The Relationship between Entropy and Heat

The entropy, S, of a system is a state function just like internal energy, E, and enthalpy, H. As with these other quantities, the value of S is a characteristic of the state of a system. eoo (Section 5.2) Thus, the change in entropy, AS, in a system depends only on 

For the special case of an isothermal process, AS is equal to the heat that would be transferred if the process were reversible, divided by the absolute temperature at which the process occurs  

Although many possible paths can take the system from one state to another, only one path is associated with a reversible process. Thus, the value of is uniquely defined for any two states of the system. Because S is a state function, we can use Equation 19.2 to calculate AS for any isothermal process between states, not just the reversible one. 

How can S be a state function when AS depends on q, which is not a state function  

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We recognize this as eq. (4.28). which we derived previously. In many textbooks this is the preferred statement of the second law because the relationship between entropy and heat is immediate and does not require additional derivations. The problem with approach is that this inequality must be accepted without any physical justification. Mathematically, however, this statement is completely equivalent to our definition for an adiabatic process, eq. (4.28) indeed reduces to eq. (4.2) and from there on, we recover all of the other results obtained in this chapter. 

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