Thermodynamics

Entropy is an extensive property, and thus the total entropy of a system isequal to the sum of the entropies of the parts of the system. An isolated systemmay consist of any number of subsystems (Fig. 7–6). A system and itssurroundings, for example, constitute an isolated system since both can beenclosed by a sufficiently large arbitrary boundary across which there is noheat, work, or mass transfer (Fig. 7–7). Therefore, a system and its surroundingscan be viewed as the two subsystems of an isolated system, andthe entropy change of this isolated system during a process is the sum of theentropy changes of the system and its surroundings, which is equal to theentropy generation since an isolated system involves no entropy transfer.That is,S gen ¢S total ¢S sys ¢S surr 0(7–11)where the equality holds for reversible processes and the inequality for irreversibleones. Note that S surr refers to the change in the entropy of the surroundingsas a result of the occurrence of the process under consideration.Since no actual process is truly reversible, we can conclude that someentropy is generated during a process, and therefore the entropy of the universe,which can be considered to be an isolated system, is continuouslyincreasing. The more irreversible a process, the larger the entropy generatedduring that process. No entropy is generated during reversible processes(S gen 0).Entropy increase of the universe is a major concern not only to engineersbut also to philosophers, theologians, economists, and environmentalistssince entropy is viewed as a measure of the disorder (or “mixed-up-ness”)in the universe.The increase of entropy principle does not imply that the entropy of a systemcannot decrease. The entropy change of a system can be negative duringa process (Fig. 7–8), but entropy generation cannot. The increase ofentropy principle can be summarized as follows:7 0 Irreversible processS gen • 0 Reversible process6 0 Impossible processThis relation serves as a criterion in determining whether a process isreversible, irreversible, or impossible.Things in nature have a tendency to change until they attain a state of equilibrium.The increase of entropy principle dictates that the entropy of an isolatedsystem increases until the entropy of the system reaches a maximumvalue. At that point, the system is said to have reached an equilibrium statesince the increase of entropy principle prohibits the system from undergoingany change of state that results in a decrease in entropy.Subsystem1Subsystem2Subsystem3Chapter 7 | 337(Isolated)N∆S total = Σ ∆S i > 0i=1SubsystemNFIGURE 7–6The entropy change of an isolatedsystem is the sum of the entropychanges of its components, and isnever less than zero.Isolated systemboundarymSystemSurroundingsm = 0Q = 0W = 0Q, WFIGURE 7–7A system and its surroundings form anisolated system.Some Remarks about EntropyIn light of the preceding discussions, we draw the following conclusions:1. Processes can occur in a certain direction only, not in any direction.A process must proceed in the direction that complies with the increaseof entropy principle, that is, S gen 0. A process that violates this principleis impossible. This principle often forces chemical reactions tocome to a halt before reaching completion.