In the paper, the relations of heat or work between a reversible process and its realistic process are discussed, which could be applied to the chemical reactions and Rossini and Frandsen experiment and so on. It is proved the ratios of work to temperature and internal energy change to temperature are all the state function in the reversible process, otherwise, the Clausius inequality will be violated. In an isothermal process of reversible Stirling cycle, the internal energy change is equal to zero for the gas. Thus, the new equation calculating the internal energy change has been obtained for the gas, namely that dU=CVdT, it is convenient and easy calculative.

This research investigates relationships between resistances with heat and work. It is completely proven that the ratio of work to temperature for the realistic process is no less than that for the reversible process. The equalities and inequalities on the heat, work and ratio of work to temperature could be applied to the gravitational field and chemical reactions. The relationships between path functions and state functions are studied in the chemical reactions. Some criteria for spontaneous directions have been suggested such as the equalities and inequalities on the heat, work, and ratio of work to temperature, except the Clausius inequality and must be ordinarily obeyed in the spontaneous process.

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.

The internal energy change of ideal gas does not depend on the volume and pressure. The internal energy change of real gas has not any relation with the volume and pressure, which had been proved. If the internal energy change had not any relation with the volume and pressure, we could confirm the first law of thermodynamics in theory. Simultaneously, the internal energy change is the state function that shall be able to be proved in theory. If the internal energy change depended on the volume and pressure, we could not prove that the internal energy change is the state function and the chemical thermodynamics theory is right. The extended or modified Bernoulli equation can be derived from the energy conservation law, and the internal energy change, heat, and friction are all considered in the derivation procedure. The extended Bernoulli equation could be applied to the flying aircraft and mechanical motion on the gravitational field, for instance, the rocket and airplane and so on. This paper also revises some wrong ideas, viewpoints, or concepts about the thermodynamics theory and Bernoulli equation.

Abstract-According to the Clausius inequality, it can be proven that the quotient of work-temperature in the real process is no less than one in the reversible process. On the basis of the Carnot theorem, it can be proven that the work in the real process is no less than one in the reversible process, or the heat in the reversible process is no less than one in the real process. The real process includes the reversible and irreversible process. The above-mentioned results haven't any relation with paths. The inequality of quotient of work-temperature could be applied to other works. The He(II) motion in superfluid obeys the inequality of quotient of work-temperature.