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PTT 201/4 THERMODYNAMIC SEM 1 ( 2012/2013)

PTT 201/4 THERMODYNAMIC SEM 1 ( 2012/2013). CHAPTER 7: Entropy. Objectives. • Apply the second law of thermodynamics to processes. • Define a new property called entropy to quantify the second- law effects. • Calculate the entropy changes that take place during.

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PTT 201/4 THERMODYNAMIC SEM 1 ( 2012/2013)

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  1. PTT 201/4THERMODYNAMIC SEM 1 (2012/2013) • CHAPTER 7: • Entropy

  2. Objectives • Apply the second law of thermodynamics to processes. • Define a new property called entropy to quantify the second- law effects. • Calculate the entropy changes that take place during processes for pure substances, incompressible substances,and ideal gases. • Examine a special class of idealized processes, called isentropic processes, and develop the property relations forthese processes. • Derive the reversible steady-flow work relations • Introduce and apply the entropy balance to various systems. 2

  3. WHAT IS ENTROPY? ( A measure of molecular disorders ormolecular randomness) Boltzmann relation A pure crystalline substance at absolute zerotemperature is in perfect order, and its entropy is zero (the third law of thermodynamics). The level of molecular disorder (entropy) of a Disorganized energy does not create muchuseful effect, no matter how large it is. substance increases asit melts or evaporates. 3

  4. The paddle-wheel work done on a gas increases the level ofdisorder (entropy) of the gas,and thus energy is degraded during this process. In the absence of friction, raising aweight by a rotating During a heat transfer process, the shaft does not net entropy create any disorder(entropy), and thusenergy is not increases. (Theincrease in the entropy of the coldbody more than degraded during thisprocess. offsets the decrease in the entropy of the hot body.) 4

  5. ENTROPY (How to measure the entropy- based-on from Clausius inequality) Clasius inequality Formal definitionof entropy The system considered inthe development of theClausius inequality. The equality in the Clausius inequality holdsfor totally or just internally reversible cyclesand the inequality for the irreversible ones. (based-on energy balance) 5

  6. A quantity whose cyclicintegral is zero (i.e., aproperty like volume) The net change in volume (aproperty) during The entropy change between two specified states is the same whether the process is reversible or irreversible. a cycle is always zero. A Special Case: Internally ReversibleIsothermal Heat Transfer Processes This equation is particularly useful for determiningthe entropy changes of thermal energy reservoirs at constant temperature. 6

  7. Class Discussion • EXAMPLE 7-1

  8. Some Remarks about Entropy 1. Processes can occur in a certaindirection only, not in any direction. A process must proceed in the direction thatcomplies with the increase of entropy principle, that is, Sgen ≥ 0. A process that violates this principle is impossible. 2. Entropy is a nonconserved property, and there is no such thing as the conservation of entropy principle. Entropy isconserved during the idealized reversible processes only andincreases during all actual processes. 3. The performance of engineering systems is degraded by the presence of irreversibilities, and entropy generation is ameasure of the magnitudes of the irreversibilities during thatprocess. The greater the extent of irreversibilities, the greater the entropy generation. It is also used to establish criteria for the performance of engineering devices. 7

  9. Class Discussion • EXAMPLE 7-2

  10. ENTROPY CHANGE OF PURE SUBSTANCES Entropy is a property, and thus thevalue of entropy of a system is fixedonce the state of the system is fixed. Schematic of the T-s diagram for water. Entropy change The entropy of a pure substanceis determined from the tables (like other properties). 8 Where m is specified mass

  11. Class Discussion • EXAMPLE 7-3

  12. ISENTROPIC PROCESSES A process during which the entropy remains constant is calledan isentropic process. During an internally reversible, adiabatic (isentropic) process, theentropy remains constant. The isentropic process appears as avertical line segment on a T-s diagram. 9

  13. Class Discussion • EXAMPLE 7-5

  14. ENTROPY CHANGE OF LIQUIDS AND SOLIDS (INCOMPRESSIBLE SUBSTANCES) Derived from equation 7-23, Liquids and solids can beapproximated as or known asGibbs equation incompressible substances since their specific volumesremain nearly constant during a process. For an isentropic process of an incompressible substance 10

  15. Class Discussion • EXAMPLE 7-7

  16. THE ENTROPY CHANGE OF IDEAL GASES From the first T ds relation (Eq 7-25). From the second T dsrelation (Eq 7-26) Ideal gas properties 11

  17. Constant Specific Heats (Approximate Analysis) Entropy change of an ideal gas on a unit-mole basis Under the constant-specific- heat assumption, the specificheat is assumed to be constantat some average value. 12

  18. Variable Specific Heats (Exact Analysis) We choose absolute zero as the reference temperature and define a function s° as On a unit-mass basis The entropy of an ideal gas depends on both T and P. The function sorepresents only the On a unit-mole basis temperature-dependent part of entropy. 13

  19. Class Discussion • EXAMPLE 7-9

  20. Isentropic Processes of Ideal Gases Constant Specific Heats (Approximate Analysis) Setting this eq. equal to zero, we get The isentropic relations of idealgases are valid for the isentropicprocesses of ideal gases only. 15

  21. Isentropic Processes of Ideal Gases Variable Specific Heats (Exact Analysis) Relative Pressure and Relative Specific Volume The use of Prdata for calculating the exp(s°/R) isthe relativepressure Pr. final temperatureduring an isentropic process. Refer Table A-17 Pv=RT (ideal gas relationship), R=constant The use of vrdata for calculating the finaltemperature during an T/Pris the relativespecific volume vr. isentropic process 1

  22. Class Discussion • EXAMPLE 7-10 • EXAMPLE 7-11

  23. REVERSIBLE STEADY-FLOW WORK From energy balance for steady-state device (- sign means work is produced by the system) When kinetic and potential energiesare negligible (+ sign means work is done on the system) The larger the specific volume, thegreater thework For the steady flow of a liquid through adevice that involves no work interactions(such as a pipe section), the work term iszero (Bernoulli equation): Reversible workrelations for steady-flow and closedsystems. produced (orconsumed) bya steady-flowdevice. 17

  24. Class Discussion • EXAMPLE 7-12

  25. ENTROPY BALANCE Entropy Change of a System, ∆Ssystem When the properties of thesystem are not uniform Energy and entropybalances for a system. 19

  26. Mechanisms of Entropy Transfer, Sin and Sout 1 Heat Transfer Entropy transfer by heat transfer: Entropy transfer by work: Heat transfer is always accompanied byentropy transfer in the amount of Q/T,where T is the boundary temperature. No entropy accompanies work as it crossesthe system boundary. But entropy may begenerated within the system as work is dissipated into a less useful form of energy. 20

  27. 2 Mass Flow Entropy transfer by mass: When the properties of the masschange during the process Mass contains entropy as well asenergy, and thus mass flow into or out of system is always accompanied by energy andentropy transfer. 21

  28. Entropy Generation, Sgen Entropy generation outside system boundaries can be accounted for by writing an entropy balance on an extended system that includes the system and its immediate surroundings. Mechanisms of entropy transfer for ageneral system. 2

  29. Closed Systems The entropy change of a closed system during a process is equal to thesum of the net entropy transferred through the system boundary by heat transfer and the entropy generated within the system boundaries. 23

  30. Control Volumes The entropy of a substance alwaysincreases (or remains constant in The entropy of a controlvolume changes as a resultof mass flow as well as heattransfer. the case of a reversible process)as it flows through asingle-stream, adiabatic, steady- flow device. 24

  31. Class Discussion • EXAMPLE 7-17 • EXAMPLE 7-18 • EXAMPLE 7-19 • EXAMPLE 7-20 • EXAMPLE 7-21

  32. EXAMPLES Entropy balance for heattransfer through a wall Entropy balance fora throttling process 25

  33. Entropy Generated when a Hot Block Is Dropped in a Lake or Entropy Generation in a Heat Exchanger 26

  34. Entropy generation associated witha heat transferprocess Graphical representation of entropy generation during a heat transfer process 27 through a finite temperature difference.

  35. THANK YOU..

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