Conservation principles for the isentropic case qnet 0

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Unformatted text preview: quations, assuming constant specific heats Chapter 7 - 67 Student Study Guide for 5th edition of Thermodynamics by Y. A. Çengel & M. A. Boles 7-68 Process and Process Diagram: First assume an isentropic process and then apply the nozzle isentropic efficiency to find the actual exit velocity. Conservation Principles: For the isentropic case, Qnet = 0. Assume steady-state, steady-flow, no work is done. Neglect the inlet kinetic energy and changes in potential energies. Then for one entrance, one exit, the first law reduces to Ein = E out V22s m1h1 = m2 (h2 s + ) 2 The conservation of mass gives m1 = m2 = m The conservation of energy reduces to V2 s = 2(h1 − h2 s ) Using the ideal gas assumption with constant specific heats, the isentropic exit velocity is V2 s = 2C p (T1 − T2 s ) The isentropic temperature at state 2 is found from the isentropic relation Chapter 7 - 68 Student Study Guide for 5th edition of Thermodynamics by Y. A. Çengel & M. A. Boles 7-69 T2 s FG P IJ =T HPK 1 2 1 ( k −1)/ k = (500) K = 410.0 K FG 0.5P IJ H PK 1 1 (1.4 −1)/1.4 V2 s = 2C p (T1 − T2 s ) = F . kJ IJ (500 − 410.0) K 10 m / s 2G 1005 kJ / kg H kg ⋅ K K 3 2 2 = 442.8 m s The nozzle exit velocity is obtained from the nozzle isentropic efficiency as V22a / 2 ηN = 2 V2 s / 2 V2 a = V2 s m m 0.95 = 421.8 η N = 442.8 s s Chapter 7 - 69 Student Study Guide for 5th edition of Thermodynamics by Y. A. Çengel & M. A. Boles 7-70 Entropy Balance The principle of increase of entropy for any system is expressed as an entropy balance given by Ein Sin System ∆Esystem ∆Ssystem ∆Sgen≥0 Eout Sout F Total I F Total I F Total I F Change in theI GG entropy JJ − GG entropyJJ + GG entropy JJ = GG total entropy JJ H enteringK H leaving K H generated K H of the system K or Sin − Sout + S gen = ∆S system The entropy balance relation can be stated as: the entropy change of a system during a process is equal to the net entropy transfer through the system boundary and the entropy generated within the system as a result of irreversibilities. Entropy change of a system The entropy change of a system is the result of the process occurring within the system. Chapter 7 - 70 Student Study Guide for 5th edition of Thermodynamics by Y. A. Çengel & M. A. Boles 7-71 Entropy change = Entropy at final state – Entropy at initial state ∆Ssystem = S final − Sinitial = S2 − S1 Mechanisms of Entropy Transfer, Sin and Sout Entropy can be transferred to or from a system by two mechanisms: heat transfer and mass flow. Entropy transfer occurs at the system boundary as it crosses the boundary, and it represents the entropy gained or lost by a system during the process. The only form of entropy interaction associated with a closed system is heat transfer, and thus the entropy transfer for an adiabatic closed system is zero. Heat transfer The ratio of the heat transfer Q at a location to the absolute temperature T at that location is called the entropy flow or entropy transfer and is given as Entropy transfer by heat transfer: Sheat = Q (T = constant ) T Q/T represents the entropy transfer accompanied by heat transfer, and the direction of entropy transfer is the same as the dire...
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