Entropy: A concept that is not a physical quantity

: This study has demonstrated that entropy is not a physical quantity, that is, the physical quantity called entropy does not exist. If the efficiency of heat engine is defined as η = W/W 1 , and the reversible cycle is considered to be the Stirling cycle, then, given ∮ dQ/T = 0, we can prove ∮ dW/T = 0 and ∮ d/T = 0. If ∮ dQ/T = 0, ∮ dW/T = 0 and ∮ dE/T = 0 are thought to define new system state variables, such definitions would be absurd. The fundamental error of entropy is that in any reversible process, the polytropic process function Q is not a single-valued function of T, and the key step of Σ [( Δ Q)/T)] to ∫ dQ/T doesn’t hold. Similarly, ∮ dQ/T = 0, ∮ dW/T = 0 and ∮ dE/T = 0 do not hold, either. Since the absolute entropy of Boltzmann is used to explain Clausius entropy and the unit (J/K) of the former is transformed from the latter, the non-existence of Clausius entropy simultaneously denies Boltzmann entropy.


I. Introduction
What is entropy?This question has been debated for over 100 years.
Historically, Clausius proposed the existence of new system state variable entropy (S) in 1865 based on the equation   0 / T dQ obtained from the reversible cycle of thermodynamic system.He considered the entropy difference between any two equilibrium states of a thermodynamic system as: 1,2,3,4,5 Only such a difference can be calculated in thermodynamics.Correspondingly, Clausius proposed the well-known law of entropy increase.Subsequently, Boltzmann proposed the formula   ln k S 1,2,3 for absolute entropy in 1872, where k is the Boltzmann constant and Ω the thermodynamic probability.In addition, Boltzmann suggested entropy as the degree of disorder in a system or the measurement mark of order.This is considered to be the best interpretation of entropy and has been in use till today.
The above conclusions, which can be found in many textbooks of thermodynamics and statistical physics, are presently widely accepted and learned.Despite the uncertainty in what entropy really is, entropy has commonly been used as an important physical quantity.
However, there are still many unresolved problems and contradictions difficult to justify in the above conclusions.This indicates entropy is problematic.

A. The origin of entropy
To illustrate that entropy is not a physical quantity, we will briefly review its origin.
First, the efficiency of heat engine is defined as 1,2,3,4,5 that is, taking the ratio of W to Q 1 as the efficiency of heat engine, where W is the net work done by system to the outside world and 1 Q the heat absorbed by the system from the outside world in a heat engine cycle.Regarding the Carnot cycle, there is , where η is related to the constant temperature of two heat sources, rather than the working substance of the system.Accordingly, the thermodynamic temperature scale θ is defined as . When an ideal gas is the working substance of the system, we can prove that: The symbol T is used to represent the thermodynamic temperature scale, that is, , where Q 2 is the heat released (negative value).Then, the arbitrary processes of reversible cycles are approached and replaced by an infinite number of Carnot cycles, resulting in the equation   0 / T dQ . 1,2,3,4,5So far as it goes, dQ/T is considered as a complete differential and the new system status quantity entropy is determined by   0 / T dQ .

B. Entropy is not a physical quantity
Entropy comes from   0 / T dQ .Thus, to prove entropy is not a physical quantity, we only need to prove that   0 / T dQ cannot define a physical quantity or it is untenable in itself.
As we known,   0 / T dQ comes from the equation in Carnot cycle, which has been used to define the thermodynamic temperature scale.The basis of its existence lies in the combination of Carnot cycle and definition of the efficiency of heat engine.It should be noticed that the equation for the efficiency of heat engine is a definition, and the Carnot cycle is only different from other reversible cycles by the form.Therefore, Carnot cycle should not occupy a status higher than other forms of cycles, and its role in defining the thermodynamic temperature scale is not unique.
In this section we will prove that   0 / T dQ cannot define a physical quantity and it is untenable in itself.
First, the efficiency of heat engine needs to be redefined.
As the efficiency of heat engine is meaningful only to the observer, how we define it is not related to objective processes of the heat engine system.Therefore, the efficiency of heat engine can reasonably be defined via other pathways.Here, we redefine the efficiency of heat engine as the ratio of the net work to work done by the heat engine system to the external world in a cycle: That is, the work 1 W done by the system to the external world in a cycle will replace the heat 1 Q absorbed by the system from the external world in the original definition W done by the system to the external world in a cycle cannot entirely be transformed into net work W , and likewise, the heat absorbed by the system from the external world in a cycle cannot entirely be used to do net work to the outside -Kelvin's statement of the second law, these two definitions apparently have the same meaning.Here the second law is expressed in another form: no such an engine can transform all its work to net work to the external world in a cycle.Apparently, this is equivalent to the Kelvin's expression.
For example, a heat engine uses a certain amount of working substance to do work From ( 1 ) we find: TV cycle (Stirling cycle).abeda consist of two reversible isochoric processes (bc and da), and two reversible isothermal processes (ab and cd).The heat source, which exchanges energy power with the system in an isothermal process, is considered as the work source for a better understanding of the followings.This cycle is referred to as TV cycle for short, and the heat engine doing TV cycle (Stirling cycle) is the TV engine.
In this section we will prove that all reversible engines (TV engines) only working between two work sources with constant temperature share the same efficiency, and the efficiency of irreversible engines is lower than that of reversible engines.
Taking any two reversible engines E and E' for example, both engines work between two work sources with constant temperature θ 1 and θ 2 .They are certainly TV engines and have arbitrary working substance.
Given that θ 1 and θ 2 represent the high-and low-temperature work sources, respectively, we get θ 1 >θ 2 .Here, θ can take any temperature scales.If we let E and E' do the same net work (ΔW 1 and ΔW 2 , respectively) to the external world in a cycle, then we will find ΔW 1 = ΔW 2 = W (similar to Carnot cycle).Using W If we incorporate E' and reversely-moving E into one heat engine, the only result of the system recovery after a combined cycle is that the system absorbs work (ΔW = W 2 -W 2 ') from the low-temperature work source (heat source θ 2 ) and automatically does work to the high-temperature work source (heat source θ 1 ).That is, there is equal heat ΔW = W 1 -W 1 ' =W 2 -W 2 ' automatically sent from the low-(heat source θ 2 ) to the high-temperature work source (heat source θ 1 ).This is directly in contradiction with Clausius' expression of the second law, indicating η' > η doesn't hold.
Likewise, we can prove η > η' is untenable based on the assumption regarding reversely moved E'.So, we should have: If E' is an irreversible engine, i.e., non-TV engine, then E' cannot move reversely.There should be: Given that E' is an irreversible engine, and that a combined cycle of E' and the reversible engine E recovers the system and the external world, the equal mark in η' ≤ η doesn't hold upon the premise of irreversible engine E'.This is because, if we have η = η', a combined cycle of reversely-moving E and forwardly-moving E' will obviously completely recover the system and the external world.Then, E' can only be a reversible engine, in contradiction to the fact that E' is an irreversible engine.Therefore, if E' is an irreversible engine, we should have: In this way, according to the definition (1), we have proved that all reversible engines (TV engines) that only work between two work sources with constant temperature share the same efficiency.The efficiency of irreversible engine is lower than that of reversible engine, showing no relationship with the working substance.
As the efficiency of TV engine is not related to working substance, the thermodynamic temperature scale (absolute thermometric scale) can be defined as: That is, the ratio of two thermodynamic temperatures is the ratio of the work W 1 and W 2 exchanged between the TV engine working between two work sources with constant temperature (heat sources) and the work sources.
When the working substance is an ideal gas and the system does TV cycle, we have: By comparing (6) and (7), we obtain for the ideal gas, that is, the thermodynamic temperature scale defined by ( 6) is equivalent to the thermodynamic temperature scale defined by . Still, we use symbol T to represent the thermodynamic temperature scale: where W 2 is the work that the external world has done to the system (negative value).This indicates that when any system does TV cycles, the sum of the work (positive or negative value) exchanged between the system and each work source (heat source) and the thermodynamic temperature ratio of the work source is zero.
Following the exactly same process of deduction of   0 / T dQ , a serial element TV cycles are employed to split and replace any reversible cycles in the system (Figure 2).In two isochoric processes of TV cycle, there is always ΔW = 0 (i.e., dW = 0).Thus, when there are infinite element processes, or the system exchanges work (equivalent to heat) with infinite work sources The key error of entropy is that the mathematical conclusion   0 / T dQ cannot be deduced from physics.That is, the conclusion   0 / T dQ is untenable to any reversible processes of any working substance engines.The key question is that ΔQ/T→dQ/T is taken for granted in the process of deducing the relational expression   0 / T dQ .It should be noticed from the establishment conditions of differential and the deducing process of entropy that ΔQ/T→dQ/T is mathematically untenable.The major reasons are as follows:

1 W 2 W
to the external world in a cycle, and the external world does work to the system for recovery.Then, 2 1 Fig. 1 .TV cycle (Stirling cycle).abeda consist of two reversible isochoric processes (bc and da), and two reversible 1 and W 1 ' to represent the work done by E and E ' in a cycle, W 2 and W 2 ' to represent the work done by the external world to E and E', and η and η' to represent the efficiency of E and E ', we will first prove η'≤ η by contradiction: Assuming η' > η As E and E' are both reversible, we let E do reverse movement.Then, W 2 is the work done by E to the external world, W 1 the work done by the external world to E, and W the net work done by the external world to E. We have W = W 1 -W 2 .W is provided by E', and the heat absorbed by E' in the cycle ΔQ = W (= ΔW 1 = ΔW 2 ) provided by E. Thus,

Fig. 2 .
Fig. 2 .Diagram of the process of any reversible cycles split and replaced by a series of element TV cycles

(
is not related to the working substance of the system.With respect to the irreversible cycle, we obviously can deduce the conclusion  T dW < 0.So far, we have obtained the conclusion  obtain the following conclusion for reversible cycles in any thermodynamic system: has been thought to define a system state variable, i.e., entropy.a new system state variable.In addition, taking the reversible adiabatic process for example, when the system approaches a different equilibrium state 2 from equilibrium state 1, we should have: isochoric process of the system, the following equation exists for different equilibrium states 3 and 4, system state variable, they should be different from each other, despite the same dimension (J/K).Therefore, there is a state variable in the system with different values; or there are three different state variables in the system with the same unit.Although different state variables with the same unit are likely to occur in a system, it is absurd to define three variables due to the uncertainty in the only one S. is true, this equation should have defined a system state variable.However, the present study has demonstrated the absurdity regarding the definition of a physical quantity by the equation