Thermodynamics

336 | ThermodynamicsProcess 1-2(reversible orirreversible)12Process 2-1(internallyreversible)FIGURE 7–5A cycle composed of a reversible andan irreversible process.The second integral in the previous relation is recognized as the entropychange S 1 S 2 . Therefore,which can be rearranged as 2 dQT S 1 S 2 012dQS 2 S 1 TIt can also be expressed in differential form asdS dQ T1(7–7)(7–8)where the equality holds for an internally reversible process and theinequality for an irreversible process. We may conclude from these equationsthat the entropy change of a closed system during an irreversibleprocess is greater than the integral of dQ/T evaluated for that process. In thelimiting case of a reversible process, these two quantities become equal. Weagain emphasize that T in these relations is the thermodynamic temperatureat the boundary where the differential heat dQ is transferred between thesystem and the surroundings.The quantity S S 2 S 1 represents the entropy change of the system.For a reversible process, it becomes equal to 2dQ/T, which represents the1entropy transfer with heat.The inequality sign in the preceding relations is a constant reminder thatthe entropy change of a closed system during an irreversible process isalways greater than the entropy transfer. That is, some entropy is generatedor created during an irreversible process, and this generation is due entirelyto the presence of irreversibilities. The entropy generated during a process iscalled entropy generation and is denoted by S gen . Noting that the differencebetween the entropy change of a closed system and the entropy transfer isequal to entropy generation, Eq. 7–7 can be rewritten as an equality as2dQ¢S sys S 2 S 1 T S gen(7–9)Note that the entropy generation S gen is always a positive quantity or zero.Its value depends on the process, and thus it is not a property of the system.Also, in the absence of any entropy transfer, the entropy change of a systemis equal to the entropy generation.Equation 7–7 has far-reaching implications in thermodynamics. For anisolated system (or simply an adiabatic closed system), the heat transfer iszero, and Eq. 7–7 reduces to¢S isolated 0(7–10)This equation can be expressed as the entropy of an isolated system duringa process always increases or, in the limiting case of a reversible process,remains constant. In other words, it never decreases. This is known as theincrease of entropy principle. Note that in the absence of any heat transfer,entropy change is due to irreversibilities only, and their effect is always toincrease entropy.1