ME235Lecture%2013

ME235Lecture%2013 - Thermodynamics Vm235 Lecture 13 Chapter...

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1 Thermodynamics Vm235 Lecture 13 Chapter 9 Second Law Analysis for a C. V. HW 5: 9.24, .31, .32, .40, .51, .68, .80 Entropy change for a system (c.m.): Summary – Chap - 8 For solids & In general : Æ Compute from Tables: Æ () 2 1 2 1 1 2 . , , 1 0 T Q dS T s x s s or s x s x s S T Q S S or S fg f g f gen gen rev for dS irr for + = + = + = > + = δ ± ² ³ ± ² ³ liquids: Æ 1 2 1 2 ln : ; 0 ; T C s s get We dv with Pdv du Tds + = ln ln ln ln : . & ; & ln ln 2 2 0 2 2 0 1 2 0 0 0 0 1 2 2 1 0 1 2 2 1 0 1 2 + = = = = + = = v P v P v P v P v v R T T C P P R T T C s s then const C C If T func C C v v R T dT C P P R T dT C s s For Ideal gas: Tables , ln , & 0 1 2 0 0 1 2 0 0 1 2 0 0 1 1 1 1 6 = = T T P T T T v P T dT C s where P P R s s s s or C C for ion approximat polynomial a use may We Principle of entropy increase: = + = 0 . . gen surr m c net S dS dS dS
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2 Rate of change of entropy inside . . . C.S. + = + = gen m c gen m c S T Q dt dS equation rate Thus S T Q dS mass control for ± ± . . . . , ; : Recall δ CV = + in – out + generation + + = + gen v c e e i i v c e e i i v c S Q s m s m T Q s m s m dt dS volume control For . . . . . . : ± ± ± ± ± ± ± . . N N () = + + = + + = surface S C at Temp v c B gen A gen gen B B A A v c S C through V C to in HT to due entropy in increase dA T A Q T Q Similarly S S S s m s m S Where T . . . . . , , . . ilities) irreversib (internal generation entropy . . . : ... & ... : ± ± ± ± ± Steady State Process: ( ) = = = = . . . . . . : 0 ; 0 ; 0 ; 0 v c v c v c Thus dt d All dt dE dt dm dt dS ± N + = = = + = . . . . ilities) irreversib (internal generation entropy . . ; 0 , gen v c i e e i e v c gen v c i i e e Q S T Q s s m m m dt dm Since S T Q s m s m ± ± ± ± ± ± ± ± ± ( ) N > + + = + = 0 . . . . : : & gen v c i e gen v c i e s T q s s or S T s s m exit inlet one only If ± ±
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3 () N + + = + = ilities) irreversib (internal generation entropy . . . .
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This note was uploaded on 09/15/2010 for the course ME 235 taught by Professor Borgnakke during the Fall '07 term at University of Michigan.

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ME235Lecture%2013 - Thermodynamics Vm235 Lecture 13 Chapter...

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