复旦大学：《热力学与物理统计》课程教学课件（PPT讲稿）第二章 均匀物质的热力学性质

第二章均匀物质的热力学性质 1.基本热力学函数 2.麦氏关系及应用 3.气体节流和绝热膨胀

第二章 均匀物质的热力学性质 1. 基本热力学函数 2. 麦氏关系及应用 3. 气体节流和绝热膨胀

§21基本热力学函数 1.内能 dU=TdS-pdk U=U(, v),dvs/aU aU ds+ dy aU aU =7(S,V)2p p(S,v) S a-U aT ap avas aSa O aS

§2.1 基本热力学函数 1. 内能 dU = TdS − pdV V V U S S U U U S V U V S ( , ), d d  d         +        = = ( , ), p(S,V) V U T S V p S U T V S  =         = = −        = S V U V S U    =    2 2 S S V p V T          = −       

2.焓H=U+p dh=Tds+vd H=H(S, P),dHa aH ds+ T=/OH aH T(S, P), v V(S, p) a OH aT as aSap aS

2. 焓 dH = TdS +Vdp p p H S S H H H S p H p S ( , ), d d d            +        = = ( , ), V(S, p) p H T S p V S H T p S =            = =        = S p H p S H    =    2 2 H =U + pV S S p V p T         =          

3.自由能F=U-7S dF=-SdT- pdy F=F(T,V), dF_OF OF dT+ dT OT aF aF S s(T,V),p= T. aT 02F02F aS ap ovat aTaV aT OF OF OF U=F+TS=F H=U+ pV=F aT aT

3. 自由能 dF = −SdT − pdV T V F T T F F F T V F V T ( , ), d d  d         +        = = ( , ), ( , ) V T F F S S T V p p T V T V       = − = = − =           T V F V T F    =    2 2 F =U −TS T V F U F TS F T         = + = − V V T F V T F H U pV F T          −        = + = − T T V p V S          =       

4.吉布斯函数(自由焓)G=H-7S=F+p dG=-SdT+vdp G=G(,p),dG=/oG aG dtt dp aT P aG aG S =S(T,p)2 y(T, p) aT P丿 a2G aG aS apot oTop aT H=G+TS=G-TaG G aG U=H-pV=G aT OT

4. 吉布斯函数（自由焓） dG = −SdT +Vdp p p G T T G G G T p G p T ( , ), d d d            +        = = ( , ), V (T, p) p G S T p V T G S p T =            = =        = − T p G p T G    =    2 2 G = H −TS = F + pV T p G H G TS G T         = + = − p T p G p T G U H pV G T            −        = − = − T T p V p S         = −          

§22麦氏关系及应用 1.麦克斯韦关系 aT ap S U (-)S aT aS H aS F\oV丿 aT (-)pT aS P OT

§2.2 麦氏关系及应用 S S V p V T          = −        S S p V p T         =           T T V p V S          =        T T p V p S         = −           U H F G (−)S (−) p V T 1. 麦克斯韦关系

2.基本热力学函数的确定 内能同U=7S-pd aS aS S=S(T,V),ds dT+ dE aT aS O aS aS aT U=U(, V), du p dy du dt+ aT aU dT+ aT S aU aT aT aT dU=CpdT+ )叫 ds= dr op dv T aT

2. 基本热力学函数的确定 内能 dU = TdS − pdV V V U T T U U U T V U V T ( , ), d d  d         +        = = V V S T T S S S T V S V T ( , ), d d  d         +        = = p V V S T T T S U T V T d d d       −         +        = T T V p V S          =        V V V T S T T U C          =        = p T p T V U T V  −         =        p V T p U C T T V d V d d       −        = + V T p T T C S V V d d  d        = +

aCy O2S aS aS T ap T aVot aTaV aT2 aT C(7,T)=C1(T,V)+ 6(2/d p=C(T,Vp=p(T,V)由实验测定, U=U(7,V),S=S(7,V)即可确定

CV 0 = CV (T,V0 ), p = p(T,V) 由实验测定， T V V T p T T V S T V T S T V C           =    =     =        2 2 2 2              = + V V V V V V T p C T V C T V T 0 ( , ) ( , ) d 2 2 0 U =U(T,V), S = S(T,V) 即可确定。 T T V p V S          =        T CV V0 V

焓dH=Tds+ap aS aS S=ST,P), ds dT+ OT aS as\dT+ aT H=H(T,p),d〃(0/xpp dh=t aT aH dt+ OT aH aS aH OT aT T dh =CdT+V-TI ds=PdT aT OT

焓 dH = TdS +Vdp p p H T T H H H T p H p T ( , ), d d d            +        = = p p S T T S S S T p S p T ( , ), d d d            +        = = V p p S T T T S H T p T d d d         +            +        = T T p V p S         = −           p p p T S T T H C          =        = T T p V V T p H         = −           p T V H C T V T p d p d d                 = + − p T V T T C S p p d d  d        = −

aC S S 02 aS T T apot aTop aT2 aT 02V 1(G,p)=C(7,P)-7 aT2 CD=C(7,P,V=(72p)由实验测定, H=H(T,p),S=S(7,P)即可确定

Cp 0 =Cp (T, p0 ),V =V(T, p) 由实验测定， T p p T V T T p S T p T S T p C           = −    =    =           2 2 2 2              = − p p p p p p T V C T p C T p T 0 ( , ) ( , ) d 2 2 0 H = H(T, p), S = S(T, p) 即可确定。 T T p V p S         = −           T p 0 p Cp