Chapter_7_2

Conservation principles for the isentropic case qnet 0

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online