Some properties of the entropy

It is not difficult to show that the entropy of a closed system in an equilibrium state is an extensive property. Suppose a system of uniform temperature T is divided into two closed subsystems A and B. When a reversible infinitesimal change oeeurs, the entropy changes of the subsystems are d5A = dqp,/T and d e = dq /T and of the system d5 = dqj T. But dq is the sum of d A and dq, which gives d = d A + d B- Thus, the entropy changes are additive, so that entropy must be extensive 5 =Sa+Sb.  

How ean we evaluate the entropy of a particular equilibrium state of the system We must assign an arbitrary value to one state and then evaluate the entropy change along a reversible path from this state to the state of interest using AS = f dq/ Tb). 

We may need to evaluate the entropy of a nonequilibrium state. To do this, we imagine imposing hypothetical internal constraints that change the nonequilibrium state to a constrained equilibrium state with the same internal structure. Some examples of such internal constraints were given in Sec. 2.4.4, and include rigid adiabatic partitions between phases of different temperature and pressure, semipermeable membranes to prevent transfer of certain species between adjaeent phases, and inhibitors to prevent chemical reactions. 

We assume that we ean, in principle, impose or remove such constraints reversibly without heat, so there is no entropy change. If the nonequilibrium state includes macroscopic internal motion, the imposition of internal constraints involves negative reversible work to bring moving regions of the system to rest. If the system is nonuniform over its extent, the 

We know that during a reversible process of a closed system, each infinitesimal entropy change dS is equal to dq/ and the finite change AS is equal to the integral /(dq/ 7b)— but what can we say about d5 and AS for an irreversible process  

---