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 ne...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.展开更多
The classical thermodynamics reflects the significant relationship between the heat and the temperature. On the basis of the relationships, according to the mathematical derivation, this paper structures the conceptio...The classical thermodynamics reflects the significant relationship between the heat and the temperature. On the basis of the relationships, according to the mathematical derivation, this paper structures the conceptions of generalized heat, generalized thermodynamic temperature, generalized entropy and so on. The series of conceptions in the classical thermodynamics is merely a special case of the generalized thermodynamics. Based on these conceptions of generalized thermodynamics, this paper presents the new expressions of the first law and the second law of thermodynamics. In other words, these expressions are endued with new explanations. The Eq. LZ = kTS given by this paper provides theoretical basis for these new expressions.展开更多
We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is e...We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is extracted from the systematic algorithm. The entropy correction term depends on the extra-dimension number of the brane as expected, but the interplay between the correction term and the extra dimensions is more complicated. With the unified first law of thermodynamics well-founded, the generalized second law of thermodynamics is discussed and it is found that the second law can be violated in certain circumstances. Particularly, if the number of the extra dimensions is larger than one, the generalized law of thermodynamics is always satisfied; otherwise, the validity of the second law can only be guaranteed with the Hubble radius greatly smaller than the crossover scale rcof the 5-dimensional DGP model.展开更多
文摘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.
文摘The classical thermodynamics reflects the significant relationship between the heat and the temperature. On the basis of the relationships, according to the mathematical derivation, this paper structures the conceptions of generalized heat, generalized thermodynamic temperature, generalized entropy and so on. The series of conceptions in the classical thermodynamics is merely a special case of the generalized thermodynamics. Based on these conceptions of generalized thermodynamics, this paper presents the new expressions of the first law and the second law of thermodynamics. In other words, these expressions are endued with new explanations. The Eq. LZ = kTS given by this paper provides theoretical basis for these new expressions.
基金Supported by National Foundation of China under Grant Nos.10747155 and 11205131the Ministry of Science and Technology of the National Natural Science Foundation of China key project under Grant Nos.11175270,11005164,11073005,and 10935013Chongqing Science and Technology Commission under Grant No.2010BB0408
文摘We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is extracted from the systematic algorithm. The entropy correction term depends on the extra-dimension number of the brane as expected, but the interplay between the correction term and the extra dimensions is more complicated. With the unified first law of thermodynamics well-founded, the generalized second law of thermodynamics is discussed and it is found that the second law can be violated in certain circumstances. Particularly, if the number of the extra dimensions is larger than one, the generalized law of thermodynamics is always satisfied; otherwise, the validity of the second law can only be guaranteed with the Hubble radius greatly smaller than the crossover scale rcof the 5-dimensional DGP model.
