A wrong therory in physics textbook--Therory of Entropy

[shufeng-zhang]

When define heat engine efficiency as:n = W/ W1 , that is, replacing Q1 in the original definition n=W/ Q1 with W1 , W still is the net work the heat engine applied to the outside in one cycle,W1 is the work the heat engine applied to the outside in the cycle,let the element reversible cycle be Stirling cycle , if circuit integral dQ/T =0 is tenable,we can prove circuit integral dW/T =0 and circuit integral dE/T =0 !

If circuit integral dQ/T=0, dW/T=0 and dE/T=0 really define new system state variables, the three state variables are inevitably different from each other; on the other side, their dimensions are the same one, namely J/K, and they are all state variables. So, we have to “make” three different system state variables with same dimensions, and we don’t know what they are, no doubt, this is absurd.

In fact , replaceing delta Q with dQ is taking for granted, if only we review the definition of differential, we know that the prerequisite of differential is there is a derivability function as y=f(x), however,there is not any function as Q=f(T) here at all, so, delta Q can not become dQ.

On the other side, when delta Q tend towards 0, lim(deltaQ/T)=0 but not lim(deltaQ/T)= dQ/T.

So, circuit integral dQ/T=0?circuit integral dW/T=0 and circuit integral dE/T=0 are untenable at all !

 

See paper Entropy : A concept that is not physical quantity

 

 

OR (PDF)

 

shufeng-zhang china Email: [email protected]

[modest]

Hello, shufeng-zhang. Welcome to Hypography.

 

In fact , replaceing delta Q with dQ is taking for granted, if only we review the definition of differential, we know that the prerequisite of differential is there is a derivability function as y=f(x), however,there is not any function as Q=f(T) here at all, so, delta Q can not become dQ...

 

So, circuit integral dQ/T=0?circuit integral dW/T=0 and circuit integral dE/T=0 are untenable at all !

 

I didn't read your paper, and I'm not expert in thermodynamics, but I have heard of the issues you mention in your post, and I can perhaps point out some references. All of the texts that I have seen make clear that Carnot efficiency is ideal and not physically possible. I'll quote Hyperphysics,

 

In order to approach the Carnot efficiency, the processes involved in the heat engine cycle must be reversible and involve no change in entropy. This means that the Carnot cycle is an idealization, since no real engine processes are reversible and all real physical processes involve some increase in entropy.

Carnot Cycle

 

It is also understood that Clausius theorem (1854),

[math]\oint \frac{dQ}{T} \leq 0[/math]

is an equality only in the idealized and physically impossible reversible case. The issues you have with [math]dQ[/math] go by the term inexact differential. I'll quote wolfram:

Inexact Differential

 

An infinitesimal which is not the differential of an actual function and which cannot be expressed as

[math]dz = \left( \frac{\partial z}{\partial x} \right)_y \ dx + \left( \frac{\partial z}{\partial y} \right)_x \ dy,[/math]

the way an

exact differential

can. Inexact differentials are denoted with a bar through the d. The most common example of an inexact differential is the change in heat [math]d\mkern-6mu\mathchar'26 Q[/math] encountered in thermodynamics.

Inexact Differential -- from Wolfram MathWorld

And, wikipedia says some relevant things on inexact differentials in thermodynamics. I'll just quote the opening paragraph.

In thermodynamics, an "inexact differential" or "imperfect differential" is any quantity, particularly heat Q and work W, that are not state functions (a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state), in that their values depend on how the process is performed. The symbol [math]d\mkern-6mu\mathchar'26[/math], or δ (in the modern sense), which originated from the work of German mathematician Carl Gottfried Neumann in his 1875 ''Vorlesungen über die mechanische Theorie der Wärme'', indicates that Q and W are path dependent. In terms of infinitesimal quantities, the first law of thermodynamics is thus expressed as:

 

[math]\mathrm{d}U=\delta Q-\delta W[/math]

 

where δ

Q

and δ

W

are inexact (path-dependent), and d

U

is exact (path-independent).

Inexact differential - Wikipedia, the free encyclopedia

~modest

[shufeng-zhang]

Dear modest:

 

I'm glad to see your reply,thank you!

 

But you say you didn‘t see my paper.

 

I don’t want to argue for the thread and you reply, I only suggest you think carefully if you are interested in what I post， and it would be best to read the paper.

 

Thank you!

shufeng-zhang