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.



*- . aajR . . TM.-??, , .


--

? (9 . .

, . . : V = y{x
t

,,).

(19.1)

, )

) . *. , (19.1). , , (19.1) ( ). .


*-*<*) З

(19.3)

,, = -^- = '(). (19.4)

, (19.3) (19.4) . : = (). (19.5) (19.5) (19.3), , , , (J). , (19.5) ,

. 12. .

,. (19.3) (19.5) (19.3). , ) ) , , , , , (,), (19.3), -- . , , (19.3) . , etf ty,


-- = -)

87 (19.6)

<{>. (19.6) (19.3), (19.4) , , ) ; , (19.3) (19.6) , , 0). (19.6) (19.3). (19.3) (,), . = З*=*

(19.7) (19.8)

ЗSf = y -- px.

(19.3), (19.4) (19.8) , . , (19.6) (19.3). (19.8) (19.4) d\ = --pdx--xdp + dy -- -- xdp - = - . (19.10) (19.6), (19.8) (19.10) , (19.3). , . (19.4) = -4?. *+... , dx &- + (19.11) (19.9)

(19.12)


-W< 19 > . , , . : = (), -1> = () ,
=

"1 '

~

==

**"З

09.14)


= -- ; + , (/

= + .

{) ^ = (), , , () -- (). . . . , , , () (). (19.1) ( + 1)- , , , . , . (xit ..., xk) (xir ..., ). , (?+]) ( + 1)- , , , . - , .... ,, . , (19.14):


--

Pi
,

pЛ.*t?. *

*.)З

+2
2 З ^ x lt .. . , ,, p x ,... . pft

t = tO>i. З- ft- *Л?.З?. ? J ? -Л(*i . - . **. ЗЛ. *J

, :, , , . . (19.17) *(?* ! ?Л) = ?^(2..... * ) , (19.18) / -- , 1- .






/-

/?(*1


**)- 2"5"*^

(199

)

(19.18) ,

. = I , (19.19). , / = 1. ? 20 . . . . -- (19.7) . . , .

S = S(U, V, ,,.. , ). (20.2) (? 17 18), . . (? 10)


--

91

(w\..

,,, >0 '

< 20 - 3 >

, . (20.2) U, U = U(S,Vtnl,...,nJ dU = TdS--PdV + ^ Л(20.4) < 20 - 5 )

. (20.1) , (20.5) -- . , . . . , '" () \ + X] = X,. (20.6) , ( ) , . , ? 15, , ; = />;. (20.7) , , , . -


92

III

_

[. (8.8) (10.26) ], . . . . , . . & . . , . . . .

*;~
Pi = ~-

?
(20.9)

. , . , Pi = P,(Xtt...,Xa), (20.10) . (20.10) . . , , -- .


--



SdT -- VdP + 2 *(4*i


=

А-

. ^ (20.1) (20.5) . . , (20.6) ' " , . (19.18). . : . , (17.1) (17.2) . . (18.1)--(18.6 ) . . . ,

{З%З),..

.,, =

<

2(

>

(^..--

-

<

2(

>

. df

JV__^L

.16)


I

III

, . , ? 24 25 . (20.5) (20.13) w a s " dv{ es ) ~ [ dv ) 8 . - . (20.5) (20.14), "- = --( = -(-?
dsdv as{ dv ) \ ds }v.Л

(20.18)
y

'

, , T(dP/dQ)y. . (20.16),

(З?З),..--(-H .
. ? 24 . , , . . , V, ( ).



, , dU . U=U(T, V, n)

- (-in, ?+. ,iv+(-?i. ,*З <20-20Л
(20.21) . ,


-- |. , (20.21) . (20.13) , (20.21), , , . , (20.4) (20.21), . , , (20.4) (20.21) (20.21) , (20.4) . (20.20) ? 8 . , ,, . , = U/n,

95

C

H?L

(20

- 21a >

. , . , , (20.1) (20.5) , . , , , ( , -- , ( )~ ,

(1/, /,-- /).

. : (20.22) (20.23)


Зf-fV. V. ); T = T(S,V,n), P = P(S,V,n),

(20.24)

(20.25) (20.26)

(i = |i(S,V,ft) . (20.27) , P = P(T,V,n) (20.28) , U = U(T, V, n) (20.29) . . (20.22) (20.23) , (20.28) (20.29) (20.22) (20.23). [ (7.7)], ? 7. (20.28) . , , . (19.18) (20.8) (20.9). (20.30)



(20

-3i>


--

97

. , . . , . (20.32) ( = 3) = ^\ />,=/>, , -?- , I) . (20.33)

XJX3 XJ/XJ , Pt. , . (20.33) =--;' = --, ? = ---; (20.34) (20.35)

s = -; _ -?- , ~: ? = -j. (20.36) (20.37)

, . . , (20.6). . . , (20.7),


98

III

-- . . . (19.18), (20.4) aU~U(<*S, aV, an). (20.38) = 1/ (20.36), a = u(s,v, 1), du = ~ds , (20.31), JlL -- UL -- T
,

(20.39) (20.40)
F

+ -^-dv. JOL -- JUL
dv

f20 411
(41

~

dS ~

J>

~

dV "

-

'

(20.40) du = Tds -- Pdv. (20.42) (20.39) (20.42) , . , (20.42) , . . , ., . . (20.13)--(20.15) , (20.4) : U = TS -- PV + ^ * nf < 20 - 43 )


--

99

= TdS + SdT -- PdV -- VdP + J З* **< + >
iI

(20.44) (20.5) t*i = 0 . (20.45)

-- . --

Л,4-Л-]. . (20.46)
, ? .Л, -- . . ? 21 . , . , ? 20, , . , . , , , , ; --


100

III

. . , , , . , . , . , . , . , , ? 19, . , Xt , . , . . , , . , . , (? 15). , , (21.40), - -\-b-T, -- .


--

101

, , . , * . U = U(,, ... , X,) (/З> m -f 2). (21.1)

Xj {1 (21.2), .

dt/ = 2 P < d X ? /=З1

<2I-3>

. **=-V -- YPtXt. (21.4)

, ,

(21.4) (21.3) d4tk = -^iXldP,+ ^ P,dX,. (21.6)


102

111

ft < . . (20.43)

(21.4)

/3+I
, , . Pt ( ) {. , -$.--* . (21.9,

Xj , , Pj. ,

{-,

(21.10)

k = . (21.4) (21.7)

= 2 Pt Xt - 2 *' " А
, (21.6), dWr= ^X,dP
t

<

211

>

= 0.

(21.12)

, -- . ,


-- (-) , . . , . , , , . , . (21.4), * U = t/(S , V,n,, ...,n j (21.13) , ? 20 . . , , . H=H(S, , ,, ... , ,,,) (21.14)

103

. (21.4) H = U + PV, (21.6) (21.15)

dH = TdS+ VdP+ ^ M"i -

(21-16)

:
(
=

; (-2

-V ; (

=f t

,.

(21 17)

. , З .


104

lit

. . , . 1, , , W* = -- W, , , . . - , . ,

, , . , , , . , . , (21.18), . , , ( R). , , (21.18), dr * = -- d(U + UR). (21.20)

, -- dU R = PdVR =--PdV = --d(PV). (21.21)

(21.15), (21.20) (21.21) -W>s.P. *-***. (21.22)


-- 105

, , . (21.19) (%
i ( 1

= dQ.

(21.23)

, , . ( , ) , (21.23) . -- , . ? 24, . , . , . , (20.20) (20.21): H = H(T,P,nit...,nJ (21.24)

dn,.

(21.25)

? 24. , (21.25) .. , -=*З 1 (21.23),


(^.^, , . F = F(T,V,ntr...,nJ (2I.27) . (21.4) : F = U -- TS, (2I.28) (21.6) dF SdT~PdV + VMn, .
;-- i

(21.29)

:

. (), . . , .' , , (21.18), , , . = const --dUR = --dQR=--dQ~TdS= (21.28), (21.32) -- (dF)T a = dW*. diTS). (21.32) (21.33)


-- 107

, , . ? Л ? Л ( --F), . , ( ). , (21.30) (20.28). Л . , , ( , ), . , . G = G(T,[P,nl,...,nJ (21.34) . (21.4) : G = U -- TS+PV = H -- TS=F + PV, (21.35) (21.36) (21.6) dG = --SdT + VdP + 21*1*1,.
(\

<,. (\

_

, . ,


R R', (), (). , . , , dW* = --d(U + UR+ UR.). (21.38) dUR (21.32), dUR- -- (21.21). (21.35), -- (dG) T t ,, = dW*. (21,39) - . . , , . , . (21.8)

0=2



|

"

(21

-40)

, . , . 2 = 2 ( , V, t* lt ... , t O (21.41) , , . (21.4) Q = (J -- TS -- I*f n
lt

(21.42)


-- 109 (21.6) dQ SdT~ PdV-- 2?(dp|. = --

/=i

= -% (21.28), (21.35), (21.40)(21.42)

(21.44)

Q^~ PV. (21.45) PV. , , . .