Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44SummaryCHAPTER 7ENTROPYLecture slides byMehmet KanogluCopyright © The McGraw-Hill Education. Permission required for reproduction or display.Thermodynamics: An Engineering Approach 8th EditionYunus A. Çengel, Michael A. BolesMcGraw-Hill, 20152Objectives•Apply the second law of thermodynamics to processes.•Define a new property called entropy to quantify the second-law effects.•Establish the increase of entropy principle.•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 for these processes.•Derive the reversible steady-flow work relations.•Develop the isentropic efficiencies for various steady-flow devices.•Introduce and apply the entropy balance to various systems.3ENTROPYClasius inequalityThe equality in the Clausius inequality holds for totally or just internally reversible cycles and the inequality for the irreversible ones.Formal definition of entropy4Entropy is an extensive property of a system.A quantity whose cyclic integral is zero (i.e., a property like volume)A Special Case: Internally ReversibleIsothermal Heat Transfer ProcessesThis equation is particularly useful for determining the entropy changes of thermal energy reservoirs.5THE INCREASE OF ENTROPY PRINCIPLEThe equality holds for an internally reversible process and the inequality for an irreversible process.Some entropy is generated or created during an irreversible process, and this generation is due entirely to the presence of irreversibilities.The entropy generation Sgen is always a positive quantity or zero.Can the entropy of a system during a process decrease?6The increase of entropy principle7Some Remarks about Entropy1. 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, 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 is conserved during the idealized reversible processes only and increases during all actual processes.3. The 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.8ENTROPY CHANGE OF PURE SUBSTANCESEntropy is a property, and thus the value of entropy of a system is fixed once the state of the system is fixed. Entropy change9ISENTROPIC PROCESSESA process during which the entropy remains constant is called an isentropic process.10PROPERTY DIAGRAMS INVOLVING ENTROPYOn a T-S diagram, the area under the process curve represents the heat transfer for internally reversible processes.Mollier diagram: The h-s diagram1112WHAT IS ENTROPY?A pure crystalline substance at absolute zero temperature is in perfect order, and its entropy is zero (the third law of thermodynamics).Boltzmann relationGibbs’ formulationW the total number of possible relevant microstates of the systempi sum of all microstates’ uncertainties, i.e., probabilitiesBoltzmann constant13141516THE T ds RELATIONSthe first T ds, or Gibbs equationthe second T ds equationDifferential changes in entropy in terms of other properties17ENTROPY CHANGE OF LIQUIDS AND SOLIDSSince for liquids and solidsLiquids and solids can be approximated as incompressible substances since their specific volumes remain nearly constant during a process.For and isentropic process of an incompressible substance18THE ENTROPY CHANGE OF IDEAL GASESFrom the first T ds relation From the second T ds relation19Constant Specific Heats (Approximate Analysis)Entropy change of an ideal gas on a unit–mole basis20Variable Specific Heats (Exact Analysis)We choose absolute zero as the reference temperature and define a function s° asOn a unit–mole basisOn a unit–mass basis2122Isentropic Processes of Ideal GasesConstant Specific Heats (Approximate Analysis)Setting this eq. equal to zero, we get23Isentropic Processes of Ideal GasesVariable Specific Heats (Exact Analysis)Relative Pressure and Relative Specific VolumeT/Pr is the relativespecific volume vr.exp(s°/R) is the relative pressure Pr.The use of Pr data for calculating the final temperature during an isentropic process.The use of vr data for calculating the final temperature during an isentropic process24REVERSIBLE STEADY-FLOW WORKThe larger the specific volume, the greater the work produced (or consumed) by a steady-flow device.When kinetic and potential energies are negligibleFor the steady flow of a liquid through a device that involves no work interactions (such as a pipe section), the work term is zero (Bernoulli equation):25EXAMPLE: Compressing a Substance in the Liquid versus Gas Phases26Proof that Steady-Flow Devices Deliver the Most and Consume the Least Work when the Process Is ReversibleActualReversibleWork-producing devices such as turbines deliver more work, and work-consuming devices such as pumps and compressors require less work when they operate reversibly.Taking heat input and work output positive:27MINIMIZING THE COMPRESSOR WORKIsentropic (Pvk = constant):Polytropic (Pvn = constant):Isothermal (Pv = constant):When kinetic and potential energies are negligibleThe adiabatic compression (Pvk = constant) requires the maximum work and the isothermal compression (T = constant) requires the minimum. Why?28Multistage Compression with IntercoolingThe gas is compressed in stages and cooled between each stage by passing it through a heat exchanger called an intercooler.To minimize compression work during two-stage compression, the pressure ratio across each stage of the compressor must be the same.29ISENTROPIC EFFICIENCIES OF STEADY-FLOW DEVICESIsentropic Efficiency of Turbines3031Compressors are sometimes intentionally cooled to minimize the work input.Isothermal efficiencyFor a pumpWhen