Please notice that , in thermodynamics, when we're discussing "process" or "cycle", we're discussing a process or a cycle of a specific path(trajectory).
The arbitrary cycle that a set of element Carnot cycles " replace" ( in fact, it cann't be replaced) is just a cycle of a specific path(trajectory).
We never discuss "process" or "cycle" in general, for that is meaningless.
In thermodynamics, a "process" is defined by a trajectory in thermodynamic state space from a starting point A to the end point B, and a "cycle" is just a closed trajectory going back to A. Now, there is freedom of choice of the in-between states that the system undergoes. You might have reversible, or irreversible trajectories between two points. Even for reversible processes, you can choose among different ways to evolve the system from A to B. For example, consider A and B have different pressures and temperatures. You can first do an isothermal compression/expansion and then add heat to get to B, or first add heat, and then change the pressure isothermally. The resulting amounts of work and heat exchange would be different between these two processes. The Carnot cycle is just one set of these choices for a cycle between two temperatures, that gives the maximum output work to input heat ratio (efficiency). In practice, it is not even a good choice for energy production. Something like a Rankine cycle is mostly used.
In thermodynamics, a "process" is defined by a trajectory in thermodynamic state space from a starting point A to the end point B, and a "cycle" is just a closed trajectory going back to A. Now, there is freedom of choice of the in-between states that the system undergoes. You might have reversible, or irreversible trajectories between two points. Even for reversible processes, you can choose among different ways to evolve the system from A to B. For example, consider A and B have different pressures and temperatures. You can first do an isothermal compression/expansion and then add heat to get to B, or first add heat, and then change the pressure isothermally. The resulting amounts of work and heat exchange would be different between these two processes. The Carnot cycle is just one set of these choices for a cycle between two temperatures, that gives the maximum output work to input heat ratio (efficiency). In practice, it is not even a good choice for energy production. Something like a Rankine cycle is mostly used.
Hi Mohsen Sadeghi,
Yes, what you said is right, although it's almost irrelevant to what I said here.
What I want to emphasize is:
in thermodynamics, when we're discussing "process" or "cycle", we're discussing a process or a cycle of a specific path(trajectory).
We never discuss "process" or "cycle" in general, for that is meaningless.
As already said, a thermodynamic process refers to any change in the thermodynamic variables whereas a cycle is a closed process, where the final and initial state of the system is the same.
There are relevant aspects in a cycle (not in other processes) that can be considered as "general". For instance, thermodynamic potentials (energy, enthalpy, free energy) and other functions of state (entropy) remain constant at the end of the cycle.
What I emphasized is:
in thermodynamics, when we're discussing "process" or "cycle", we're discussing a process or a cycle of a specific( given) path(trajectory).
e.g., the "arbitrary" cycle that a set of element Carnot cycles " replace" ( in fact, it cann't be replaced) is just ONE cycle of ONE specific path(trajectory).
We never discuss "process" or "cycle" in general, for that is meaningless.
Furthermore, a question that I often ask to my students is related to the difference between processes and cycles, in relation to the Kelvin-Planck statement of the 2nd Law. The question is:
Is it possible in a thermodynamic process to fully transform heat into work? The answer is obviously YES (for example, during the isothermal expansion of an ideal gas). On the contrary, this is forbidden by the 2nd Law for a heat engine (closed cycle).
Of course, the essential difference between general processes and cycles explaining the question above, is that in the latter all thermodynamic variables return to the initial state after each cycle, what does not occur in the former case.
Hi Miguel A Ramos,
What you said is a good problem, although it seems very simple.
I think this question should be answered this way:
1) First of all, the kelvin statement of Second law of thermodynamics is about system CYCLE process.
2) The second law of thermodynamics is a LAW but not a theorem, this means that it can only be verified but not be proved,
it IS TAKEN AS a principle that must be obeyed.
So, if a ( cycle ) process ( such process is imaginary, e.g., a closed adiabatic curve) contradicts the 2nd Law, ACCORDING TO the second law, we conclude that it is not true.
If anyone can give an authentic and dependable counterexample (a counterexample that can be PROVED), the second law of thermodynamics is overthrown!
However, up to now, no such counterexample was found.
The second law of thermodynamics is right, but, my paper has demonstrated that the entropy theory is wrong.
There is no the so-called entropy at all.
A comment, or a question about " ... my paper has demonstrated that the entropy theory is wrong. There is no the so-called entropy at all." -
I am a bit puzzled: though entropy is not a physical quantity, isn't it still a useful concept of physics?
What about "probability", then? - An axiomatic mathematical concept, not a physical quantity, I assume, and still very useful in life.
Hi Jochen Mau,
Entropy is derived from the wrong derivation, there is NO such physical quantity as entropy.
So, entropy is not a concept of physics, it didn't exist at all
So, your message is that entropy cannot be a useful concept because it does not exist ... in physics,. It does not exist, whether as a physical quantity (= something that can be measured) or whether as a mere concept (= something of thought only, something you may not be able to measure) . It does not exist in theory and it does not exist in reality.
Is this what you say?
Hi Jochen,
Yes, it does not exist in theory and it does not exist in reality.
The problem of entropy is that it doesn't exist but not it is unmeasurable.
It has nothing to do with measurement.
Just as phlogiston does not exist, there is NO such physical quantity as entropy, it is derived from the wrong derivation.
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The key mistake of entropy is:
In fact, Q = f(T, V, P) !
( and W= f(T, V, P) 、E= f(T, V, P) ),
so, △Q/T can not become dQ/T !
Q = f(T, V, P) is a process quantity which varies with path, it has innumerable forms between the same original and terminal states, and has a unique form for fixed reversible process path.
When the given path is fixed, Q = f(T, V, P) is the system state variable.
P, V and T are all variables (two variables of T, V and P are generally independent) for any reversible process.
Hence, regarding (1/T)dQ = (1/T)df(T, V, P) = dF(T ,V ,P) (here, P, V are constant),
P, V should be variables but become constant !
so, ∫T 1/TdQ = ∫T dF(T, V, P) is meaningless .( in ∫T , T is subscript )
and, dQ/T = df(T, V, P)/T is meaningless in itself .
Conclusion: △Q/T can not become dQ/T, the so called entropy does not exist.
Thanks, Shufeng, for your quick response! I need some time to think about it, in particular to also think about the implications in areas where "entropy" is used. And to think about any carry-over by analogy of your reasoning to concepts of a similar kind (?) in other areas of physical world.
1: The Second Law is not absolutely valid
Continuum Mech.Thermodyn. 28(2016)1887-1903
2: Processes and cycles are well defined as trajectories
in suitable state spaces. Therefore, I do not understand
the original question.
J.Non-Newtonian Fluid Mech. 96(2001)255-290
3: Entropy is defined as a state function, on a general state
space in non-equilibrium and on the equilibrium sub-space
in equilibrium. That is not a question of existence but one
of defining.
What is your problem ??
Hi W. Muschik,
It seemed that you didn't read my paper and those updates at all.
Could you please read my paper and those updates ?
The entropy is a valid physical quantity. The problem with it is that it has nothing to do with the system itself, but instead, with our information about the system. It is nowadays easier to start from Boltzmann entropy, S=k log (w) (which, by the way, is not derived by Boltzmann, but by Planck) In this equation, w is the NUMBER of microstates that the system can be in. If you want to use probability, you should use this formula:
S = sum_i (-p_i * log (p_i) )
with the i representing a microstate, and p_i the probability of finding the system in that microstate. So, it's a concept related to INFORMATION about the system.
A "microstate" is recognized by the position and momenta of the particles in the system, whereas when you are just looking at it from the thermodynamics point of view, you have "macrostates", recognized by macroscopic observables such as temperature and pressure. So, corresponding to a macrostate, there usually are many many microstates, all giving rise to the same values of observables.
The second law of thermodynamics is a very simple statistical law. It only holds in the limit of a large number of microstates. What the 2nd law tells you is that if you leave an isolated system at some macrostate, it would MOST PROBABLY move to another macrostate which has more microstates attributed to it. The equilibrium state is nothing but the macrostate with the most number of microstates. The 2nd law is quite stupidly obvious in this sense. Because the system has to evolve according to some microscopic dynamics, and it should hop between different microstates without going back to any of the previous ones (because the underlying physics is reversible and you should be able to follow the system back to its origin). So, in this chain of microstates, if you look at the system at some later time, it is more probable for it to be hovering around the macrostates that have more microstates attached to them.
That is the 2nd law and the entropy defined as S = sum_i (-p_i * log (p_i) ) is a very well-defined physical quantity. Any problem that you might have with the concept of thermodynamic entropy goes to the relation between the entropy defined by dS = int (dQ / T) [the old concept] and the information entropy [the modern concept].
To M.S.
All what you wrote is correct. But we need the 2nd law in consitutive
theory to describe material properties of e.g. tooth-paste. The "modern concept" is not helpful for this task: Microstates and tooth-past do not
fit together.
Best regards
W.M.
Shufeng Zhang, your attitude is quite wrong. If you don't like my answer, just ignore it. It is a free forum, after all. You don't need to be insulting. And if you think you are proving something fundamental, you are also wrong.
What I was trying to show with my response was that any claim that the entropy is not a valid physical quantity is bound to be wrong. Because we now have a pretty good understanding of the underlying meaning of entropy, and this century-old thermodynamics approach should at best converge to our current understanding.
Now, I have some remarks regarding your manuscript:
1. (page 2) The claim that the eq. Q2/Q1 = theta_2 / theta_1 comes from the assumption that the working substance is an ideal gas is wrong. This can be shown for any reversible cycle working between temperatures theta_1 and theta_2.
2. (page 2) dQ/T is NOT a complete differential in the general case. It is only a complete differential for infinitesimal heat exchange.
3. (page 3) The eq. Q2/Q1 = T2/T1 is not exclusive to Carnot cycle. It holds for any reversible cycle working between T1 and T2.
4. (page 3) Your definition of thermal efficiency is incomplete. In your proposed cycle, ALL the processes are heat exchange processes (the isothermal process is not adiabatic). The a-b and b-c also exchange work with the environment. You have just chosen to ignore all these heat exchanges and define an efficiency based on work exchange. This has nothing to do with a reasonable definition of efficiency as output/input.
5. The way you went about proving that eta' = eta is wrong. In the first part of the proof you say that the net work absorbed by the reverse E (which is equal to W) is provided by E' and all the heat absorbed by E' (which is also equal to W) is provided by E. So, here you have assumed that the E cycle absorbs W amount heat and has transformed it all to work in a reversible cycle. This is in contradiction with the 2nd law. So, you cannot make this assumption. You need to redo your proof.
Cycle is a process in which system undergoes different processes and return back to the first state. Process is the system in which materials undergoes different states and form a new material of different property or state When the path connecting the change of states of the system is specified, then this path is called Process. Example: constant pressure process, constant volume process etc. When a system goes through different change of states and return backs to the original state, i.e., all the properties are identical to the original state, then the system is said have gone through a thermodynamic
Hi, Shufeng
Suggest that you read through the history about the definitions of heat Q, temperature T, and then how to define entropy S.
If you read a bit about the theory of dissipative structures, you may get better with the classical concepts including entropy.
In addition, do remember and understand the definitions of all sorts of "system" and "State" by thermodynamics.
In other words, if you find a bit flaw with entropy, so what is the better concept? Before you find out a better concept that can better our understanding to the world, the existing one is still a good one.
The above for your comments.
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