing work on the system".

Work is change of energy.

 or δQ as in the first law) between two states, since thermodynamic work is not path dependent for reversible adiabatic process, does this mean that heat is also not path dependent for a reversible process with no work input?
Ah - you are thinking of the process of adding heat - called "heating" (or "cooling") the system - as in an isochoric process.

But if no pV work is done isn't the path fixed?

 Is the path dependent nature of thermodynamic work and heat between the two states solely because there are two "source" of energy (work and heat for closed system) and one can play with different ratios of the two to get the same energy change of the system?
Now I'm with you - you can put a container on a hot source, or you can do mechanical work on it, both will increase the internal energy.
 Recognitions: Homework Help http://www.youtube.com/watch?v=1Sd8hcf_NZY ... talks in a simpler way about different irreversible processes in thermodynamics. It should help with the earlier question - I'm sorry, it's 30mins of dull talk, however the lecturer has some good analogies and it's those that I think will help. He also deals with the processes in a very general way that makes many of the connections you are trying for. I've been trying to find a treatment of an isenthalpic process as being particulaly relevant to your questions ... this had dQ=0 but TdS>0, it's irrversible, and iirc it follows an isotherm on the PV diagram [dh=0=cpdT]... which means that W≠∫pdV in this case. You have to analyze it with a T-s diagram. For the kind of things that real-gas models have to take into account, wikipedia has a nice summary. From there you should be able to see how the extra terms you ask about get to be included. The question you have asked are a tad general for quickie pat answers - you have more reading to do. The above should point you in fruitful directions.
 Hi Thank you very much for the link, hopefully it'll be able to answer some of my questions. In the meantime, I was reviewing Moran and Shapiro's fundamental of thermodynamics, and had a question about the state principle for simple systems. I attached the segment of the book that talked about it. I was just confused about their explanation of the state principle. To me it seems to say that if I have a rigid tank and I start heating the system from state 1 to state 2, only one state property is required to define all other state properties as no work is being done. However, I am confused as if for example the container has ideal gas, the ideal gas equation still dictates that two state variables be known to find another regardless of the system? Also, does this principle apply to specific internal energy and enthalpy of gases given that if a gas is calorically or thermally perfect h and u are functions of temperature only, and also in Anderson's Modern Compressible Flow, these two properties are said to depend on chemical reactions and intermolecular forces, with no mention of the state principle? Does h and u depend on more than two variables for a non-simple system and what if the gas is thermally or calorically perfect? Returning to my question about equilibrium, in Anderson's Modern Compressible Flow, he state that "equilibrium is evidenced by no gradients in velocity, pressure, temperature, and chemical concentration throughout the system i.e. the system has uniform properties." To me this statement implies that some rigid insulated tank that contains Gas A would be considered in equilibrium, but if I have another insulated rigid tank of gas (Gas B) at a different temperature and pressure and I put the two tanks side by side and I consider both tanks as the system, the system is now not at equilibrium even though the components of the system is at equilibrium? Thanks very much Attached Thumbnails

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 To me it seems to say that if I have a rigid tank and I start heating the system from state 1 to state 2, only one state property is required to define all other state properties as no work is being done.
This is correct - if the container is rigid.
 I am confused as if for example the container has ideal gas, the ideal gas equation still dictates that two state variables be known to find another regardless of the system?
This is also correct - but recall that, in this case, the container is rigid. This means that the volume cannot change.
 Also, does this principle apply to specific internal energy and enthalpy of gases given that if a gas is calorically or thermally perfect h and u are functions of temperature only, and also in Anderson's Modern Compressible Flow, these two properties are said to depend on chemical reactions and intermolecular forces, with no mention of the state principle? Does h and u depend on more than two variables for a non-simple system and what if the gas is thermally or calorically perfect?
Note that the state principle described is for simple systems ... you are describing complicated systems so what do you think the answer is?

Also - consider the stress on "independence" in the description of the state principle.
 Returning to my question about equilibrium, in Anderson's Modern Compressible Flow, he state that "equilibrium is evidenced by no gradients in velocity, pressure, temperature, and chemical concentration throughout the system i.e. the system has uniform properties." To me this statement implies that some rigid insulated tank that contains Gas A would be considered in equilibrium, but if I have another insulated rigid tank of gas (Gas B) at a different temperature and pressure and I put the two tanks side by side and I consider both tanks as the system, the system is now not at equilibrium even though the components of the system is at equilibrium?
No. If the two tanks are thermodynamically isolated, then each is a separate thermodynamic system. It is an error to consider them as a combined system in this context.

 No. If the two tanks are thermodynamically isolated, then each is a separate thermodynamic system. It is an error to consider them as a combined system in this context.
That is one view, but I see no reason for not considering them jointly as a single thermodynamic system.

In that event RED is correct the system is not in stable equilibrium.

Here is another example from chemistry.

Some paper is sitting on my desk in an atmosphere containing oxygen.

Is it in equilibrium?

No because if I apply a match it will catch fire and continue to burn spontaneously after removal of my flame.

That is because the final burnt state has lower energy and higher entropy than the initial state.

However I need to add the activation energy before anything happens.

It is the same with the two tanks of gas - there is an energy and entropy available from their mixing (assuming no chemical reaction), its just that the activation energy of breaching the tank walls is required as a starter.

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 Quote by Studiot That is one view, but I see no reason for not considering them jointly as a single thermodynamic system.
The fact they cannot interact in any way does not deter you? Interesting...
 In that event RED is correct the system is not in stable equilibrium. Here is another example from chemistry. Some paper is sitting on my desk in an atmosphere containing oxygen. Is it in equilibrium? No because if I apply a match it will catch fire and continue to burn spontaneously after removal of my flame. That is because the final burnt state has lower energy and higher entropy than the initial state. However I need to add the activation energy before anything happens.
But in this example, the paper and air are not thermodynamically isolated.

 It is the same with the two tanks of gas - there is an energy and entropy available from their mixing (assuming no chemical reaction), its just that the activation energy of breaching the tank walls is required as a starter.
Yes - you have to bring them into contact.

OP is talking about the definition of "equilibrium" in thermodynamics. In the real world - nothing is in stable equilibrium ... ever. But that does not affect the definition of the equilibrium.

OPs example cites a "system" where each component is in thermodynamic equilibrium and wants to say that the differences (temperature say) means that the system is, by definition, not in equilibrium.

Since the systems are not changing, they are not affecting each other. Ergo, the system is in equilibrium.

In terms of the text book extract provided, this would be understood as two separate thermodynamic systems in the abstract sense.

 The fact they cannot interact in any way does not deter you? Interesting...
No it doesn't there exists a thermodynamic potential for the process to take place which is not altered by the fact that there is a (temporary) barrier in place. The isolation between the tanks is mechanical, not thermodynamic.

In thermodynamics there are several types of equilibrium, as with any other branch of physics.

Note I said the tanks or paper are not in stable equilibrium.

They are technically in metastable equilibrium, but I'm sure you appreciate this.

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 Quote by Studiot No it doesn't there exists a thermodynamic potential for the process to take place which is not altered by the fact that there is a (temporary) barrier in place. The isolation between the tanks is mechanical, not thermodynamic.
Ahhh I see - but you were responding to my statement: If the two tanks are thermodynamically isolated, then each is a separate thermodynamic system.
... I wrote that as an attempt to make a clear distinction between thermodynamically ideal situations used in the models and real-world situations. Notice the "if".
In that statement I was specifying "thermodynamically isolated" as a model - not as an approximation or anything. I'll concede that there is no such absolute in the real world.

In the real world there is no such thing as a permanently stable equilibrium that could apply to the description ... things will always fall apart eventually. Do you really think this is what OP had in mind when he asked the question?

While there are, indeed, many different types of equilibrium, OP was asking about a particular definition of equilibrium that had been found. It was to this definition that I offered my reply. It is the kind of thing that occurs near the start of a thermodynamics course alongside other idealizations like "diathermal wall" end suchlike.

So we are agreeing in general - I'm replying from an idealized model, you from real life.
Lets allow OP to tell us which was relevant to the question?

Simon, if you are familiar with chemical kinetics you will understand that thermodynamics tells us the answer to the question

'Can something happen spontaneously?'

It does not usually answer the questions 'will it happen spontaneously?' or 'How fast does it happen?'

 So we are agreeing in general
Yes I already said that I am just adding value.

The description of equilibrium as the condition of no change is of little value in applying the classical equations of thermodynamics since they rely heavily on reversible processes, being those that are in equilibrium.

Taken literally such a description would imply that no process can ever take place!

A better description of equilibrium is the idea of what happen to an infinitesimal displacement from equilibrium.

In stable equilibrium the system restores itself whatever the direction of the displacement.

In metastable equilibrium restoration depends upon the direction.

In the attached sketches a small push to the left or right return the ball in stable equilibrium, but only to the right in metastable equilibrium.

This allows us to introduce the idea of a quasi static or reversible process.
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 A better description of equilibrium is the idea of what happen to an infinitesimal displacement from equilibrium.
Yes it is.

In fact this allows for the idea to be extended easily to a dynamical equilibrium.
(Note: your examples are also in the lecture I linked to earlier.)

The book is using poor pedagogy.
Just reading through the few bits shown to us here you can feel your brains congeal.
We must be able to point OP at an introductory lecture course or something better than that book.

 Quote by Simon Bridge In the real world there is no such thing as a permanently stable equilibrium that could apply to the description ... things will always fall apart eventually. Do you really think this is what OP had in mind when he asked the question? While there are, indeed, many different types of equilibrium, OP was asking about a particular definition of equilibrium that had been found. It was to this definition that I offered my reply. It is the kind of thing that occurs near the start of a thermodynamics course alongside other idealizations like "diathermal wall" end suchlike. So we are agreeing in general - I'm replying from an idealized model, you from real life. Lets allow OP to tell us which was relevant to the question?

Hello

Thanks very much for the responses. When I posed the question about equilibrium, I was not thinking about the real world cases Studiot had pointed out but I can see how they are important. However, I don't think that I'm at a stage where I can understand these complexities; I'm more focused on getting the fundamentals from an idealized perspective first before considering real-world cases.

The aim of my original question was just trying to understand what is equilibrium and the difference between equilibrium and steady state. Based on the definition in Anderson, it seems that if I have a turbine whereby there would be a gradient of at least one state property, the turbine would not be considered at equilibrium but at steady state? Also, by this definition a system in equilibrium would have to have no gradients in entropy as well so the inlet and exit of a control volume must have the same entropy?

If these cases are true, I'm now confused about what constitutes a thermodynamic state. In the Moran and Shapiro book I am reading they introduce a thermodynamic state as a condition where the system is at equilibrium, such as the end states from pushing a piston from state 1 to 2 or the intermediate states of a quasistatic process. However, for a slightly more complex system like a turbine at steady state which will probably have a gradient of some sorts, can the system even have a state as constituted by the term steady state?

With regards to my question about specific internal energy and enthalpy, I'm still confused about whether the state principle dictates that they must be functions of 2 state variables and why they are only functions of one for certain idealizations?

Lastly, the insulated rigid tank mentioned in my earlier post, although volume is constant, can the specific volume change? For instance, if I add in more gas to this tank or have another identical tank with more gas in mass , would these constitute the same system or be considered different systems?

Thanks very much
 'Steady State' usually refers to what are known as the flow equations, for example in your turbine. So fluid is constantly entering and leaving the turbine, carrying with it physical quantities such as energy, entropy, mass, momentum etc. We say that the system is in a steady state when there is no change to these fluxes, ie the difference between (X) in and (X) out is a constant. However the process undergone within the turbine may be reversible or irreversible. So a constant mass of fluid may be flowing through the turbine and undergoing irreversible ( or irreversible) expansion, loosing some heat in the process. The rate of work output from the turbine and the rate of heat lost will also be constant if the turbine is in a steady state. However the process is only an equilibrium one if the process is reversible.

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To add to what Studiot said - with our usual difference in perspective ;)
 Quote by Red_CCF The aim of my original question was just trying to understand what is equilibrium and the difference between equilibrium and steady state.
You are not the only one and some authors do not make a clear distinction. For example, in the lecture I gave you (have you watched it yet) the lecturer describes the state of a ball rolling down a hill as an equilibrium.

Usually we would think of an equilibrium as being a state in which a system naturally remains. A weight hanging from the end of a string has an equilibrium point that is easy to picture for example: where the weight is directly below the hook.

A steady state of the weight-on-string thing would be when it is hanging at equilibrium - but also when it is swinging with a constant amplitude and period.

So to say that something is in a steady state has a bit of leeway.
 it seems that if I have a turbine whereby there would be a gradient of at least one state property, the turbine would not be considered at equilibrium but at steady state?
If it were turning steadily - if the turning were fluctuating then it would neither be in steady state nor equilibrium.
 Also, by this definition a system in equilibrium would have to have no gradients in entropy as well so the inlet and exit of a control volume must have the same entropy?
I'll defer to studiots answer here ;)
 If these cases are true, I'm now confused about what constitutes a thermodynamic state.
It is any set of values that completely describes the system.
 In the Moran and Shapiro book I am reading they introduce a thermodynamic state as a condition where the system is at equilibrium,
That would not agree with my understanding - a system may pass through thermodynamic states. But they may be thinking of the system being in thermodynamic equilibrium with itself just to be pedantic. After all, when you do something like push in a piston, not all the gas changes temperature at the same time - there would be an initial gradient that settles down in a while. Similarly if you heat something - you may join a heat source via a diathermal wall ... again, not all the gas under study will heat to the same temperature at the same time: there will be convection etc. For the entire bottle of gas (or whatever) to be considered to be in a well defined state, then there should be no internal fluctuations.
 With regards to my question about specific internal energy and enthalpy, I'm still confused about whether the state principle dictates that they must be functions of 2 state variables and why they are only functions of one for certain idealizations?
In the example you gave, there are only two parameters that vary - count them - ergo, knowing one, and the relationship between them, you know everything.

 Lastly, the insulated rigid tank mentioned in my earlier post, although volume is constant, can the specific volume change? For instance, if I add in more gas to this tank or have another identical tank with more gas in mass , would these constitute the same system or be considered different systems?
The simple model you are being treated to at this early stage only admits the three variables - and only works for specific types of systems - there are other models that would apply to the other examples. Try not to get ahead of yourself. No - that's not right - rather: try to be aware as you read that you are not being supplied with everything in one go: the authors are providing stepping-stones to more complicated methods.

You do risk overreaching yourself by trying for more complex models before you understand the core concepts. Make sure you can do the problems in the chapters you have read.

 You do risk overreaching yourself by trying for more complex models before you understand the core concepts. Make sure you can do the problems in the chapters you have read.