New Method Proving Clausius Inequality

It is impossible that proving the internal energy change has the relations with volume and pressure. About the second law of thermodynamics, many mistakes of formulations need to be put right and modified, and many new concepts are surveyed too. The equality and inequality on the ratios of internal energy change to temperature and work to temperature are discussed. The relation between the reversible paths and their realistic paths is also researched. In an isothermal process, the internal energy change for the gases is equal to zero, but the internal energy change is not equal to zero for the phase transition or chemical reaction. The Clausius inequality can be derived from the equation calculating the internal energy change in mathematics; it is the new method proving the Clausius inequality. These change laws of thermodynamics could be applied to the gravitational field and mechanical motion and so on.


Introduction
In text, the heat and work are taken as positive if the energy is supplied to the system and negative if the energy is lost out of the system. other W expresses the other work (also called the non-expansion work), and d p V − indicates the pressure-volume work (namely the expansion work).
According to the first law of thermodynamics [1] [2] [3], if the expansion work doesn't exist, the internal energy change is equal to the non-expansion work in the adiabatic process. If any work doesn't exist, the internal energy change is equal to the heat in a constant volume process (namely that d d

New Concepts about the Ratios of Internal Energy Change to Temperature and Work to Temperature
In a spontaneous or realistic process, according to the first law of thermodynamics, we can obtain [4] [5] ( ) ( ) The criterion equation for a process is obeyed as the follows In a spontaneous or realistic process, the following equations must be also where, the equality is usually for a reversible process, the inequality is for an ir- ( ) . In a process, T i and T f are the thermodynamics temperature of system in the initial state and final state, respectively. T expresses the thermodynamics temperature of system transforms from T i to T f . T res is the thermodynamics temperature of surroundings or reservoirs, and T res can vary or influence the thermodynamics temperature of system except the adiabatic system. Of course, T res is the same as T in any reversible process or constant temperature process. T res is not always considered as a constant in a realistic process. Any spontaneous or realistic process has to obey the Clausius inequality [6] [7] [8].
, where, ΔS g is called the entropy generation [9] [10] [11]. In a spontaneous or realistic process, we can gain 0 g S ∆ ≥ . In the adiabatic process, ΔS g is not equal to zero for an irreversible process.
is defined as the ratio of work to temperature generation. In a spontaneous or realistic process, we have is the path functions called the entropy flow [12]. When the solids and liquids are cooled, it will release the heat and its temperature will fall, the entropy change is negative value which conforms to the Clausius inequality, it is very reasonable nature results, but the entropy generation is no less than zero in the processes, that is, 0 g S ∆ ≥ . In a process, ΔS is unable to be varied by the entropy flow or path or energy like work and heat, since it is the state functions. The entropy generation could be changed from negative to positive by the entropy flow or path or energy. In the living things, the entropy generation in the glucose synthesized reaction will be changed from negative to positive. If there is not any energy supplied to system, the damage cells in the living things could not be repaired, and the life will end and die.

New Method Proving the Clausius Inequality
The internal energy change has to be equal to zero for the ideal and real gases in any isothermal process, namely that, 0  [13], the high pressure gas slowly expands and enters the air through the valve and pipeline, the water heated by heater in trough will keep constant temperature, but the expansion gas is open will still do work to air, so the heat is unable to be accurately determined. Therefore, it is regretful that the Rossini and Frandsen experiment could not prove the internal energy change having a relation with the pressure and volume for the gas. In the Rossini and Frandsen experiment, the pressure-volume work is equal to If the latent heat and chemical reactions do not exist, we can obtain [4] d d The gases, solids and liquids all obey Equation (5). If the phase transition or chemical reactions exist in the constant temperature and constant pressure, the internal energy change will be given by where, the enthalpy change is the latent heat or chemical reaction heat in the constant temperature and constant pressure. Therefore, the internal energy change is the state functions for the phase transition or chemical reactions.
If the phase transition or chemical reactions does not exist for the closed system, we can obtain d d Attentively, T is often not the constant in the isothermal irreversible path (B), but i f res Thereinafter, using Equation (4) will prove the Clausius inequality is absolutely correct. According to Equation (5), we can prove Equation (4) is absolutely right in In order to guarantee that above-mentioned inequality is absolutely right, according to Equation (4), the value of On the basis of Equation (4), we have In order to guarantee that aforesaid inequality is absolutely right, according to Consequently, according to Equation (4), we can find There are two results generated by Equation (4), but their conclusions are contrary. Which result should be selected? We need to eliminate a wrong answer from the next procedures.
When any work doesn't exist, we can gain Therefore, on the basis of Equation (4), we can get where, expresses absolute value symbol of quantity. In the isothermal process, Accordingly, we can confirm The aforementioned results prove the Clausius inequality is right. These Equations (2)

Relation between the Reversible Paths and Its Realistic Paths in the Gases and Chemical Reactions
In a spontaneous or realistic process, we would assume [4] ( ) where, the equality is for the identical reversible paths (if any work doesn't exist, the equality is also for the irreversible paths), the inequality is for other irrevers- On the basis of Equation (11)  If the chemical reaction and other work all exist in the constant pressure and isothermal process, we have , which are criteria when the other work exists in the constant pressure and isothermal chemical reactions (see Figure 1).

Maxwell Relations and Joule-Thomson Throttling Experiment
Maxwell [17] thought the thermodynamics functions obey the following relations, namely that They are all obtained by commutation relations, but these commutation relations are not always correct. Moreover, the both sides (namely that, the left side and right side) per Maxwell equality correspond to the different processes, their results for the gases are no-confidence. Simultaneously, the Maxwell relations are also not right for the unclosed system. Therefore, the Maxwell relations are not right and disobey the Clausius inequality.
Because the other work does not exist, hence, 0 H ∆ = (where, ΔH is the enthalpy change). We know V U C T ∆ = ∆ , thus, the temperature change is given So that, the average value of Joule-Thomson coefficient JT The Joule-Thomson throttling experiment is an irreversible process, thereof, JT µ is not the state function. The temperature in the chamber 1 will raise since the work is done by surroundings. The temperature in the chamber 2 will fall since the gas does work to surroundings. Therefore, the formula (13) calculating the temperature change in the Joule-Thomson throttling experiment is an approximate equation.

Applying to the Earth Gravitational Field and Motional Body
In the gravitational field, mgΔh is the gravitational potential energy change, m is the mass, g is the acceleration of gravity, Δh is the elevation change. In a process, the relations among the gravitational potential energy change, kinetic energy change, and internal energy change had been investigated [18] [19] [20]. Attentively, the motion path in the reversible process is the same as the realistic process. According to the conservation law of energy, we can get where, p is the pressure between system and surroundings (it isn't internal pressure [21] W b cannot cause the heat change directly, but it can influence the kinetic energy change. In a process, the absorbed heat is positive, the released heat is negative. If the obtained energy including heat and work with the mechanical work could not be repeatedly calculated for the motional body, but they should be able to transform into the kinetic energy. For the closed gas, the mechanical work with the pressure-volume work is unable to be repeatedly calculated. For instance, the bullet and rocket could obtain the heat energy from the burned ammunition and fuel, but the obtained heat need to avoid repeating calculation with the mechanical work in Equations (15), (16) (see Figure 3). In the parachute, W b has to be considered. In the pipeline system of fluid, the mechanical work and pressure-volume work have to be all considered.
where, in a reversible process,

C. S. Jin
In the isothermal process, Equation (4) is not the criterion. If any work doesn't exist, Equation (3) is not the criterion. It is not surprising the He(II) superfluid, particles, and gases disobey the conservation law of mechanical energy.
The conservation law of mechanical energy is a bad conservation law. Equations (1)-(5), (10), (11) should be able to apply to a single particle or big object. The pressure-volume work of gases could be generated easily. In any case for a particle or big object, the friction work is all positive value, and the friction heat will be negative. The afore-mentioned function such as ΔS W and ΔS U are all the state function for the ideal gas in a reversible process. For the vacuum state, any irreversible process does not exist for the motional body.
For the whole unclosed system, the expansion work for the chemical reactions in the constant pressure and isothermal process is not equal to ). Therefore, the system entropy may be less than zero sometime in the isolated system, but the entropy generation has to be no less than zero in the isolated system. The principle of entropy increase is not always right in the isolated system and non-isolated system.
The organisms are a type of heat engine, but they are controlled by the biological chemical reactions, DNA, and RNA etc. (not mechanism).
If assuming that the surroundings entropy or entropy flow are equal to zero, the entropy generation has to be equal to the entropy change. For the isolated system in a realistic path (B), the entropy change will become the entropy generation which is the non-state function except when ( ) 0 real Q B = . So that, the principle of entropy increase is an error for many cases. A reversible path (A) may contain a few processes in its realistic path (B), and a realistic path (B) may contain a few processes in its reversible path (A) too.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.