ME235Lecture_11 - Thermodynamics Vm235 Lecture 11 Chapter 8...

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1 Thermodynamics Vm235 Lecture 11 Chapter 8 Chapter 8 – Entropy Entropy Entropy Change Calculations: For solids & liquids: 1 2 2 1 2 1 1 2 ln : ; 0 ; T T C T CdT T du s s get We ible incompress nearly dv with Pdv du Tds = + = 0 0 : using thus , & ; ) ( ; ) ( R C C RT Pv T h h T u v P = = = = For Ideal gas: () 1 2 2 1 0 1 2 2 1 0 1 2 ln ln : ; v v R T dT T C P P R T dT T C s s get we Pdv du Tds v P + = = + = ( ) 2 2 2 2 0 0 0 0 : . & ; & v T P T then const C C If T func C C v P v P = = 1 1 0 1 1 0 1 2 ln ln ln ln v R T C P R T C s s v P + = = tables using int. , ln , & 0 1 2 0 0 1 2 0 0 1 2 0 0 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
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2 Iso“entropic” Process: No change in entropy Æ (s 2 –s 1 ) = 0 () 00 21 0 22 0 ; ; & , s i n : 0& . : 0l n l n Pv P P uu T hh T P vR T C C R t h u s u g s s C const we get TP ss C R == = = −= = = For Ideal gas: 11 ( ) ( ) 0 0 0 0 1 2 1 2 1 2 1 2 0 1 2 ln ln P v P P C C C C R P P P P P T T or P P C R T T = = = : ; : ; 1 1 1 0 0 0 0 0 gas ideal from now C C k where k k k C C C v P P v P = = = i.e. Pv k = constant A special case of a polytropic process ( ) ( ) k k v v P P v v T T get we ng substituti T T v v P P = = = 2 1 1 2 1 2 1 1 2 1 2 2 1 1 2 & : Polytropic Process for Ideal gas: i.e. Pv n = constant = P 1 v 1 n = P 2 v 2 n ln ( P ) + n ln ( v ) = const., or d ( ln ( P )) + n d ( ln ( v )) = 0, if n=constant. i.e. You can also easily derive: 1 1 2 = = n n V mv P Work done if the control mass is ideal gas: 1 2 1 1 1 2 1 2 2 2 1 = = n n n V V P P T T V mv P 1 ; 1 constant constant 1 1 1 2 2 1 2 1 2 1 + = = = + + n n V V V dV dV P W n n n Isobaric process P=const n=0 ; Isothermal process T=const n=1 Isochoric process v=const n= ; Isoentropic process s=const n=k 1 ; 1 1 1 1 1 2 1 1 2 2 1 1 1 1 1 2 2 2 = = + + = + + n n T T mR n V P V P n V V P n V V P n n n n
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3 Polytropic Process: PV n = constant. dP + (n/V).dV = 0 Isobaric process P=const n=0 ; Isothermal process T=const n=1 ; recall: PV=RT=const Isochoric process v=const n= ; Isoentropic process s=cons n=k Isoentropic process s const nk ──
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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_11 - Thermodynamics Vm235 Lecture 11 Chapter 8...

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