Moran_9e_LectureSlides_ch06_KKS(1) PDF

Chapter 6 Using Entropy Lecture 30  Learning Outcomes ►Explain key concepts related to entropy and the second law, including entropy transfer, entropy production, and the increase in entropy principle. ►Evaluate entropy, evaluate entropy change between two states, and analyze isentropi...

Chapter 6 Using Entropy Lecture 30  Learning Outcomes ►Explain key concepts related to entropy and the second law, including entropy transfer, entropy production, and the increase in entropy principle. ►Evaluate entropy, evaluate entropy change between two states, and analyze isentropic processes, using appropriate property data.  Learning Outcomes, cont. ►Represent heat transfer in an internally reversible process as an area on a temperature-entropy diagram. ►Analyze closed systems and control volumes, including applying entropy balances. ►Use isentropic efficiencies for turbines, nozzles, compressors, and pumps for second law analysis. Introducing Entropy Change and the Entropy Balance (1 of 2) ►Mass and energy are familiar extensive properties of systems. Entropy is another important extensive property. ►Just as mass and energy are accounted for by mass and energy balances, entropy is accounted for by an entropy balance. ►Like mass and energy, entropy can be transferred across the system boundary.  Introducing Entropy Change and the Entropy Balance (2 of 2) ►The entropy change and entropy balance concepts are developed using the Clausius inequality expressed as: ∫ (Eq. 5.13) where scycle = 0 no irreversibilities present within the system Eq. scycle > 0 irreversibilities present within the system 5.14 scycle < 0 impossible  Defining Entropy Change (1 of 4) ►Consider two cycles, each composed of two internally reversible processes, process A plus process C and process B plus process C, as shown in the figure. ►Applying Eq. 5.13 to these cycles gives, where scycle is zero because the cycles are composed of internally reversible processes.  Defining Entropy Change (2 of 4) ►Subtracting these equations: ►Since A and B are arbitrary internally reversible processes linking states 1 and 2, it follows that the value of the integral is independent of the particular internally reversible process and depends on the end states only.  Defining Entropy Change (3 of 4) ► Recalling (from Sec. 1.3.3) that a quantity is a property if, and only if, its change in value between two states is independent of the process linking the two states, we conclude that the integral represents the change in some property of the system. ► We call this property entropy and represent it by S. The change in entropy is (Eq. 6.2a) where the subscript “int rev” signals that the integral is carried out for any internally reversible process linking states 1 and 2.  Defining Entropy Change (4 of 4) ►Equation 6.2a allows the change in entropy between two states to be determined by thinking of an internally reversible process between the two states. But since entropy is a property, that value of entropy change applies to any process between the states – internally reversible or not. ►Entropy change is introduced by the integral of Eq. 6.2a for which no accompanying physical picture is given. Still, the aim of Chapter 6 is to demonstrate that entropy not only has physical significance but also is essential for thermodynamic analysis. Lecture 31  Entropy Facts (1 of 3) ►Entropy is an extensive property. ►Like any other extensive property, the change in entropy can be positive, negative, or zero: ►By inspection of Eq. 6.2a, units for entropy S are kJ/K and Btu/oR. ►Units for specific entropy s are kJ/kg∙K and Btu/lb∙oR.  Entropy Facts (2 of 3) ► For problem solving, specific entropy values are provided in Tables A-2 through A-18. Values for specific entropy are obtained from these tables using the same procedures as for specific volume, internal energy, and enthalpy, including use of (Eq. 6.4) for two-phase liquid-vapor mixtures, and (Eq. 6.5) for liquid water, each of which is similar in form to expressions introduced in Chap. 3 for evaluating v, u, and h.  Entropy Facts (3 of 3) ►For problem solving, states often are shown on property diagrams having specific entropy as a coordinate: the temperature-entropy and enthalpy-entropy (Mollier) diagrams shown here  Entropy and Heat Transfer (1 of 3) ► By inspection of Eq. 6.2a, the defining equation for entropy change on a differential basis is (Eq. 6.2b) ► Equation 6.2b indicates that when a closed system undergoing an internally reversible process receives energy by heat transfer, the system experiences an increase in entropy. Conversely, when energy is removed by heat transfer, the entropy of the system decreases. From these considerations, we say that entropy transfer accompanies heat transfer. The direction of the entropy transfer is the same as the heat transfer.  Entropy and Heat Transfer (2 of 3) ► On rearrangement, Eq. 6.2b gives Integrating from state 1 to state 2, (Eq. 6.23)  Entropy and Heat Transfer (3 of 3) From this it follows that an energy transfer by heat to a closed system during an internally reversible process is represented by an area on a temperature-entropy diagram: Lecture 32  Entropy Balance for Closed Systems (0 of 5) ► The entropy balance for closed systems can be developed using the Clausius inequality ► Consider a closed system undergoing a cycle as shown below:  Entropy Balance for Closed Systems (1 of 5) ► The entropy balance for closed systems can be developed using the Clausius inequality expressed as Eq. 5.13 and the defining equation for entropy change, Eq. 6.2a. The result is where the subscript b indicates the integral (Eq. 6.24) is evaluated at the system boundary. ► In accord with the interpretation of scycle in the Clausius inequality, Eq. 5.14, the value of s in Eq. 6.24 adheres to the following interpretation = 0 (no irreversibilities present within the system) s: > 0 (irreversibilities present within the system) < 0 (impossible) Entropy Balance for Closed Systems (2 of 5) ► That s has a value of zero when there are no internal irreversibilities and is positive when irreversibilities are present within the system leads to the interpretation that s accounts for entropy produced (or generated) within the system by action of irreversibilities. ► Expressed in words, the entropy balance is change in the amount net amount of amount of of entropy contained entropy transferred in entropy produced within the system across the system boundary + within the system during some accompanying heat transfer during some time interval during some time interval time interval Entropy Balance for Closed Systems (3 of 5) Example: One kg of water vapor contained within a piston-cylinder assembly, initially at 5 bar, 400oC, undergoes an adiabatic expansion to a state where pressure is 1 bar and the temperature is (a) 200oC, (b) 100oC. Boundary Using the entropy balance, determine the nature of the process in each case. ► Since the expansion occurs adiabatically, Eq. 6.24 reduces to give 0 2 → m(s2 – s1) = s (1) 1 where m = 1 kg and Table A-4 gives s1 = 7.7938 kJ/kg∙K. Entropy Balance for Closed Systems (4 of 5) (a) Table A-4 gives, s2 = 7.8343 kJ/kg∙K. Thus Eq. (1) gives s = (1 kg)(7.8343 – 7.7938) kJ/kg∙K = 0.0405 kJ/K Since s is positive, irreversibilities are present within the system during expansion (a). (b) Table A-4 gives, s2 = 7.3614 kJ/kg∙K. Thus Eq. (1) gives s = (1 kg)(7.3614 – 7.7938) kJ/kg∙K = –0.4324 kJ/K Since s is negative, expansion (b) is impossible: it cannot occur adiabatically. Entropy Balance for Closed Systems (5 of 5) More about expansion (b): Considering Eq. 6.24