Морозов В.Г., Фетисов Ю.К. Молекулярная физика. Курс физики. Часть 1
Подождите немного. Документ загружается.
U
U
U
1
U
2
U = U
1
+ U
2
.
Ω(U
1
, U
2
) U
1
U
2
Ω(U
1
, U
2
) = Ω
1
(U
1
) Ω
2
(U
2
),
Ω
1
Ω
2
Ω
1
Ω
2
Ω
1
Ω
2
Ω
0
(U)
U
U
1
U
2
P (U
1
, U
2
) =
Ω(U
1
, U
2
)
Ω
0
(U)
U
( )
1
U
( )
2
U
U
U
U
1
U
2
U = U
1
+ U
2
U
1
P (U
1
)
P (U
1
) = P (U
1
, U −U
1
) =
Ω
1
(U
1
) Ω
2
(U −U
1
)
Ω
0
(U)
.
P
(U
1
)
Ω
1
(U
1
)
U
1
Ω
2
(U − U
1
) U
1
f(x) = f
1
(x)f
2
(x) f
1
f
2
f(x)
x = x
(0)
U
(0)
1
U
(0)
2
= U − U
(0)
1
t
U
1
= U
(0)
1
U
2
= U
(0)
2
U
(0)
1
U
(0)
2
U
( )
1
U
( )
2
U
1
U
2
U
1
+ U
2
= U
S = S
1
+ S
2
Ω = Ω
1
Ω
2
Ω
S = k ln Ω ,
k
U Ω(U)
S → 0 T → 0.
T V
S = c onst
m T
1
T
2
T
1
> T
2
c T
∆S ∆S > 0
N
A N
A
P (A) = lim
N→∞
N
A
N
N → ∞
N
0 ≤ P (A) ≤ 1 P(A) = 0
P (A) = 1
N → ∞
A
1
A
2
A
1
A
2
P (A
1
, A
2
)
P (A
1
, A
2
) = P (A
1
) P (A
2
) ( ).
N
N(A
1
, A
2
)
A
1
A
2
P (A
1
, A
2
) =
N(A
1
, A
2
)
N
=
N(A
1
)
N
N(A
1
, A
2
)
N(A
1
)
.
N A
1
A
2
A
1
N(A
1
, A
2
)/N(A
1
) → N(A
2
)/N N → ∞
A
1
, A
2
, . . . , A
k
A
1
A
2
A
1
A
2
P (A
1
A
2
) = P (A
1
) + P (A
2
) ( ).
N(A
1
A
2
)
A
1
A
2
N(A
1
A
2
) =
N(A
1
,
¯
A
2
) + N(A
2
,
¯
A
1
) + N(A
1
, A
2
)
¯
A A
A
1
A
2
N(A
1
, A
2
) = 0 N(A
1
,
¯
A
2
) =
N(A
1
) N(A
2
,
¯
A
1
) = N(A
2
) N(A
1
A
2
) N
A
1
, A
2
, . . . A
k
A
i
A
1
A
2
. . . A
k
k
X
i=1
P (A
i
) = 1 ( ).
A
B
1
, . . . , B
m
C
1
, . . . , C
n
B
i
C
j
P (A)
i i = 1, 2, . . . , 6
P (i) = 1/6 P (1, 3)
P (1, 3) = P (1)P(3) = 1/36 A
A
P (A) = 3 · (1/36) = 1/12
x
x
1
, x
2
, . . . , x
i
, . . . , x
k
x
i
P (x
i
) x
i
P (x
i
) = lim
N→∞
N(x
i
)
N
,
N(x
i
)
P (x
i
)
x
i
X
x
i
P (x
i
) = 1,
¯x ≡ hxi =
1
N
X
x
i
x
i
N(x
i
).
N → ∞
¯x ≡ hxi =
X
x
i
x
i
P (x
i
).
ϕ(x
i
)
hϕi =
X
x
i
ϕ(x
i
) P (x
i
).
hx
2
i =
X
x
i
x
2
i
P (x
i
).
P (a < x < b) x
a b
A
i
(x = x
i
; a < x
i
< b)
P (a < x < b) =
X
a<x
i
<b
P (x
i
).
x y
P (x
i
, y
j
) P (x
i
, y
j
) x
x
i
y y
j
X
x
i
,y
j
P (x
i
, y
j
) = 1.
Φ(x
i
, y
j
)
hΦi =
X
x
i
,y
j
Φ(x
i
, y
j
) P (x
i
, y
j
).
P (x
i
, y
j
) = P (x
i
) P (y
j
).
x = x
i
y = y
j
hxyi = hxihyi ( ).
hxyi
hxyi ≡
X
x
i
,y
j
x
i
y
j
P (x
i
, y
j
) =
X
x
i
,y
j
x
i
y
j
P (x
i
) P (y
j
) =
=
X
x
i
x
i
P (x
i
)
X
y
j
y
j
P (y
j
)
= hxihyi,
P (x
i
, y
j
)
P (x
i
) P (y
j
) x
y A(x = x
i
)
P (x
i
)
A
j
(x = x
i
, y = y
j
) y
j
y
P (x
i
) =
X
y
j
P (x
i
, y
j
).
y
x
x
min
x
max
P (x)
x
x
min
≤ x ≤ x
max
N
x x
min
x
max
N x
x
x
x
Δ
x
x
min
x
i
x
max
x
(x
min
, x
max
)
N ∆x =
(x
max
− x
min
)/N
i
N → ∞
N
x i
δP
i
= P (x
i
< x < x
i
+ ∆x ).
δP
i
i
δP
i
f(x
i
) = δP
i
/∆x
f(x
i
) x
x
min
x
max
x
i
f(x
i
)
f(x)
x
δP
i
x
f(x
i
)
x ∆x
X
i
δP
i
=
X
i
f(x
i
) ∆x = 1.
∆x
f(x)
x
min
x
max
f(x)
dx
δP(x)
x
f(x)
x
δP (x)
dx x dx
dx