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1 CAPER 6 Entropy

2 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. he Clausius Inequality: 0 his inequality is valid for all cycles, reversible or irreversible Cycle integral = for reversible < for irreversible

3 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. he vaidity of the Clasisus inequality: Clasius inequality Formal definition of entropy he system considered in the development of the Clausius inequality. he equality in the Clausius inequality holds for totally or just internally reversible cycles and the inequality for the irreversible ones.

4 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. For reversible cycles: 0 ) ( : 0 ) ( int rev rev note Rev.. E. W net igh temp. reservoir at igh temp. reservoir at

Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. igh temp. reservoir at For irreversible cycles:, irrev Or, irrev Diff Rev.. E.

5 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. igh temp. reservoir at For irreversible cycles:, irrev Or, irrev Diff Rev.. E. W net Diff IRREV.. E., irrev W net, irrev ( ) ( ) irrev irrev 0 Diff, irrev 0 Diff igh temp. reservoir at Note: 0 violates the nd law of thermodynamics For all cycles, the two results are combined: 0 has to be always negative.

6 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. Entropy: Internally reversible dv 0 he net change in volume (a property) during a cycle is always zero. Any property change during a cycle is zero. Since ( ) 0,( int rev ) int rev property in the differential form. must represent a ( ) ( ) intrev A ( ) ( ) A B ( ) B 0

7 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. he value of the integral depends on the end states on;y and not the path followed. his represents the change of a property. his is called entropy, S. ds ( ) int rev ( kj ) K Entropy is an extensive property. ( int rev he entropy change of a system: S S S ) ) Example: air temperature is raised from to W S 0 du ( ) du mc v intrev d mcvd mc v ln hermal insulation ( kj K Air

the entropy changes of thermal energy reservoirs that can absorb or supply heat indefinitely at constant

8 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. A Special Case: Internally Reversible Isothermal heat transfer processes: Particularly useful for determining the entropy changes of thermal energy reservoirs that can absorb or supply heat indefinitely at constant temperature. = 300K = const ΔS = / =.5 kj/k S S ( ) o int rev kj K ( ) o int rev Constant absolute temperature o ( ) int rev = 750 kj

9 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. E INCREASE OF ENROPY PRINCIPE Consider a a cycle that is made of two processes: S S his is an irrev. cycle since part of it is irreversible. A different amount of actual heat transfer between a system and its oundings Absolute temp. of the boundary he equality holds for an internally reversible process and the inequality for an irreversible process. 9

10 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. A different amount of actual heat transfer between a system and its oundings Absolute temp. of the boundary If system is adiabatic then 0 S isolated 0 he entropy of an isolated system during a process always increases or, in the limiting case of a reversible process, remains constant. Some entropy is generated or created during an irreversible process, and this generation is due entirely to the presence of irreversibilities. he entropy generation S gen is always a positive quantity or zero. Can the entropy of a system during a process decrease?

11 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. he entropy change of an isolated system is the sum of the entropy changes of its components, and is never less than zero. A system and its oundings form an isolated system. he increase of entropy principle

12 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. Some Remarks about Entropy he entropy change of a system can be negative, but the entropy generation cannot.. Processes can occur in a certain direction only, not in any direction. A process must proceed in the direction that complies with the increase of entropy principle, that is, S gen 0. A process that violates this principle is impossible.. Entropy is a nonconserved property, and there is no such thing as the conservation of entropy principle. Entropy is conserved during the idealized reversible processes only and increases during all actual processes. 3. he performance of engineering systems is degraded by the presence of irreversibilities, and entropy generation is a measure of the magnitudes of the irreversibilities during that process. It is also used to establish criteria for the performance of engineering devices.

13 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. Example: A system and its oundings can be viewed as the two subsystems. otal entropy change is the entropy change of all the systems: S total S sys S 0 Entropy generation, Sgen S gen S sys S 0 he entropy generation S gen is always a positive quantity or zero.

14 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. he increase of entropy principle: > 0 irreversible process S gen S total Can not be negative = 0 reversible process < 0 impossible process S sys S Can be negative Example: he entropy change of a system can be negative, but the entropy generation cannot.

15 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. Closed Systems S gen S total S sys S 0 Isolated system boundary S S m( s s) S If process is adiabatic: COSED SYSEM S sys = m(s -s ) S gen S sys tot 0 m( s s ) 0 SURROUNDINGS

Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. Example: In a constant pressure process, vapor in the cyclinder condeses.

16 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. Example: In a constant pressure process, vapor in the cyclinder condeses. Determine: a) entropy change of water b) entropy change of ounding air c) whether this process is possible a) S water water water 600kJ 373K.6 kj K b) S 600 kj 98K.0 kj K c) S tot S sys S kj/k A frictionless piston sys 600kJ his process is an irreversible process and is possible

17 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. Control Volumes: Similar to the closed systems, except that this time we consider the entropy carried by the mass from flow rates across the boundaries. S S S cv ( S S) cv S e m e s e S i m s i i Entropy flow with heat entropy transport with mass S gen S total S sys S 0 ( S S) cv Se Si 0 = 0 for steady flow he entropy of a control volume changes as a result of mass flow as well as heat transfer.

18 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. S Steady flow devices in the rate form: gen m s e e m s i i 0 (kw/k) Single stream devices: S gen m ( s e s i ) 0 he entropy of a substance always increases (or remains constant in the case of a reversible process) as it flows through a singlestream, adiabatic, steady-flow device. he entropy generation of a fluid will increase as it flows through an adiabatic steady-flow device as a result of irreversibilities.

19 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. Property Diagrams Involving Entropy: he isentropic process appears as a vertical line segment on a -s diagram. During an internally reversible, adiabatic (isentropic) process, the entropy remains constant.

20 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. -s diagram of a Carnot cycle On a -S diagram, the area under the process curve represents the heat transfer for internally reversible processes.

21 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. 0 W = Δ For adiabatic steady-flow devices, the vertical distance h on an h-s diagram is a measure of work, and the horizontal distance s is a measure of irreversibilities. Mollier diagram: he h-s diagram (see Fig. A-0 for the Mollier diagram of water)

22 ISENROPIC EFFICIENCIES OF SEADY-FOW DEVICES he isentropic process involves no irreversibilities and serves as the ideal process for adiabatic devices. Isentropic Efficiency of urbines he h-s diagram for the actual and isentropic processes of an adiabatic turbine.

23 Copyright he McGraw-ill Companies, Inc. Permission required for reproduction or display. Entropy is a property, and thus the value of entropy of a system is fixed once the state of the system is fixed. he entropy of a pure substance is determined from the tables (like other properties). Schematic of the -s diagram for water.

= for reversible < for irreversible

= for reversible < for irreversible CHAPER 6 Entropy Copyright he McGraw-Hill Companies, Inc. Permission required for reproduction or display. he Clausius Inequality: δ 0 Cyclic integral his inequality is valid for all cycles, reversible