Entropy is not a state variable, and there is a physical difference between it and internal energy.
In the textbook, the ideal gas entropy: S = n * Cv * In (T) +nR * In (V);
There are two problems:
1. The natural logarithm In(x) will submerge the unit system of volume and temperature [m3], [K].
2. The unit of temperature may be [K], or [mK]; the unit of volume may be [m3], or [cm3]. The results are different and the calculation lacks stability.
Entropy is only a process quantity: DS = n * Cv * In (T2/T1) + nR * In (V2/V1); it has physical significance.
Internal energy is a state quantity, and entropy is only a process quantity. There are physical differences between them.
Internal energy U is conserved and can have the meaning of total differential dU = Ut * dT + Uv * dV - correct.
Entropy is only a process quantity, not a state quantity. Total differential is meaningless: dS = St * dT + Sv * dV - - incorrect.
Entropy is not conservative, even in reversible cycles, it can increase or decrease.
Thermodynamics has some problems in describing ideal gases.
During the process of deriving the so-called entropy, in fact, ΔQ/T can not be turned into dQ/T. That is, the so-called "entropy " doesn't exist at all.
The so-called entropy was such a concept that was derived by mistake in history.
It is well known that calculus has a definition,
any theory should follow the same principle of calculus; thermodynamics, of course, is no exception, for there's no other calculus at all, this is common sense.
Based on the definition of calculus, we know:
to the definite integral ∫T f(T)dQ, only when Q=F(T), ∫T f(T)dQ=∫T f(T)dF(T) is meaningful.
As long as Q is not a single-valued function of T, namely, Q=F( T, X, …), then,
∫T f(T)dQ=∫T f(T)dF(T, X, …) is meaningless.
1) Now, on the one hand, we all know that Q is not a single-valued function of T, this alone is enough to determine that the definite integral ∫T f(T)dQ=∫T 1/TdQ is meaningless.
2) On the other hand, In fact, Q=f(P, V, T), then
∫T 1/TdQ = ∫T 1/Tdf(T, V, P)= ∫T dF(T, V, P) is certainly meaningless. ( in ∫T , T is subscript ).
We know that dQ/T is used for the definite integral ∫T 1/TdQ, while ∫T 1/TdQ is meaningless, so, ΔQ/T can not be turned into dQ/T at all.
that is, the so-called "entropy " doesn't exist at all.
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Why did the wrong "entropy" appear ?
In summary , this was due to the following two reasons:
1) Physically, people didn't know Q=f(P, V, T).
2) Mathematically, people didn't know AΔB couldn‘t become AdB directely .
If people knew any one of them, the mistake of entropy would not happen in history.
Please read my paper and those answers of the questions related to my paper in my Projects.
1. The second law of thermodynamics loses the ability of quantitative prediction.
2. Data processing method of law 2 of thermodynamics violates scientific discipline: modifying experimental data to satisfy theory
See the picture for details.
3. The second law of thermodynamics can only be called science if it reaches the same quantitative prediction ability as Newton's second law, otherwise it is pseudoscience.
1. Logic of the Second Law of Thermodynamics: Subjectivism, Logical Jump, Interdisciplinary Argumentation.
2. New thermodynamics pursues universality, two theoretical cornerstones:
2.1 Boltzmann formula: ro=A*exp(-Mgh/RT) - Isotope centrifugal separation experiments show that it is suitable for gases and liquids.
2.2. Hydrostatic equilibrium: applicable to gases and liquids.
3. The second and third sonic virial coefficients of R143a derived from the new thermodynamics are in agreement with the experimental results.
3.1. The third velocity Virial coefficient derived is in agreement with the experimental data, which shows that the theory is still correct when the critical density is reached.
4. See Appendix Pictures and Documents for details.