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1、WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition 7 CHAPTERCHAPTER Entropy: A Measure of Disorder WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThir
2、d Edition Entropy and Clausius Inequality Entropy and Clausius Inequality The second law of thermodynamics leads to the definition of a new property called entropy, a quantitative measure of microscopic disorder for a system. Entropy is a measure of energy that is no longer available to perform usef
3、ul work within the current environment. To obtain the definition of entropy and, thus, the second law, lets derive the Clausius inequality. WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition Development of Clausius inequ
4、ity WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition This equation is called the Clausius inequality. The equality holds for the reversible process and the inequality holds for the irreversible process. Entropy and Cla
5、usius Inequality WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition Entropy and Clausius Inequality Definition of Entropy for internally reversible cycles. We conclude that the equality in the Clausius inequality holds f
6、or totally or just internally reversible cycles and the inequality for the irreversible ones. Therefore, the quantity (Qnet/T)int rev must be a property in differential form. The entropy change during a reversible process is defined as WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoTherm
7、odynamicsdynamics engelengel BolesBoles Third EditionThird Edition Consider the cycle shown below composed of two reversible processes A and B. Apply the Clausius inequality for this cycle. What do you conclude about these two integrals? B A 2 V P 1 A cycle composed of two reversible processes. WCB/
8、McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition Apply the Clausius inequality for the cycle made of two internally reversible processes: You should find: Since the quantity (Qnet/T)int rev is independent of the path and m
9、ust be a property, we call this property the entropy S. WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition Consider the cycle 1-A-2-B-1, shown below, where process A is arbitrary that is, it can be either reversible or i
10、rreversible, and process B is internally reversible. B A 2 V P 1 A cycle composed of reversible and irreversible processes. WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition The integral along the internally reversible
11、path, process B, is the entropy change S1 S2. Therefore, WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition In general the entropy change during a process is defined as where = holds for the internally reversible process
12、 holds for the irreversible process WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition The reversible, adiabatic process is called an isentropic process. Entropy change is caused by heat transfer and irreversibilities. H
13、eat transfer to a system increases the entropy; heat transfer from a system decreases it. The effect of irreversibilities is always to increase the entropy. WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition The entropy
14、change during a process is obtained by integrating the dS equation over the process: The entropy generated during an irreversible process is called entropy generation and is denoted as Sgen. Sgen is always a positive quantity or zero. Its value depends upon the process and thus it is not a property.
15、 Sgen is zero for an internally reversible process. WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition Definition of Second Law of Thermodynamics Now consider an isolated system composed of several subsystems exchanging
16、energy among themselves. Since the isolated system has no energy transfer across its system boundary, the heat transfer across the system boundary is zero. WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 ThermoThermodynamicsdynamics engelengel BolesBoles Third EditionThird Edition Applying the definition of entropy to the isolated system The total entropy change for the isolated system is WCB/McGraw-Hill The McGraw-Hill Companies, Inc.,1998 The
