γλώσσες
Σελίδες
Νομικός
B
i
ii
2000 . . . , . . () . . .
. . . .
, 2008
~ ~
-
/ /
iii
:
, .
, .
, .
, .
,
, .
:
.
:
, , , , , :
:
John Bardeen, William Shockley
Walter Brattain, 1947.
.
iv
, . . (),. , . , . , . , . , . . , . . (), . , . , . ,. , . , . . . . . . . , .. . , . . , .. . .. ... , COSMOTE, ... General. Electric
11 -
1.11.1
............................................................................................................................. 3
.............................................................................. 3
....................................................................................... 5
.......................................................................................... 8
Brown ....................................................................................................................... 9
.................................................................................................... 10
........................................................................... 10
....................................... 12
..................... 15
................................................................................................................... 17
.................................................................................................................... 17
............................................................................................................................ 20
- ....................................................................................................... 22
1.21.2
............................................................................................................................. 25
............................................................................. 25
............................................................................................................. 26
~ ......................................................................................... 27
1 .................................................................................................. 28
- ...................................................... 28
.............................................................................................................. 30
................................................................................................................ 30
.............................................................................................................. 31
........................................................................................................... 32
................................................................................................................ 32
............................................................................ 34
v
... 36
Poisson ..................... 39
................................................................................................................ 41
................................................................................................................ 42
2 .................................................................................................. 42
Carnot ............................................................................................................ 44
.............................................................................................................................. 47
............................................................................................................ 50
..................................................................................... 53
- ......................................................................................................... 58
................................................................................................................... 60
.................................................................................................................... 61
............................................................................................................................. 62
- ....................................................................................................... 65
22
2.12.1
............................................................................................................................. 73
.................................................................................................. 75
Gauss () .................................................................................................. 77
................................................................. 81
- .......................................................................... 87
.......................................................... 91
............................................................................................................. 97
...................................................... 99
.................................................................................................. 101
............................... 102
........................................................................................ 106
- .............................................................................................................. 108
........................................................... 109
.......................................................................................... 110
vi
................................................................................................... 111
..................................................................................................... 113
................................................................................................................... 115
....................................................................................................................... 122
/ ................................................................................... 123
................................................................................................................... 124
.................................................................................................................... 126
............................................................................................................................ 129
- ....................................................................................................... 131
2.22.2
............................................................................................................................. 137
................................................................................. 137
Biot Savart ................................................................................................... 138
Biot Savart .......................................................................... 140
......................... 143
......................................... 144
.................................. 145
........................................................................................................... 146
........................................................................................................ 147
......................................................................................................................... 148
Laplace - .......................................................................................... 150
....................................................... 154
................................................................................................. 155
Ampere .......................................................................... 157
............................................................................................ 159
Hall ................................................................................. 160
................................................................................................................... 162
.................................................................................................................... 163
............................................................................................................................ 165
- ....................................................................................................... 167
vii
2.32.3
............................................................................................................................. 171
- ( Faraday) ......................................... 171
E .............................................................................. 178
E ..................................................................... 183
E ....................................................... 183
......................................................................................................................... 186
................................................................................................ 187
............................................................................................................... 189
......................................................................................................................... 191
.......................................................... 195
- .................................................................... 197
.................................................................................................... 201
.................... 202
....................................................... 203
.............................................................. 204
R, L, C ............................... 206
............................................................................... 207
......................................................................... 208
................................................................................................................. 211
......................................................................................... 213
................................................................................. 213
Maxwell .............................................................................. 215
................................................................................................................... 219
.................................................................................................................... 220
............................................................................................................................ 221
- ....................................................................................................... 226
viii
, , .
~ : ; : . , . . , , , .
. . , , .
. , , , , , . . . ~ , , , , , . ~ , , , .. .
, , . , .
~ , . , , (.. , ) , .
. . , .
, , Timeo Hominem unius libri, ( )* . ,
ix
* OHANIAN, . .
. , , . , . o . . .
(SI) SI. . , . , . , . resistance reactance , , , . mol (o) , , . , , . ( ), (molar) (;) , . resistor, , , . , . , . , . . . , , u =5 2 /8 m/s, u = 3,24 m/s. , , , . , .
. 3 .
~ , , , . . . .~ . 1984 IUPAC (International Union of Pure and Applied Chemistry, ~ ), Comimission onThermodynamics ( ),
x
1 atm (101,325 k Pa) 100 k Pa (1 bar). 22,4 L 22,7 L.
273,15 (0 C), 273 . 101,325 k Pa .
. ., , .. . . . , , . . =0 cos , 0
.
.
, , 0
q q q/0
.
. , , , , . , , , , . , , , , , .
.
.
B
xi
-
1
1.1
, . , . 2,7 1019 .
: (p), (V), (). , . . . , , , . ( ), , , , . , .
().
, , ( ). , p,V, T ( ) .
BOYLE - MARIOTTE
. , .
1.1. , () . , , .
V0 , V0 / 2, V0 / 4, V0 / 8 p0, 2p0, 4p0, 8p0. :
3
1.1
, .
, , .
Boyle - Mariotte, Robert Boyle Edme Mariotte, - - 17 .
1.2. (), , .
CHARLES GAY-LUSSAC
Boyle Charles Gay-Lussac , :
(i) , .
(ii) , . 1.3 1.4.
p V = . ( = .)
4 KINHTIKH -
1.2
Boyle -Mariotte
1.4
Charles Gay - Lussac V - , p - .
1.3
Charles Gay - Lussac V - , p - .
- . 1 2 Gay -Lussac, (i) Charles,Gay - Lussac, (i) Gay - Lussac (ii) Charles.
273 C, ( 273,15 ), (i) (ii),, . .
, ( elvin), :
(i) , ,
(ii) , , .
1.5.
, , 1.6. , . .
V1, p1 1. 1 , V, p 2. Boyle
p1V1 = p2 V ~ (1.1)
, p 2, 2, V2. Gay - Lussac
(1.2)
(1.1.) (1.2)
(1.3)
, , .
n ( mol) . ( ) (p 0 = 1 atm, T0 = 273 K) V0 = n Vmol (Vmol = 22,4 L). ,
pV = .
p V
T
p V
T1 1
1
2 2
2
=
=
V
T
V
T1
2
2
p = . , (V = .)
V = . , (p = .).
5
1.5
,
1.6
,
, , p,V, T. (1.3.) :
R, :
(1.4)
(1.4) . R
L atm, , ,
, p, V, T.
2, 2 He, Boyle - Mariotte, , .
.
:
0 = 273 , p0 = 105 Pa V0 = 22,4 l .
2, 2 He pV / p0V0 , 1, Boyle-Marriote
p0V0 = pV
.
pV
p V0 01=
R =
0 082,L atm
mol K
R =
8 314,J
mol K
pV = nRT
pV
TnR=
p V
T0
0
mol
pV
Tn
p V
T= 0
0
molpV
T
p V
T= 0 0
0
6 KINHTIKH -
Pa , Boyle . .
.
1-1
150 o C , , 40%. .
, , oC, , . 1, 2 = 1 + 150 .
, p1 ,
,
T1 + 150 K = 1,4 T1 T1 = 375 K
, 1, ( )
1 = (375-273) oC = 102 C
2 = (102 + 150) oC = 252 C
1-2
. () () . 2,0 mol. 0 oC, lB / lA = 2/3. ( mol) . T .
p
T
p
T1
1
1
1
1 4
150=
+,
K
p
T
p
T1
1
2
2
=
p p p p2 1 1 140
1001 4= + = ,
7
1.7
, . ,
, , . , . , , .
, , ( ) ( ) . , . , .
:
) .
) ( ).
nHe mol= 0 80,nH mol2
1 2= ,
n n nH H He( )2 2
3
5= +
n
n n
H
H He
2
2
3
5+=
n
nH
He
23
2=
B
A
l 2=
l 3
llA
B
H
He
=n
n2
A
A
n
n
llA
B
H
He
= 2
V
V
n
nA
B
H
He
= 2pV n RT
pV n RT
A H
B He
=
=UVW
2
8 KINHTIKH -
) .
) ().
() .
(, ) , . , , . .
, .
9
BROWN
1827 Brown , . . . 1905 Einstein. (), . , , .
, . , . .
Einstein , . , , .
. , . .
, , V. , yz ( 1.8 xy). m,
, .
() ( ) x .
10 KINHTIKH -
1.8
, x .
1, 2, ... N ,
, 1 1, 2 2 .. :
1 + 2 + ... + =
12,
22, ... , N
2 1, 2, ... , N,
2 ,
( )
,
2,
(root mean square, rms)
rms r v ( ).
rms =2
N N N
NK K2 1 1
22 2
2 2
= + + +.. .
NN2 1
22
2 2
= + + +.. .
N N N
NK K= + + +1 1 2 2 . ..
NN= + + +1 2 . ..
y z. x mx mx. x mx (mx) = 2 mx.
t ( ) x t.
, , ( x) , , x , x.
t, , , (/V), (A x t) 1.9, 1/2, .
, t,
( p).
2 . - ( ), .
F
x ( ), .
, 2,
,
x y z2 2 2= =
2 2 2 2= + +x y z
2 2 2 2= + +x y z
pF
A
Nm
V= = x
2
FP
t
NAm
V= =
x x
2
x xP
t
NAm
V=
2
x x xPN
VA t m= 1
22
11
1.9
t, (x t). .
,
(1.5)
(1.6)
()
.
(1.6)
n ( mol), Avogadro NA , = nNA
Boltzmann
k = 1,381 10-23 J/K
(1.7)E kTK =3
2
kR
N A= = = 8 314
6 0221 381 10 23
,
,,
J / mol K
/ molJ / K
kR
N A=
ER
NTK
A
= 32
EnR
NTK =
3
2
nRT
V
N
VE K=
2
3
E mK =1
22
pN
VEK=
2
3
pN
Vm= 2
3
1
22
p = 13
2
= NmV
pNm
V= 1
3
2
x2
2
3= 2 23= x
12 KINHTIKH -
Ludwig Boltzmann(1844 - 1906)
.
.
(1.7)
(1.8)
(1.8)
m mol ( ),
(1.9)
1-3
, , 27 oC; [k = 1,38 1023 J/K]
EK = 6,21 10-21 J
1-4
( ) (T0 = 273 K,
p0 = 1,0 105 N/m2) 0 = 0,30 kg/m3. r = 1100 .
(1.5)
or ,
(I)
1.8 or , r
p
r =3 0
0
02
p 0 0 021
3=
E k = 3
21 38 10 30023,
J
KK
E kTK =3
2
RT
Mr =
3
RT
N mAr =
3
kT
mr =
3
r rms(= )=2
13
14 KINHTIKH -
()
r = 2000 m/s
1-5
m = 8,4 kg
= 4,2 kg/m3 r = 500 m/s. :
) , , .
) .
) ( ).
)
: NA = 6,0 1023 /mol, k = 1,4 10 - 23 J/K 28.
)
) = m /V,
( mol)
nm
= =
mol = 300 mol
8 4
28 10 3,
Vm= = = 3 3m m
8 4
4 22 0
,
,,
p = FHGIKJ =
1
3
N
m
N
m2 24 2 500 3 5 102 5, ,
p = =13
1
32 2 r
p T
r =
3 0
0 0
T
Tr r=
0
T
Tr
r
= 0
kT
mr =
3
kT
mr =
3 0
.
15
N = nNA = (300 6 10 23) = 18 1025 )
m ( )
)
( ). () [. 1.10 ()].
, , [. 1.10 () ()].
, ().
, , . .
, , , .
, .
:
, , . , . , , .
TE
kK= =
2
3
2 5 8 10
3 1 4 10
21
23
,
,K = 280 K
E kTK =3
2
Em
NK = =
1
2
1
2
8 4
18 105002
252
r-21J = 5,8 10 J
,
m
N
M
NA
FHGIKJ
E mK =1
2
2r
16 KINHTIKH -
, , . , . , , , .
, . .
, . . . . 1.11 () .
1.10
( )
1.11
.
17
, ,
p V = .
, , ( Kelvin, K)
V = . .
, ,
p = . .
,
p V = .
pV = nRT
, .
,
, m V .
, , ,
k Boltzmann.
,
, , , .
kT
m
RT
Mr = =
3 3
r =2
E kTk =3
2
pNm
V= 1
3
2
drasthriothtesA N A
drasthriothtes
1.
, , .
, .
18 KINHTIKH -
2.
) . . . , ; , 1 2.
J.C. Maxwell,
. Maxwell - Boltzmann . + . N0 .
) , 107. . ( ) 1,78 10- 25 kg. .
, + , . , . , , 100 m / s. , , , .(i) 1 2 , .(ii) , , 1 2.(iii) , ,
. . f () , + . . 1 3 .(iv) , . , . . 1,0 10- 6 m/s. ( ) : ,
f
( )
=
0
19
kT / 2, . , Brown , , . f (), . . 1,0 10-9 kg. ; 1. Ag. , , , Ag 1,0 10-9 kg. ( f () ), Ag 1000 ;
.
( ..).
20 KINHTIKH -
1
.
.
2
, , , , . :
()
()
()
() .
3
S.I.
()
()
()
()
4
.
S.I.
L
m3
/m2
5
. ,
.
() () () () .
6
. ,
() () () () .
7
;
8
() . ,
() () 3 () 6 () 9
9
, . , , ,
21
() () () () .
10
.()
, , , .
() .
11
( ) ;
() , .
() , .
() , , .
() , , .
12
e Ne, , He 6,0 10-21 J. Ne He. Ne
() 1,5 10-21 J() 3,0 10-21 J() 6,0 10-21 J() 24 10-21 J.
13
r
27 C;
() 54 C () 108 C () 381 C () 927 C
14
, ,
, . , , ; .
15
() r ;
16
, . , . .()
.
() r .
()
22 KINHTIKH -
, .
17
, , (2). , 0. , r . R( 2.127).
= 0 nI . , , . , ' . , , (2.67) ( )
, ' .
(2.68)
r R
tr
B
tr n
I
t= =2 2 0
Er t
=
1
2
E rt
2 =
E
t
l =
E
Et
l =
E
E
188
1.
2.
. ,
2.127
, , .
E
(2.68)
r > R
(2.68)
2.128 , r.
1 , 2 , 2.129. 1 1 , , ( ) 2. .
1 1, 2. 1 , 2. 2 .
, 2( ), 1 ( ), .
1 1,
2 2 . 2 , 1, 1,
(2.69)
.
t 1 I1 , 2 2 , (2.69)
2
(2.70)
, , .
t
MI
t2
2 1= =
tM
t2 1=
2 = 1
ER
r n =
2
02
tR
B
tR
I
t2 2
0= = n
Er
n=2
0
HOMA 189
2.128
, r.
2.129
1 , 1, 2 2.
, . .
1 henry (1H) ()
(, dim M = L2 MT 2 A 2)
2-34
1 L (. 2.130), 1 . 1 2 , 2 . .
1 1,
2
2
, 2 22 , (2.69)
, 2 r , . .
(.2.131). , (. 12 V). , ' , . Ruhmkorff . .
M
LA= 0 1 2
M I
LA I1 0
1 21=
N N
L I2 2 0
1 21= A
LI2 1 0
11= =
B
LI1 0
11=
1 H 1Wb
A=
190
2.131
.
2.130
, 1, 2.
JOSEPH HENRY(1797 - 1878)
A . - . . - , Faraday.
2.132 .
1 2.132 ,
, R, 1, 2 . , , , . 2 , 1 , .
2 2.133
R, . , , .
2 , . 1. , . () , ' . , , Lenz .
, , .
, , , .
, , , . , ,
(2.71)
L , . L 1 ( ) . , l, , , ,
= ~ = L I
~
= L I
N N
L I0l
=
= L I
HOMA 191
2.133 .
2.134
.V LI
tAB
=
t , , (2.71)
(2.72)
' , , .
2 . ' ; ' . ().
UL L, 0 .
' t, . t, I ,
UL = VI t
V .
UL = L I
LI = f (I) ( 2.135) UL , . 0 , , () UL , , ,
2-35
L = 0,50 H, R = 10 ,
U L IL =1
202
V L
t
=
t
L
t= =
t
t= L
L N= 0
2
l
192
2.135
.
, = 12 V (. 2.136).
) 1. , 1/4 , :
i)
ii)
iii) .
) ( ), 2. , 8/9 , :
i)
ii)
iii) , .
) , .
= VR + VL VR , VL ,
VR = IR
() 0,
, VL = 0, = I0 R,
,
i) 1/4 ,
= 0 / 2 = 0,60
ii) = 0,60 ,
1
2
1
4
1
22
02L I L I=
U UL L=1
4max
U L ILmax =1
202
IR
0 1 2= = ,
V LI
tL
=
HOMA 193
2.136
VR = IR = 6,0 V
VL= VR
iii) = 0,60 ,
= = 7,2 W ,
PR = I2R = 3,6 W
,
PL = P PR = 3,6 W) ' 1 2,
0 = 1,2 .
i) 8/9 , .
ii)
VR + VL = 0
= 0,40
iii)
PR = I2R = 1,6 W
, , 1,6 W .
8
A
s
I
t= ,0
t
IR
L=
L
tIR
=
I I= =13
0 400 , A
1
2
1
9
1
22
02L I L I=
U UL L=1
9 max
s
I
t
V
L
R= = 12
L
tV R
=
194
-
, , (2.64). , , 2.137().
, . , , . , 2.137().
2.137() ac, . .
, 2.138(),
HOMA 195
2.137()
.
2.137()
, .
2.138()
, .
2.138()
.
. ' (). . . , . ( ), , , 2 , ().
. ( 2.139). Laplace ( 2.86). , . ( ). dc.
, ~, V, , Lenz.
~ ( - ) . R () V
V ~ = I R V = ~ + I R (2.73)
, ~ = 0,
(2.73)
V I = ~ + 2R (VI) P,
( 2R) Joule, ,
, (~) .
= ~
2-36
= 150 V . , 1= 10 , , , 2 = 4,0 .
I =V
R
196
2.139
.
) () R
) , , , , - .
) .
) ,
= I1 R
) , ,
P = I2 = 600 W
R,
PR = I22R = 240 W
= R = 360 W -
P = ~ 2
) ,
- (ac C)
( 2.64) ( ), ' .
(2.64)
V = N B A (2.74)
(2.75)
V . ( )
f= =2 2
= V sin t
= =0 60 100 60, % % = = =P
P
360
6000 60,
= = Px2
V
90
RI
= =1
15
HOMA 197
2.140
.
( ) f , ( ),
, (t), . = V sin (t + ), (t + ). , t = 0.
H , , . x y
V, ( , phasor, ), 2.141, , ' . . t = 0 V x, t, = t. () V y~y
= V sin t
.
I , = V cos t, . ,
() .
= V sin t ( = 0) R, (. 2.143). Ohm,
i
,
(2.76)
(ac). . , .
i = I sin t
IV
R=
i
R
V t
R= = sin
V
fT
=1
198
2.143
.
2.141
.
2.142
.
:
. ,
= V sin t
i = I sin t
, Ohm R -
= V sin (t + ), i = I sin (t + )
, ac C (alternat-ing current).
2-37
= 120 sin 100 t [ V t s]
, R = 60 .
) .
) ,
) t = 1/600 s
) 1,0
) = V sin t
V = 120 V = 100 rad/s
= 2 f
)
, i = I sin t
i = 2 sin 100 t [i , t s]
) t = 1 / 600 s
IV
R= = 2 0, A
T1
f= = 0 02, s
f= =2
50
Hz
RV
I=
HOMA 199
2.144
.
= 60 V
) i = 1,0 A
1,0 = 2,0 sin 100 t
k1 = 0, 1, 2 ... k2 = 0, 1, 2, 3...
k1 = 0
k1 = 1
k1 = 2 ..
k2 = 0
k2 = 1
k2 = 3 ..t =29
600s
t = 17600
s
t = 5600
s
t = 25600
s
t = 13600
s
t = 1600
s
kt
kt
1
2
12 +1= s
60012 +5
= s600
t k
t k
1
2
100 = 2 +
6
100 = 2 + -6
sin = sin
1001
2 6t =
= FHG
IKJ
1206
sin
V
= FHG
IKJ
120 1001
600sin V
200
HOMA 201
f(t) [, ], 2.145. f av [, ],
. () , fav f (t), [, ]. (av) average. , [,] g (t) = f (t) + C y (t) = f (t) K C, K , g av = fav + C yav = fav K
sin t
. ( . 2.146). ~ (sin t) av = 0
(cos t)av = 0
, , ..
sin2(t) 1/2.
sin2(t)+cos2(t) = 1,
(cos )21
2t
av=
sinav
2 1
2 tb g =sin cos
av av
2 1
2
1
22t tb g b g=
sin ( ) cos( )21
2
1
22t t=
cos 2 tb gav
= 0sin 2 tb gav
= 0
sin2
t
FHGIKJ
2.145 2.146
(rms )
( ) . ,
.
rms (root mean square) Ir . .
, () , '
P = i2R
,
. (av )
Pav = (i2 )av R = Ir
2 R (2.17)
, , , , t, Joule.
, t , (i2 )av . ( f = 50 Hz = 0,020 s), , , , .
:
(2.78)
' Vr. H
VV
r V= =0
20 707,
II
r I= =2
0 707,
(sin )1
22 t av =
I I tr avsin= ( )2
I i I tr av= =( ) sin av2 2 2( )
Q I R t= r2
P
( )i2 av
202
, , ,
V = I R
(2.79)
, , , , .
(2.77) (2.79) ,
Pav = Ir2R = Vr Ir
(ac) . .. 220 V, 220 V. , ac .
I. Im .
( ) L,
= V sin t
i, ,
i I t= FHG
IKJ
cos
2
IV
L=
iV
Lt= FHG
IKJ
sin
2
Li
t=
i
V I Rr r=
V IR
2 2=
HOMA 203
2.147
/ 2.
/2. / 2 /4, 2.148. , , , , . ,
,
i = f (t). ( = V) i = f (t), , i = 0. , i/t , i = I.
L L
2.147
XL , . , L. ' , . XL , , , . 1/4 , ' 1/4 . XL , " ", (inductive reactance ) "". (resistance) () .
C,
= V sin t
() .
q = C
XV
I
V
IL = =
r
r
XL = L
Li
t=FHG
IKJ
204
2.148
.
(t )
I = C V
, / 2. , , . i , = f (t). = V / t , i. = 0 / t , i (i = I ).
Xc ,
2.149
XC , , . , . . .
XC "" , , . ' , 1/4 , , 1/4 . , XC , " " "". XC "", " ".
XV
I
V
IC = =
r
r
XC
C =1
1
C
i I = +FHGIKJsin
2
i CV t= +FHG
IKJ
sin
2
iq
tC
t= =
HOMA 205
2.149
/ 2.
2.150
.
R, L, C A
,
= V sin t
, , . , R , L /2, C /2.
= R + L + C
() (
2.151)
V ()
()
VR ,
VL,
VC.
V
V, , .
, 2.152.
,
i = I sin (t )
XL> XC ( VL> VC). XC> XL (VC> VL) tan , . R - L - C , .
.
tan V V
V
X X
RL C
R
L C= =
ZV
I
V
I= = r
r
Z R X XL C= + 2 2( )
V I R X XL C= + 2 2( )
V IR IX IXL C= + ( ) ( )2 2
V V V VR L C= + 2 2( )
206
2.151
R-L-C ()
2.152
.
HOMA 207
RV
I
V
I= = r
r
i I t= FHG
IKJ
sin
2
XV
I
V
ILL = = =
r
r
V t= sin
i I t= +FHG
IKJ
sin
2
V t= sin
XV
I
V
I CC
= = =r
r
1
zV
I
V
IR X
C= = = +r
r
2 2
i I t = sin ( ) tan V
V
X
R
C
R
C= =
V t= sin
i I t = sin ( )
i I t= sin
zV
I
V
IR Xr
r
L= = = +
2 2
tan V
V
X
R
L
R
L= =
V t= sin
zV
I
V
IR X
L= = = +r
r
2 2
zV
R X L
.= = +2 2
tan X
R R
L
=+
V t= sin
i I t = sin ( )
i I t = sin ( )
= 2
zV
I
V
IX X
L C= = = r
r
V t= sin
i I t = sin ( )
tan V V
V
X X
R
L C
R
L C=
=
V t= sin
V t= sinz
V
I
V
IR X Xr
r
L C= = = + 2
2b g
V t= sin
i I t= sin
1.
2.
3.
4.
5.
6.
7.
8.
. R - L - C .
P = i = V sin t sin (t - )
.
,
sin (t ) = sin t cos cos t sin
P = VI sin2t cos V I sin t cos t sin
sin 2t = 2 sin t cos t
(sin 2 t)av = 0
(2.80)
cos
0 1,
:
1. cos = 0 = / 2
. (2.80) av = 0. .
2. cos = 1, = 0.
, R - L - C L = XC. , ,
i) = R
ii) ( )
2 2
P V I av r rcos=
P VI V I
av cos cos= =1
2 2 2
(sin )av2 1
2t =
P VI tVI
tav av avcos (sin ) sin (sin )= 22
2
P VI t= sin cos2
sin 2 sin2 VI
t
208
iii)
iv) , .
.
R - L - C R - L R - C ,
(2.81)
2.152 Vr = IrZ, (2.80) (2.81).
2-38
R1 = 20 , R = 80
.
,
= 240 sin 200 t ( V t s)
XC = 180 3 ,
)
) , , i , , C .
) .
)
= 200
)
V IRR 1 1 1 2 20 24= = =, A V
IV
Z= = =240
2001 2
V
,
Z = + + ( ) ( ) 20 80 80 3 180 32 2
Z R R X X L C= + + ( ) ( )1 2 2
X LL = =FHG
IKJ
=200 2 35
80 3
L = 2 35
H
cos R
Z=
P I Rav r= 2
HOMA 209
V = I Z = 1,2 160 = 192 V ()
( 2.153). , VL , V ( )
,
i) i ,
= / 3
ii) i ,
= / 3.
, , S.I.
,
,
)
P I R Rav r W= + =2 1 72( )
PV I
av W= = =
4
240 1 2
472
,W
P V I V I
av r r cos= =2 2
1
2
tR1 24= +FHG
IKJ
sin 200
3 tC =
FHG
IKJ216 3 sin 200
6
t sin 200
3= +FHG
IKJ192
2i t= +F
HGIKJ
1 2 2003
, sin
tan C L
R R
= +
= =V VV V
V
V1
120 3
963
tanV
V
V
VL
R
= = =96 396
3
V IRR A V= = =1 2 80 96,
V IXL L= = =1 2 80 3 96 3, A V
= + = + =R X L2 2 22
80 80 3 160e j
V I XC C= = =1 2 180 3 216 3, A V
210
2.153
.
HOMA 211
, .
, , (). 1, 2.
, . , 1 ,
1 . 2
2 .
t2 2=
t1 1=
2.154
.
2.155
.
212
,
1, 2 , ,
2 > 1 , V2, r > V1, r , .
2 < 1 , V2, r < V1, r , .
, , . ' cos 1 , , . ' 2 , , , . cos 1 = 0 , .
,
P2, av = V2,r I2,r
(cos1) 1, , ,
P1, av = V1,r I1,r
, ' ,
P1, av = P2, av
90 % 99 %. , * . , . , , .
* , .
aP
P= 2
1
,
,
av
av
V
V
N
N
1
2
1
2
,
,
r
r
=
1
2
1
2
=
HOMA 213
, .. , . , . .
, . , Pav = V r Ir , Joule
, , , .
,
. , .
, . , , . ( ) 220V, 380V. , 220V 380V , ...
PP
VR =
FHGIKJ
av
r
2
P R r2=
2.156
. 1 , 2 , 3 .
(, ) , . (. 2.159), , (. 2.157()).
, ( . 2.160) (. 2.157()). , , . .
, (). . 2.160, 2.161. , , , .
214
2.157
.
2.161
.
2.158
.
2.159
.
2.160
.
HOMA 215
MAXWELL
1873 Maxwell Treatise n Electricity and Magnetism. , , , . Maxwell Newton, Einstein. Boltzmann, Maxwell, .
Maxwell Gauss ( Gauss) Ampere Maxwell, . Maxwell , , , . . Ampere .1. Gauss
(I)
- ,
- Coulomb2. ( Gauss)
(II)
-
B = = i i i cos 0
Q
= =i i i
0
cos
James Clerk Maxwell (1831-1879)
19 . . ~, , . , 50 .
216
.
() () , . . , .3. Faraday
(III)
- ,
, ( ) .
4. Maxwell Ampere .
Ampere .
() S, I . , ,
B i// l = 0
tII l =
HOMA 217
S. .. 1, 2. (), iC ( )
. S, (0 iC) 1 , 2. Ampere . Maxwell, , , iD. iC, , 2. t , C, q C , :
l,
,
,
=
i
tD
= 0
tA
E
t =
i A
tD = 0
i
tD = 0
ll
C A= 0l
t
E
tC = l
EC = lEC=l
i iq
tC
tD C
C= = =
B// l
218
iD , ( ), , . .
, ( ) Ampere
(V)
- .
- Biot - Savart () (IV) .
() (0iC), (IV), .
() , ( /t = .) . ( IV) ... , .
Maxwell ,
*. . Hertz, Maxwell. (H ).
, Maxwell Lorentz
.
* c () .
F q q
= + E
c =
8
0 0
1
= 2,997 924 58 10 m / s
B i
tC
/ / l = +0 0 0
B i iC D/ / l = +0 b g
HEINRICH RUDOLFHERTZ
(1857 - 1894)
.
HOMA 219
( Faraday) ' , ,
Lenz , .
l
, '
= B l sin
, .
, , , '
= B sin t t = 0
.
l, , ' , f
, , :
,
,
R .
// , , , l, ,
Faraday.
2 ' , 1 ,
, .
' , , ,
L , ( ).
' L,
L t
=
t
21=
t
//
l =
R= 2
2
B
f= =B l l22
2
B
B
B
B
t
=
drasthriothtesA N A
220
, ,
= V sin (t + ) i = I sin (t + )
H , Joule , .
, .
= V sin t
R, L, C , :
i = I cos (t )
'
Pav = Vr I r cos
- .
.
.
ZV
IR L
C= = +
FHG
IKJ
2
21
tan L
CR
=
1
VV
r =2
II
r = =2
0 707, I
U L I= 12
2
1. 1200
300 , .
1200 . ;
;
1200 . . .
1200 y .
. ( ) . .
2. - LENZ
() 1,5 m . . ; .
drasthriothtes
() Lenz ( 2.109).() 300 , .
. - 30 V, . ; ( ). ; .
3. (2.132 2.133) - 4,5 V- 3,5 V.- - 300 - (10 , 5 )
4. () . .() ( ) ;-
.- ()
0,3 mm.- 10 cm
3 mm- 50 cm .-
20 mm 1,5 cm.- .
HOMA 221
1
, . . () ().()
()
.
222
() ( Joule) .
2
, , .
, ;
3
Lenz () () () ()
4
, .
, 0 t0:
() () () () 20 t0
5
,
, 0
.
, . () ().
() , .
() () , .
() , .
6
,
, . . ,
;
7
, , ,
R. A, . . .
t = 0 , , . , .
F
B
B
B
B
t
0
0
t0 02
HOMA 223
, .
8
, , .
, ,
;
9
t = 0 .
. , ;
10
, .
,
() +x () y() +y () x
11
t = 0 ,
. , t = 0 , :() () () ()
12
() Faraday () 2.122 ().() ,
.() ,
.() ,
.() ,
, , .
13
. , , , .
a
F
224
, . .
14
, .
.
, , , , -
, R ;
15
. 1, .
, ;
16
1, 2 . 1 L1 = 33 mH. 1 ,
1, 2 2 = 1 / 3 . :() 99 mH() 11 mH() 33 mH() 66 mH
17
, l, L. l = l / 3 . l :
() () 3L
() () 9L
18
. UL, ,
;
19
t = 0 . , ;
L
9
L
3
a
t< 0
HOMA 225
20
= 110 sin (157 t) [ V t s] , ( V), ( s) :
() = 11 sin 157 t
() = 110 sin 314 t
() = 220 sin 314 t
() = 220 sin 157 t
21
, , 1 h W. , , ,
() 1 h () 2 h
() ()
22
= V sin (2 f t)
o V , f .
XL , , f ;
23
C = V sint.
XC , f ;
24
,
= V sin t
V , .
R = f1 (), L = f2 (), C = f3 (), = f (),
R , XL , ZC .
25
, = V sin t. V , . , ;
1
2h
1
4h
226
26
, , . . , ; o . .
27
R - L - C , . , () R() C() f() L
28
K R - L - C . .
29
= V sin t () ()()
,
() t = 0, T/4
() , ,
()
30
R - L - C 1 ,2 , . 1 2 . R.
31
, ;
1
100 0,40 m2. = 0,50 T, . , 0,80 s, , 90.
2
, = 0,30 m, , .
, 2,0 /s. 3,0 , .
B
-
HOMA 227
3
, 0,40 m2 0,50 , , -
, . 30. = f (t) 0 t 4,0 s, .
4
500 , 10 cm2. 4,0 2,0 .
. , 90
( ), 0,030 C.
5
100 , 10 cm 20 . . 2,0 cm, 5,0 10 . . (2 10)
6
() = 1 m (),
() = 4,25 m 1 /m(). = 1 (). () , , = 1 m/s (). , () = 1,25 m.
7
l = 1,0 m = 30. R1 = 2,0 . , , l = 1,0 m 0,1 kg R2 = 0,50 . . = 1,0 , . :()
.()
(g = 10 m/s2 ).
8
x, y ,
= 10 V r = 1,0 , . l = 1,0 m, m = 0,10 kg, R = 4,0 , , Ax y.
B
228
= 1,0 . g = 10 m/s2. . , , . FL = f (), FL Laplace, .
9
= 1,0 m, = 2,0 m, R = 10 , = 10 m/s, . t = 0 = 1,0 , . 4,0 m .() = f (t) I = g (t)
, t = 0 . .
() Laplace Joule().
10
l = 1,00 m, , ,
l1 , l2 , . -
= 1,00 , 60 . f = 50,0 Hz, .
11
, , 50,0 Hz = 1,00 . . () = 40,0 cm () = 60,0 cm . .
12
2,0 /m, .
l = 0,50 m . 3,0 Hz B = 1,0 T. , 30.
13
20 /cm, 1,0 cm 50 A/s. , 4,0 cm . 0,50 . . , .
14
.
, > 0.
t=
ll
1
2
2
3=
HOMA 229
, r, . , q .() , .()
.()
, r, , q.
15
1, 2 . 1 5,0 . 2 80 , 20 . 1 , 200 C. .
16
500 5,0 cm2. 0,25 , 0,20 . .
17
, L = 1,0 H, 4,0 t = 0
= 6 ,0 V . () 0 () ,
= 0 / 3.
18
200 V. 103 kg () 7,2 m/min, 12 . (g = 10 m / s2 ).
19
12 V 6,0 . , 0,50 . () , ,
()
20
10 , 0,10 m2 50 Hz B = 0,50 T. .
21
, = 0,20 m, 50 , , . = 300 rad/s = 0,40 . t = 0 . , .
22
. = f (t)
23
. t = 1,0 ms, ()
() () 25 ms
24
, ,
25
i = I sin 100 t
, t = 0, i = Ir .
26
R = 100
= 220 sin (100 t) [ V t s] ()
()
.
27
220 V.() ;() J kWh
, 400 , 5,0 h
28
500 g 50 oC, , (Vr = 220 V). 80 % , . 10 min, . :1 J = 0,24 cal c = 1 cal /g K.
29
L=0,10 H = 200 sin 500 t [ V t s]. , , 100 V;
30
, , 10 . :() i = f (t), i
.() L .
31
C = 10 - 4 F ()
= V sin 400 t [S.I.]. = 100 V,
i = 3,00 A. V i = f (t).
32
, R = 40 , Vr = 117 V = 400 rad/s. 80 V 50 V.()
R L
() .
() , .
33
160 V, 320 W Vr = 200 V = 400 rad/s. () ()
() , .
t t= 100 2 sin 200 V s,
i I
t= sin 2
230
34
R, L, C . , , 100 0,2 H (). - () V1 = 160 V
= 1 ()()
1,5 . .
35
, R = 20,0 L = 0,200 H, C = 20,0 F Vr = 197 V =400 rad / s.()
.
() Cx , . ;
36
, . ,
5 0,0 V, 5,00V 5,00V. 37,5 W. () () = f(t)() ,
, .
37
() () ,
.
i t i A t= 2 50, ,sin 314 s
t t= 300 2 sin 400 V s,
HOMA 231
232
: .
: .
: .
: .
: .
: , .
: .
: . .
Foucalt: , .
Laplace: , .
( ): ( ) () ( ).
( ): () () .
: mol , .
() : , .
E : .
: .
: , , Joule. : ,
233
, , .
: . . .
Maxwell: .
: -. .
: .
: .
: .
: .
:
: , .
: 100%, , .
: , ,
.
: .
: , , . .
Lenz: - . .
Maxwell - Boltzmann: H , .
: , .
Brown: () .
: , .
: .
: .
234
Ampere: .
Biot - Savart: , , .
Gauss: .
: . .
: . .
: - , .
:
, .
: , .
: - , .
Hall: , , .
: . (/) .
: . .
: , .
235
1
() . ( ) , .
= {} []
.
= {}{} [][] = {}[]
{} [] ()
.
. { } () -
. .
: (/ )
, .
, (m s1), t(s), IF (mA), VF (V).
1
m s
{ }{ }
[ ][ ]
= =
1 237
10,0
1,0 2,0 3,0 t/ s
20,0
/ms1 IF/mA
0,0
0,5
1,0
10
VF/V
0,0
0,2
0,4
0,6
()
( = /)
km/h , t s, l m :
{}km/h = 3,6 {l}m /{t}s
3,6 .
. - .
(coherent) , . (.. S.I )
()
, , , B,C, . Q
Q = ABC + ...
(). .
(dimension) Q : dim Q = A B C
(
) A , B ,C, A, B, C, , , .
S.I. ( , Systme International d unite~s) ( ) , 7 : , , , , ( ) , . ( ). , m (), kg (), s (),A (), K(), mol (, ) cd ().
= lt
338
(molar)
LT 1
-1
LMT -2
L2MT-2-1-1
1
: L, M, T, I, , N, J.
= = = = 0. - = 00 = 1.
S.I. dim Q = L M T I N J
( ) ( ) ..
, dim E = M L2 T 2
, kg . m2/s2 = 1 J = 1 joule ().
, . (m). H , , (J).
() (S.I.) . . () . . .
. . ( , , ..) .
E m= 12
2
1 239
2
O S.I.
(Systme International dunits) S.I., 11 1960 (ConfrenceGnrale des Poids et Mesures, C.G.P.M.). S.I. , , :
1. , metre, mtre) (m) 1 / 299 792 458
) The metre is the length of the path travelled by light in vacuum during a time interval of1 / 299 792 458 of a second
) Le mtre est la longueur du trajet parcouru dans le vide par la lumire pendant une dure de 1/299 792 458 de seconde. (17th CGPM 1983 Resolution 1)
2. , kilogram, kilogramme
) To (kg) .
) The kilogram is the unit of mass; it is equal to the mass of the intrernational prototype of the kilo-gram.
) Le kilogramme est l unit de masse; il est gal la masse du prototype international du kilo-gramme. (1st CGPM 1889 and 3rd CGPM 1901)
3. , second, seconde
) (s) 9 192 631 770 () -133.
) The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transitionbetween the two hyperfine levels of the ground state of the cesium - 133 atom.
) La seconde est la dure de 9 192 631 770 priodes de la radiation correspondant la transition entreles deux niveaux hyperfins de l e~tat fondamental de l atome de cesium - 133. (13th CGPM, 1967,Resolution 1).
4. , ampere, ampre) To () ,
1 , 2 107 .
) The ampere is that constant current which, if maintained in two straight parallel conductors of infi-nite length, of negligible circular cross section, and placed 1 meter apart in a vacuum, would producebetween these conductors a force equal to 2 10 7 newton per metre of length.
) L ampre est l intensit d un courant constant qui, maintenu dans deux conducteurs parallles,rectilignes, de longueur infinie, de section circulaire ngligeable, et placs une distance de 1 mtre lun de l autre dans le vide, produirait entre ces conducteurs une force gale 2 10 7 newton par mtre
240
de longueur. (9th CGPM, 1948, Resolutions 2 and 7).
5. , kelvin, kelvin
) T (), , 1/ 273,16
13 C G P M (1967, A 3) .
( ) (Celsius), t ,
t = T T0 0 = 273,15 . (
oC). .
) The kelvin, unit of thermodynamic temperature, is the fraction 1/273,16 of the thermodynamic tem-perature of the triple point of water.
) Le kelvin, unit de temperature thermodynamique, est la fraction 1/273,16 de la temprature ther-modynamique du point triple de l eau. (13th CGPM 1967, Resolution 4).
6. (), mole, mole
) (mol) 0,012 - 12.
, , , , .
: - 12 , () .
) The mole is the amount of substance of a system which contains as many elementary entities asthere are atoms in 0,012 kilogram carbon 12.
When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions,electrons, other particles or specified groups of such particles.
) La mole est la quantit de matire d une systme contenant autant d entits lmaintaires qu il ya d atomes dans 0,012 kilogramme de carbone 12.
Lorsqu on emploie la mole, les entits lmentaires doivent tre spcifies et peuvent tre des atomes,des molcules, des ions, des lectrons, d autres particules ou des groupements spcifis de telles par-ticules. (14th CGPM 1971, Resolution 3).
7. , candela, candela
) (cd) , 540 1012 (Hz) 1/683 (W/sr).
) The candela is the luminous intensity, in a given direction, of a source that emits monochromaticradiation of frequency 540 1012 hertz and that has a radiant intensity in that direction of (1/683) wattper steradian.
) La candela est l intensit lumineuse, dans une direction donne, d une source qui emet une radi-ation monochromatique de frquence 540 1012 hertz et dont l intensit energetique dans cette direc-tion est 1/683 watt par stradian. (16th CGPM 1979, Resolution 3).
2 241
3
(SI)
To (SystmeInternational d Units), SI. 1, .
~ (coherent-ly) , , . . , , 2.
SI 3.
SI Meter Convention ( ), 17 20 1875 1921. 47 . (Confrence Gnrale des Poids et Mesures, CGPM), . (Comit International des Poidset Mesures, CIPM). (ConsultativeCommittees, CC), . (Bureau International des Poids et Mesures, BIPM), Svres CIPM. SI 11CGPM 1960, , . BIPM (Consultative Committee for Units, CCU), (CIPM), CGPM ( ) CIPM SI. , ~ (Commission for Symbols, Units, Nomenclature,Atomic Masses and Fundamental Constants of the International Union or Pure and Applied Physics,
242
m
kg
s
A
K
mol
cd
()
meter
kilogram
second
ampere
kelvin
mole
candela
()
1 S.I.
IUPAP). ( ) E . SI .
A 1995 20 CGPM 1 ( ), , , (rad) (sr) 2.
3 243
, ()
, ,
,
,
( )
.
()
()
rad
sr
Hz
N
Pa
J
W
C
V
S
Wb
H
F
T
oC
lm
lx
Bq
m/m=1
m2/m2=1
m/s
m/s2
rad/s
rad/s2
s-1
rad/s
kg.m/s2
N/m2
N.m, kg.m2/s2
N.s, kg.m/s
J/s
A.s
J/C, W/A
V/A
A/V, -1
V.s
Wb/A
C/V
V/M, N/C
Wb/m2, N/(A.m)
C/m2
A/m
K
cd.sr
lm/m2
s 1
()
radian
steradian
hertz
newton
pascal
joule
watt
coulomb
volt
ohm
siemens
weber
henry
farad
tesla
degree
Celsius
lumen
lux
becquerel
K
2 S.I.
( ) (), . (italics), (roman), .. F = 15 N.
. . , .. tesla, (T), meter (m). ( ) , .. , gram, g, gm, , second, s, sec, , .. mol, cd Hz. s , .. 3 kg, 3 kgs. , .. 3 meter 3 meters, 3 .
(degree) , , ( kelvin K, kelvin, oK). t, t = T T0 = 273,15 , ( (Celsius), C).
SI 106 . ~ . . (.. pF, F).
244
1024
1021
1018
1015
1012
109
106
103
102
101
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
yotta
zetta
exa
peta
tera
giga
mega
kilo
hecto
deca
deci
centi
milli
micro
nano
pico
fempto
atto
zepto
yocto
()
()
()
()
E
P
T
Z
M
k
h
da
d
c
m
n
p
f
a
z
y
3 S.I.
(.. 1 cm = 102 m (1 cm)3 = 1 cm3 = (10 2 m)3 = 10 6 m3). ~ , , , (.. megahertz, Megahertz, Mhertz).
kilogram () , , . kilogram gram g.
() (.. . m N m). H , (.. m/s, m. s1), (.. m/s, m/s/s). , (.. W/(m2 . K4) W . m2 . K 4). (.. kJ/mol, W/cm2).
(.. meter second meter/second, meter.second, ). ~ , ( ), () (.. newton meter newton - meter, newton.meter).
(.. 299 792 458, 299.792.458) ( ). ISO ( ) . .
, (.. 3 m, 3m 3-m). N . (,) .. 0,3 J ,3 J , 3,0 J 3, J. , 0,1 1000 (.. 200 kN, 0,5 mA).
3 245
(attenuation), (level)
min
h
do
L
t
Np
B
1 min = 60 s
1 h = 60 min = 3600 s
1 d = 24 h = 86 400 s
1o = ( /180) rad
1 = (1/60) = (/10 800)rad
1 = (1/60) = (/648 800)rad
1 L = 1 dm3 = 10-3 m
1 t = 1000 kg
1 Np = 1
1 B = 0,5 (ln 10) Np
minute
hour
day
degree
minute
second
liter
metric ton
neperbel
4 S.I. S.I.
SI SI
~ SI . , SI . 4 SI. , , ~ ~~ L l () 1 (). SI , 5.
S.I. ,
1 = 1852 ,1 knot () = 1 = 0,514 m/s,
1 are = 100 m2,
1 hectare () = 104 m2,
1 bar = 105 N/m2 = 100 kN/m2,1 angstrom = 100 pm
1 barn = 10- 28 m2
1,602 177 33 (49) 1019 J (49) 33 0,000 000 49 10-19 J.
246
eV
u
ua
1,60217733(49) 10-19 J1,6605402(10) 10-27 kg
1,49597870691(30) 1011 m
5 S.I. S.I.
S.I.
1 in () = 2,54 cm ()
1 ft () = 12 in () = 0,304 8 m ()
1 yd () () = 3 ft () = 0,914 4 m ()
1 mile () = 5280 ft () = 1,609 344 m ()
1 L () =10 3 m3 ()
1 (1 min) = 60 s
1 (1 h) = 60 min = 3600 s
1 (1 d) = 24 h = 86 400 s
1 kg f = 9,806 65 N()
1 atm = 101 325 Pa()1 orr = 1/ 760 atm ()= 133,322 4 Pa1 mm Hg = 13,595 1 mm H2O= 133,322 4 Pa1 at = 1 kgf / cm2
= 98 066,5 Pa () == 0,967 841 atm1 mm H2 O = 10
4 at = 9,806 65 Pa()
1 (1 CV = 1 PS)= 75 kg f m/s ()= 735,498 75 W ()1 hp = 745,699 9 W ()= 550 ff lbf/s
1 cal15 = 4,185 5 J( 1 g , , 14,5 oC 15,5 C 101,325 k Pa 1950)
1 G = 10 4 T
- ()kg f (kp)
atmtorr mm Hg at
mm H2O
()
Fahrenheit ()o F
15 Ccal15 ( cal)
, gaussGs( G)
M
3 247
t tFo o
F C= +
9
532
1 year () a, atrop () = 365,242 20 d = 31 556 926 s
1 angstrom (1 Ao
) = 10 10 m ()
1 () = /180 rad = 0,017 453 3 rad
g n = 9,806 65 m/ s2 ()
1 pound, lb (, ) = 0,453 592 37 kg ()
1 acre = 4840 yd2 () = 4 064,856 m2
1 (US) .. = 9702 in3 = 158,987 3 L
1 pound - force (lbf) ( - ) = 4,448 222
1 tu ( ) = 788,169 ft lbf = 1 055,056 J
. . , .
:
L, J , ()
n, () t,
P tF
Avogadro L, NA Q, q
, J , i
j, J
Fg , (G), (W), (P) V,
() U, V
, ()
p, P r , K
( )
n r
r M 0
r ( )
W H 0
I P, N ( )
TIME (2006)
, , Committee on Data for Science and Technology of the International Council of Scientific Unions (CODA-TA), . (3/ 2008), 2006.
(.) NIST (ational Institute of Standards and Technology - ) ... ... ( ) .
248
From: http://physics.nist.gov/constants
Fundamental Physical Constants Frequently used constantsRelative std.
Quantity Symbol Value Unit uncert. ur
speed of light in vacuum c, c0 299 792 458 m s1 (exact)magnetic constant 0 4 107 N A2
= 12.566 370 614... 107 N A2 (exact)electric constant 1/0c2 0 8.854 187 817... 1012 F m1 (exact)Newtonian constantof gravitation G 6.674 28(67) 1011 m3 kg1 s2 1.0 104
Planck constant h 6.626 068 96(33) 1034 J s 5.0 108h/2 h 1.054 571 628(53) 1034 J s 5.0 108
elementary charge e 1.602 176 487(40) 1019 C 2.5 108magnetic flux quantum h/2e 0 2.067 833 667(52) 1015 Wb 2.5 108conductance quantum 2e2/h G0 7.748 091 7004(53) 105 S 6.8 1010
electron mass me 9.109 382 15(45) 1031 kg 5.0 108proton mass mp 1.672 621 637(83) 1027 kg 5.0 108proton-electron mass ratio mp/me 1836.152 672 47(80) 4.3 1010fine-structure constant e2/40hc 7.297 352 5376(50) 103 6.8 1010
inverse fine-structure constant 1 137.035 999 679(94) 6.8 1010
Rydberg constant 2mec/2h R 10 973 731.568 527(73) m1 6.6 1012Avogadro constant NA, L 6.022 141 79(30) 1023 mol1 5.0 108Faraday constant NAe F 96 485.3399(24) C mol1 2.5 108molar gas constant R 8.314 472(15) J mol1 K1 1.7 106Boltzmann constant R/NA k 1.380 6504(24) 1023 J K1 1.7 106Stefan-Boltzmann constant(2/60)k4/h3c2 5.670 400(40) 108 Wm2 K4 7.0 106
Non-SI units accepted for use with the SIelectron volt: (e/C) J eV 1.602 176 487(40) 1019 J 2.5 108(unified) atomic mass unit1 u = mu = 112m(
12C) u 1.660 538 782(83) 1027 kg 5.0 108= 103 kg mol1/NA
Page 1
249
From: http://physics.nist.gov/constants
Fundamental Physical Constants Physico-chemical constantsRelative std.
Quantity Symbol Value Unit uncert. ur
Avogadro constant NA, L 6.022 141 79(30) 1023 mol1 5.0 108atomic mass constantmu = 112m(
12C) = 1 u mu 1.660 538 782(83) 1027 kg 5.0 108
= 103 kg mol1/NAenergy equivalent muc2 1.492 417 830(74) 1010 J 5.0 108
in MeV 931.494 028(23) MeV 2.5 108Faraday constant1 NAe F 96 485.3399(24) C mol1 2.5 108
molar Planck constant NAh 3.990 312 6821(57) 1010 J s mol1 1.4 109NAhc 0.119 626 564 72(17) J m mol1 1.4 109
molar gas constant R 8.314 472(15) J mol1 K1 1.7 106Boltzmann constant R/NA k 1.380 6504(24) 1023 J K1 1.7 106
in eV K1 8.617 343(15) 105 eV K1 1.7 106k/h 2.083 6644(36) 1010 Hz K1 1.7 106k/hc 69.503 56(12) m1 K1 1.7 106
molar volume of ideal gas RT/pT = 273.15 K, p = 101.325 kPa Vm 22.413 996(39) 103 m3 mol1 1.7 106Loschmidt constant NA/Vm n0 2.686 7774(47) 1025 m3 1.7 106T = 273.15 K, p = 100 kPa Vm 22.710 981(40) 103 m3 mol1 1.7 106
Sackur-Tetrode constant(absolute entropy constant)252 + ln[(2mukT1/h
2)3/2kT1/p0]T1 = 1 K, p0 = 100 kPa S0/R 1.151 7047(44) 3.8 106T1 = 1 K, p0 = 101.325 kPa 1.164 8677(44) 3.8 106
Stefan-Boltzmann constant(2/60)k4/h3c2 5.670 400(40) 108 Wm2 K4 7.0 106first radiation constant 2hc2 c1 3.741 771 18(19) 1016 Wm2 5.0 108first radiation constant for spectral radiance 2hc2 c1L 1.191 042 759(59) 1016 Wm2 sr1 5.0 108second radiation constant hc/k c2 1.438 7752(25) 102 m K 1.7 106Wien displacement law constantsb = maxT = c2/4.965 114 231... b 2.897 7685(51) 103 m K 1.7 106b = max/T = 2.821 439 372... c/c2 b 5.878 933(10) 1010 Hz K1 1.7 106
1 The numerical value of F to be used in coulometric chemical measurements is 96 485.3401(48) [5.0 108] when the relevant current ismeasured in terms of representations of the volt and ohm based on the Josephson and quantum Hall effects and the internationally adopted conven-tional values of the Josephson and von Klitzing constants KJ90 and RK90 given in the Adopted values table.2 The entropy of an ideal monoatomic gas of relative atomic mass Ar is given by S = S0 + 32R ln Ar R ln(p/p0) +
52R ln(T/K).
Page 1
250
From: http://physics.nist.gov/constants
Fundamental Physical Constants Adopted valuesRelative std.
Quantity Symbol Value Unit uncert. ur
relative atomic mass1 of 12C Ar(12C) 12 (exact)molar mass constant Mu 1 103 kg mol1 (exact)molar mass of 12C M(12C) 12 103 kg mol1 (exact)conventional value of Josephson constant2 KJ90 483 597.9 GHz V1 (exact)conventional value of von Klitzing constant3 RK90 25 812.807 (exact)standard atmosphere 101 325 Pa (exact)
1 The relative atomic massAr(X) of particleX with massm(X) is defined byAr(X) = m(X)/mu, wheremu = m(12C)/12 = Mu/NA = 1 uis the atomic mass constant, NA is the Avogadro constant, and u is the atomic mass unit. Thus the mass of particle X in u is m(X) = Ar(X) uand the molar mass of X is M(X) = Ar(X)Mu.2 This is the value adopted internationally for realizing representations of the volt using the Josephson effect.3 This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.
Page 1
251
MA
, . - . SI .
=def
, =d
a =def
b, p =d
m a b
a b To a = b
a b a b
~, a ~ b, a b To a b
a, M a
~- ~- (
x a
(x a)
ex, exp x ( e) x
T
() .
SI
cos x x x
sin x x x
x x
tg x
x x
cotan x
x xseccos
xx
= 1
= 1tan x
cottan
xx
= 1
= sincos
x
x
tansin
cosx
x
x=
1
x a
1
sin ( a)x 1
x a1
sin ( a)x
252 3
x x
cosec x
A
arcsin x x x
arccos x x x
arctanx x x
( arctg x)
arccot x x x
arcsec x x x
arccsc x x x
( arccosec x)
sin -1 x, cos-1 x .. ( -1 x,-1 x, ..), , , sinn x, cosn x .., (sin x)n, (cos x)n ..
( SI). , .
loga x a x
, x, log x,
log x x
.
ln x ln x = log e x
x ( e = 2,718 281 8 ...)
lg x lg x = log 10 x
( 10)
lb x lb x = log 2 x
x ( 2)
log x ln x, lg x, lb x, log e x, ..
= 1sin x
cscsin
xx
= 1
3 253
, , (bold) , , .
a, a
a, a, a
a ( a,
a)
ea
a,
a = a
ea
ex ,
ey ,
ez
i,
j,
k
ei (i = 1, 2, 3)
ax , ay , az a
ai (i = 1, 2, 3)
a
a = ax
ex + ay
ey + az
ez
T axex .. ax ..
. . . . () . . . ( ) () . ( ).
.
254
4
. . , , . , . . , . 56,72 mm, , (56,72 0,02) mm, () 56,70 mm 56,74 mm. 0,02 mm , . , (). . , .
A I,
. . , . . , .
.
:
1,35 3
0,107 3
0,050 20 4
500 3
500,0 4
50 101 2 5 102 1 1,520 105 4 1,7 10 4 2
, () .
4 255
, 0,516 784 252. 0,517, . , .
1,723 , 1,7. , . 1,75 , 1,8 ( ), . . , , , , () .
1,75 , , 1,8 (), 2,65 2,6 (). , 10, . , 500, 3. 5 101 5,0 102 0,50 103 .. , .
. , , ,2 . , L, 2 L, 2 . L .
() ()
. , ( ) ().
()
. . . .
3,25 0,21/0,8 = 0,90,851 0,80 = 0,680,075 2 /0,012 = 6,3
1,35 104 0,73/2 102 = 0,5 102
()
( ). .
256
. .
10,00 1 103 ()
0,000 3 104 ( )
0,85 102 ()
102 ()
10,00 1 + 0,000 3 0,85 = 9,15124 100 ()
5,0 102 101 ()7,8 101 ()
101 ()
124 5,0 102 + 7,8 = 3,7 102
( ) 10. ,
1,24 102
5,0 102
0,078 102
1,24 102 5,0 102 + 0,078 102 = (1,24 5,0 + 0,078) 102 = 3,7 102
.
, .
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: .
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.
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. .
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, , !
5 2 7/
4 257
1) n 2 > n 12) ()3) ()4) /m 2, m 35) ()6) ()7) 8) ()9) ()
10) () , () 11) (), ()12) ()13) ()14) 15) 16) () , () , () 17) 18) 19)
1) V1 = 0,3733 V22) 380 K3) 2,2 kg4) 840 K5) 277 K6) () 4,3 L () 4,0 10 3 kg
7) () ()
8) 2,5 cm9) 83,1 cm
10) () = 0 () r H = 4 r 011) 0,5 10 3 m/s12) 300 m/s13) 14) 800 m/s15) () 671 m/s, 507 m/s () 525 K16) 3,0 10 20 J17) () 360 , 7,6 10 21 J, () 1500 m/s18) () 200 , () 707 m/s, () 1/2
m
m1
2
30
29=
259
1
1) ()2) ()3) ()4) (), ()5) W >W >W 6) ()7) 1 (), 2 ()8) ()9)
10) 11) ()
() 12) 13) ()14)
1) () 10 J, () 12 J2) 3) 1,1 10 5 J4) () 600 , () 62400 J, () 24930 J
() 37470 J5) 83 6) 125 J7) () 87,5 J, () 275 J8) () 370 J9) () 45 J
10) 31%11) 0,512) () = 5/ 3,
() WAB = 1120 J, WB = 0, W = 180 J, QAB = 2800 J, Q = 1860 J, Q = 0
15) 16) ()17) 18) ()19) 20) 21) 22) ()23) ()24) (), (), ()25) ()26) (), ()27) ()
() 33,6%13) f = 514) 18%15) () 3600 J, () 0,4, () 24 KW16) 0,5217) () 40%, () 800 J, () 4 J/ K18) () 13 100 J, 0, 6050 J, () 53,8%
() 70,5 W, () 20,2 J/ K19) () 6,1 10 4 J, () 740 J/ K20) 46 J/ K21) () 0, () 52 500 J, () 143 J/ K22) () 2,0 10 5Pa, 600 K, () 0,46 J/ K23) 26 190 J24) () f = 3, () S = 025) () 0, () 11,5 J/ K26) () 600 K, () 488 , 1,08 atm27) 1,528)
260
H
1) 2) 3) ()4) ()5) ()6) (), ()7) 8) ()9) ()
10) ()11) ()12) ()13) ()14) ()15) (), ()16) (), ()17) (), ()18) ()19) ()20) ()21) 1 > 222) (), ()23) (), ()
1) (i) (ii) (iii)
2) () 0, () 3,14 m 2 / C, () 3,14 Nm 2/C
3)
4) . 0,6 m 2,4 m . 1 m 4 m .
5) 18 J6) 3,0 10 2 J7) 7
8)
9)
10) t = 5,7 10 8 s s = 2,8 cm11) () 10 cm, 5,0 cm, () 1,4 105 m/s, = 45
() 50 V12) () 1,0 s, () 1,0 cm, () 0,89 105 m/s, = 27
W kq
a= +
2
4 2( )
xk e
m= 6
2
02
E
r=
2 0
1
8 0
q
1
2 0
q
q
q
0 0
1
6,
2
24) ()25) (), ()26) 27) 28) ()
13) () 20 eV, () 80 eV, () 80 V14) 6,4 10 3 km
15)
16)
17) () 12 10 3 m/s, () 1,1 10 4 m/s
18)
19) () ()
()
20) () 0 / 2, () 8 Gm / 7 02
21) 50%22) 1,00 10 5 V23) 24) () 1,5 105 V/m, () 8,0 1016 C, () 3,3 m/s225) 4,0 F26) () 2,0 F, () 8 C, 16 C, 24 C
() 32 106 J, 64 106 J, 48 106 J27) () 0, 0, () 9,60 C, 38,4 C28) q1 = q2 = 8,0 C, q3 = 4,0 C, q4 = 12 C,
q6 = 5,0 C, q7 = 15 C
29) () 5,0 mA, 0,10 W, 2,2 104 J
3
24 2
Gm
a( )+
Gm
a
2
4 2( )+ +G ma
2
4 2( )
4
3a
Gm
aamax = 2 3,
EGm
a= 3
2
2
261
1) ()2) ()3) ()4) ()5) (), ()6) , 7) (y), (x)8) (), ()9) (), ()
10) 11) ()12) 1 (), 2 ( Na
+ )13)
1) 15 2) 3,8 10 4 3) 5,0 10 5 4)
6 cm 3 cm .5) 4
6)
.
7) 8,3 cm8) 1,0 m
R0 2
21 3 14
tan+ =, ,
14) ()15) (i)
, (ii)
16) (), ()17) () (), () ()18) ()19) ()20)
9) (i) 3,2 10 5 m/s, (ii) 6,4 10 5 m/s,(iii) 16 10 5 m/s
10) (i) 0,10 T, (ii) /
11) R = 9 cm, = 42 cm12) 19 cm
13) ()
() 6,5 10 9 s, () W = 0() 1,0 10 23 kg m/s
14) () 3,5 10 4 m/s, () 7,2 cm, () 2,1 s15) 0,10 T16) 45 o
17) 11 A18) 1,0 10 4 N19) 100 A20)
21)
22) 7,96 A
B r
R= 0
22
( ) cm cm= =3 1 7,
( )3 10 0 541 T T,
262
E
1) (), ()2) 3) ()4) ()5) (), ()6) 7)
8)
9) 10) ()11) ()12) (), ()13)
14)
15) ()16) ()17) ()18) 19) 20) ()21) ()
1) 25 V2) 0,06 3) 0 s 1 s: I = 0,16 A
A 1 s 3 s: I = 0 3 s 4 s: I = 0,16 A
4) 0,36 T5) 16 C6) 0,3 0,2 0,1 7) () 5 m/s, () 2 V
8) 5 m/s,
9) () 0 s 0,2 s: = 10 t, I = 1 AA 0,2 s 0,4 s: = 2Wb = ., I = 0A 0,4 s 0,6 s: = 6 10 t, I = 1
() 2 J, 2 J10) 15,7 V11) 132 V12) 5,6 A13) 1,6 10 4 N/C, 78 14) ()
F
L =105
22) To B XL f f23) XC f f24) 25) 26) 27) ()28) 29) (), (), ()
() q r 2
15) 4,0 mH16) 0,20 H17) () 1,5 , () 4,0 /s18) 50%19) () 2,0 , () 9,0 V20) 160 V21) = 240 sin 300 t
22)
23) () 6 ms
()
() 1 24) 25) 1/400 s26) () i = 2,2 sin (100 t), () 484 W, 027) () 310 V, () 2,2 10 6 J, 0,60 kWh28) 220 29) 3,5
30) () , () 50 mH
31) 125V,
32) () 15 , 50 mH, () cos = 0,6, cos = 0,94() 160 W, 60 W, 220 W.
33) () 20 , () 0,15 , () 41,6 F34) R = 60 , L = 0,1 H35) () 320 W, () 31,2 F, 1940 W36) () 19,8
()
()
tan = 1,33 R = 5,00 sin 314 t
37) () /2, () I
2
tC sin= F
HGIKJ
5 00 3142
,
t sin= +50 0 314, b g
t= +FHG
IKJ
49 5 3144
, sin
i t= +FHGIKJ5 400 2
sin
i t= FHG
IKJ
10 2 2002
sin
i t= +FHGIKJ2
1000
3 2sin
t= +FHGIKJ80 100
5
6sin
263
32, 39 189Ampere Andre Marie 158Ampere 157ampere 154 () 214 213 213 50 191 191
Van Allen 146 99 101Biot-Savart 138Boltzmann Ludwig 12Boyle 3Brown 9
195 195Gauss Karl 77Gauss 77Gay-Lussac 4
106 106 82 82 104 113 114 114 115 186 114 104 100, 102 100 84 81 () 101 () 87 87, 101
36 206 197
198 207 192 10, 13 202 202 100 74 47 214 187 178 183 183 183 171 204 190 27 26
213 90 73 196 117 214
25 25 25 42 28
12 8 10 31 30 34 30
97 57Carnot Sadi 44Carnot 44Carnot 45 5
265
266
Kelvin Lord 43 3Clausius 43, 47 15coulomb 154 32 148
Laplace 151Lenz 174
143 141 137 140 159 3Maxwell Boltzmann 18Maxwell James 215Maxwell 215 208 10 10 10 117 28 29 211 41 42 42 3Millikan 126
TV / 123Oersted 137 185
122 153 58Poisson 39 110 108 111 115 217 10 75 155
3, 25 206 190 82 82 209
Farad 109Faraday Michael 171Faraday 185Faraday 174Faraday 171 147Foucault 186
205 109
Physics 1901RNTGEN, WILHELM CONRAD, Germany, Munich University, b. 1845, d. 1923: "in recognition of the extraordinary serviceshe has rendered by the discovery of the remarkable rays subsequently named after him".
Physics 1902The prize was awarded jointly to: LORENTZ, HENDRIK ANTOON, the Netherlands, Leyden University, b. 1853, d. 1928; and ZEEMAN, PIETER, the Netherlands, Amsterdam University, b. 1865, d. 1943: "in recognition of the extraordinary service they rendered by their researches into the influence of magnetism upon radiationphenomena"
Physics 1903The prize was divided, one half being awarded to: BECQUEREL, ANTOINE HENRI, France, cole Polytechnique, Paris, b. 1852, d. 1908: "in recognition of the extraordinary services he has rendered by his discovery of spontaneous radioactivity"; the other half jointly to: CURIE, PIERRE, France, cole municipale de physique et de chimie industrielles, (Municipal School of Industrial Physics andChemistry), Paris, b. 1859, d. 1906; and his wife CURIE, MARIE, ne SKLODOWSKA, France, b. 1867 (in Warsaw, Poland), d. 1934: "in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discov-ered by Professor Henri Becquerel"
Physics 1904RAYLEIGH, Lord (JOHN WILLIAM STRUTT), Great Britain, Royal Institution of Great Britain, London, b. 1842, d. 1919: "for his investigations of the densities of the most important gases and for his discovery of argon in connection with these stud-ies"
Physics 1905LENARD, PHILIPP EDUARD ANTON, Germany, Kiel University, b. 1862 (in Pressburg, then Hungary), d. 1947: "for his work on cathode rays"
Physics 1906THOMSON, Sir JOSEPH JOHN, Great Britain, Cambridge University, b. 1856, d. 1940: "in recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases"
Physics 1907MICHELSON, ALBERT ABRAHAM , U.S.A., Chicago University, b. 1852 (in Strelno, then Germany), d. 1931: "for his optical precision instruments and the spectroscopic and metrological investigations carried out with their aid"
Physics 1908LIPPMANN, GABRIEL, France, Sorbonne University, Paris, b. 1845 (in Hollerich, Luxembourg), d. 1921: "for his method of reproducing colours photographically based on the phenomenon of interference"
Physics 1909The prize was awarded jointly to: MARCONI, GUGLIELMO, Italy, Marconi Wireless Telegraph Co. Ltd., London, Great Britain, b. 1874, d. 19
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