The Second Law and Clausius

As the first law is sometimes referred to as the law that defines the fundamental thermodynamic property U, the internal energy of the system, the second law is considered to define the other fundamental property, the entropy S. Classical thermodynamics, via Clausius s thorough analysis [3] of thermodynamic cycles that extract work from available heat, has produced the relation between S and the heat added reversibly to the system at a temperature T  

This relation plays an important role in the derivation of the universal and fundamental thermodynamic relation 

From this relation the differential dS can be expressed as the following function of the differentials of pressure and temperature  

and also composition are the state variables most often used to characterize the state of the system, as they can be easily measured and controlled. As we show in Part II, Equations 2.5 and 2.14 are important to perform the thermodynamic analysis of a process ATS-m, which expresses the change in entropy of a reaction at 298 K and at standard pressure. The reaction is defined to take place between compounds in their standard state, that is, in the 

Finally, equilibrium processes can be defined as processes between and passing states that all have the same thermodynamic probability. On the one hand, these processes proceed without driving forces on the other hand, and this is inconsistent and unrealistic, there is no incentive for the process to proceed. These imaginary processes function only to establish the minimum amount of work required, or the maximum amount of work available, in proceeding from one state to the other. 

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