- . . - , . . .
- , , m0 , = const, <v> =Ö3kT/m0. , , , , , . . .
, N , . , .
f(v), .
, dv, dN(v), , . f(v) dN (v)/N, v v+dv, . .
f(v)=dN(v)/Ndv
, f(v) :
(44.1) , ( ) ( ). (44.1) . 65. v , v2, f(v), , v . v.
dN(v)/N, v v+dv, . 65. ,
, . , f(v)
, , . (44.1) ( ) v, f(v):
v= 0 v=¥ (44.1), v, , v:
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(44.2) , (. 66) ( ). , , , .
<v> ( )
.
- c , , . . , , , , .
, , , . (. 67), h + dh p+dp ( dh>0 dp<0, ). p + dp , Ah , :
- (p +d p)=r gh,
r h (dh , ).
,
d=-rgdh. (45.1)
pV = (m/M)RT ( , ),
,
(45.1),
h 1 h 2. 1 p 2(. 67), . .
(45.2) . , , . , , (45.2)
h.
( ). (45.3). , , .
(45.3) , (42.6) p=nkT:
n h, n 0 h=0. M = m 0 N A (NA , m 0 ), R=kNA,
m0gh= , . .
(45.5) . , , .
, (45.5) , .
f(v) ,
, : 1) v=Ö2RT/; 2) <v>=Ö8RT/(p)=1,13v; 3) <v> =Ö3 RT/ = 1,22v (.65).
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e. v e=m0v2/2. (44.4) v =Ö (2e//m0
dv=(2m0e)-1/2de,
(dN(e) , , e e+de.
,
<e>
. . , (43.8).
, , . l, . , , < l >.
, , d (.68). , . . ( ).
1 , <v>, (z) , 1 ,
< l >=<v>/<z>.
<z> d, . , , d, . . d (. 69).
1 :
<z>=nV,
n , V = = pd2<v> (<v> , 1). ,
<z>=npd2<v>.
,
.. (l) n . , (42.6) , n .
,
-
, - .
1. . . (17731858), , , , , , . , (1), . , , , ( ). . 80 : , . , , . , - .
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2. . . (18881970). . . 70. , , . . , , , .
, , s. . , , .
, , s, . , , .
3. . . . 71. , , , . , . , . , , , . . , , . .
4. . (. (45.4)), (18701942) . , , . ,
m , m 1 : m=4/3pr3r, m1 = 4/3pr3r1 (r , r , r1 ).
n1 n2 h 1 h 2, a k=R/NA,
N a, . , , , (45.4).
, , , , . ( ), ( ) ( ). . , .
1. . , , , . ., , .
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:
j E , , , , l , dT/dx , . ,
( j dT/dx ). l, , . ,
v ( , 1 1 ), r , (v) , < l > .
2. . , , ; , , . - . , . , . . , , .
:
jm=-Ddp/dx (48.3)
j , , , , D ( ), dr/dx ,
. , ( j
dr/dx ). D , . ,
D=1/3 <v> < l >. (48.4)
3. (). (), , , - , , , , , , , , .
(31.1), () :
h (), dv/dx , , , S , F.
, , . (48.5)
jp , , ,
, dv/dx . , (
dv jp dv/dx ), h , ;
(48.1), (48.3) (48.6), , , . , - , , , .
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, - l, D h. . , , . (48.2), (48.4) (48.7) . l, D h:
, .
.
, , . , . , < l > d , . < l > d (< l ><<d), (< l >£d), (< l > > d) (< l >>> d) . .
, , , , . . , () 0,13 , , 13,3 1, (10-7 10-14 . .).
. 72. . 1 1 ', 2, .
3. 1 , 3
4. 1' 3
4
5 . .
( ), , , . (. 73). , , 1, 2 , ( ).
, , , ( 3), . ( ), 10-7 . .
. (1 2) (), (.74). () 1 2 . ; . (, ) , 300 .
, . , .
. , . . , . . , , , , .
1 2, 1 T 2(. 75) .
(< l> <<d), ( 1 = 2 ). (<l>>>d), , , , , , , . .
n 1<v1>=n2<v2>, (49.1) n1 n2 , <v1> <v2> . , n= p/(kT) <v>=Ö(8RT/(pM)), (49.1)
. . . (. 76) 1 2, , , .
50. .
U () (, , , . .) . , .
, . . ( , ).
, . 1 (), . (. 77, ) ,
. (r>0, J= mr20, T =Jw2/20).
, (. 77,). . (, ) . , (i=5). (. 77,0) : . , . .
. , , 1/3 <e0) (43.8):
: , , , kT/2, , kT. , ( ), , . ,
i , :
i =i + i +2 i .
; i .
( ), , , NA :
, v .
, , . , . , , , , , . . () . , , ( ). , : . . ; , .
, (, ), U 1, Q , , U 2, , . . . , , , . , D U=U 2 -U 1 Q, , , :
D U=Q-A,
Q= D U+A. (51.1)
(51.1) : , , .
(51.1)
dQ=dU+dA,
dQ=dU+dA, (51.2)
dU , d , d Q . dU , d A d Q . (51.2).
(51.1) , , , . . ().
, DU=0. , ,
A=Q,
. .
, , , ( ).
(49.2) , , . . , , . . .
, . , , , (. 78). , , d l,
dA=Fdl=pSdl=pdV,
S , S dl=dV . ,
dA=pdV. (52.1)
A, V 1 V 2,
(52.1):
. (52.2) , .
, V. , . 79. dV pdV, . . d V . , V 1 V 2, , , p = f(V) V1 V2.
, . , . ( ), ( , ). .
53.
, , 1 1 :
- (/()).
, , 1 1 :
v = m/M , .
- (/()).
m
= , (53.2)
.
, .
(51.2) 1 (52.1) (53.1):
CmdT = dUm + pdVm. (53.3)
, (. (52.1)) :
. . v 1 1 . (50.1),
Cv = iR/2. (53.5)
, (53.3)
, dUm/dT ( , V, ) v (. (53.4)); pVm=RT (42.4) T(p =const),
Cp = Cv + R. (53.6)
(53.6) ; , v . , , .
(53.5), (53.6)
Cv:
g=Cp/Cv=(i+2)/i. (53.8)
(53.5) (53.7) , . - . , , . , .
(. 50), Cv = 7 / 2 R. v (. 80) , Cv : (50 ) Cv= 3 / 2 R, Cv= 5 / 2 R ( 7/2 R!) v=7/2/R. , , , , .
. , ( , ). , , , ( ). , 5/2 R 7/2 R. ( -
, , , .
(V = const). () , V , (. 81), 1 2 , 1 3 . , . .
dA=pdV = 0.
53, (dQ=dU +dA) , , , :
dQ =dU
(53.4), dUm = CvdT.
(= const). () , V , V
. (. (52.2)) V 1 V 2
, . 82. (42.5) ,
(54.2)
R: T2-T1=1, 1 R=, . . R 1 1 .
( (53.4))
, (54.3).
(T =const). 41, :
pV= const.
() , V (. .60), , , . (52.2) (42.5) :
T =const :
(dQ = dU+dA) ,
dQ=dA,
. . , , :
, , , .
.
, (dQ=0) . -
. , , , . ( ), . .
(dQ=dU+dA) ,
dA=-dU, (55.1)
. . .
(52.1) (53.4), (55.1)
pV=(m/M)RT,
(55.2) (55.3) :
, /v =g (. (53.8)),
dp/p=-gdV/V.
1 2 V 1 V 2, ,
p 2 /p l=(V1/V2)g.
p 1vg1 = p 2vg2.
1 2 ,
Vg= const. (55.4)
, .
, V , (55.4)
:
(55.4) (55.6) . (. (53.8) (53.2))
( ). (Ne, He .), , i = 3, g=1,67. (2, N2, O2 .) i= 5, g=1,4. g, (55.7), .
() , V (.83). , (pVg=const) , (pV =const). , 1 3 , , .
, . (55.2)
V 1 V 2, T 1 T 2
, (55.5), (55.8)
, 1 2 ( , . 83), , . , , .
, , . Cv , (d T= 0) ¥, (dQ=0) . , , .
(C = const) :
pVn = const, (55.9) n= (C- )/(-Cv) . , = 0, n=g (55.9) ; =¥, n=1 ; =, n = 0 , = v, n =¥ . , .
56. ().
( ) , , , . (.84). , , (1 2) (2 1) . ( 1 a2V 2 V 1 1) (dV>0), ( 2b1V 1 V 2 2) (dV<0), , , , , . ( ), (. 84, ), ( ), (. 84,).
, .
, .
, , . (51.1)
Q=DU+A=A, (56.1)
. . , , . , ,
Q=Q1-Q2,
Q1 , , q 2 , .
, , , , , . , , .
. , , , ; , . (- , ..), . . -: 1) ; 2) ; , . . . .
57. ,
1865. . . Q, , , .
, , d Q/T. , , , :
(57.1), , , d Q/T , , . ,
, d Q/T, S.
(57.1) ,
DS=0. (57.3)
, , , :
DS>0. (57.4)
(57.3) (57.4) , , . (57.3) (57.4)
DS³0, (57.5)
. . ( ), ( ).
1 2, , (57.2),
, . (57.6) . , .
(57.6),