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-
:
[ .
[ .
[ .[ ,
, .
[ (mol), (), Avogadro ( ) .
[ T Kelvin K.[
.
[ P -V, P-T, V-T.[ (, , -
).
[ -
L atmR 0, 082
mol K
= J
R 8, 314mol K
= .[ .
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10. N - -
[ , .
[ .
[ kgmol
.
[ s.t.p. : 52
NP 1atm 1,013 10
m= = T 273 K .
[ .
[ 2 2 2 rms
= .[ : KV A .[
p M R T = .
- : -
[ F 0 . , - .
,
P: 2N / m (5 2
1atm 1,013 10 N / m= )
V: 3m (
3 6 3 3 31cm 10 m ,1L 10 m = = )
T: ( T 273= + )
: 3kg/m (3 3 31g/cm =10 kg/m )
R: J
R 8, 314mol grad
=
S.I.
L atm0,082
mol grad
=
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11. - N -
: PV nRT= , mPV RTM
= , P RT= (n
mol )
: :
A A B B
P / T P / T ( nR / V , Charles)
AB: ( ) : ( ).
A A B BV /T =V /T ( nR / P,= Gay-Lussac)
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12. N - -
: : .
A A B BP V =P V ( nRT,= Boyle)
:
P 2N / m
V 3m
2
m (m Nm )= kg
A
N , N , n , Avogadro,
molA(N nN )=
3kg/mT K
2 2m / s
rms (: 2rms = ) m / s
k BoltzmannA(k R / N )=
.
:
21P
3=
2
1 3K= m = kT
2 2
3RT 3kT
M m= =
Joule
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13. 1
1 . .
.
2EN
.
.
().
.mn
m
P V n R T P V R
= = =
m
V P M R T
= = .
A
Nn
N
=
A
RP V N P V N k T
N = = .
. ( )2
N m 1P 1
3 V
= ( m : )
N m m =
2 21 1P
3 3= = .
( )n R T 1 N 2K 3 n R
1 K TV 3 V 2 N
= =
A
3 R 3K T K kT
2 N 2 = =
.
2
1 3 3k K m k
2 2 m= = =
A
3R 3R
N m M= =
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14. 2
. 2003.
. 26: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.10, 1.11, 1.13
. 31: 1.30, 1.31, 1.32, 1.33, 1.34, 1.35
. 32: 1.36
.
.. 14 - 20: 1.2, 1.3, 1.4,
1.5, 1.6, 1.7, 1.8, 1.9, 1.10
.. 29 - 31: 1.11, 1.12,
1.13, 1.15, 1.17
. 25: 1
. 37: 1.. 23, 24: 1.3, 1.4, 1.9
.. 35 - 37: 1.11, 1.14, 1.17
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15. 3
1. .
. .
. .
. P V P T .:
. :
: ()
:
: ()
. : A BA B
P P
T T=: B
B
V V
T =
:
V V= :
V V
T =
.
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16. 3
2. .
5 - 21cm .
= 1
27 C -
=1
l 30cm .
=
P 1atm .
. .
.
=
2
127 C . 2
l
;
. .
i. .
ii. .
: 52
N1atm 10
m= .
:
. , F
F .
: F 0 W F F= + =
5
2
W N 1,5 10
A m= + =
. :
1 2 1 2 22 1
1 2 1 2 1
V V A A T40cm
T T T T
= = = =
.i. : 5atm 2
NP P 10
m= =
ii. F 0 5 2W N P 0,5 10A m
= =
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17. 3
3. 2g He
- . =
1P 0, 82atm
1V 20L .
. 1
T .
. e
, ,
=2 1
5T T
4.
He .
. He - .
.
: RL atm
R 0, 082mol K
= , He gM 4 mol= 5 21atm 10 N / m .:
mn 0,5 mol
M= =
. 1 11 1 1 1P V 0,82atm 20L
P V nRT T 400KL atmnR
0,082 0,5molmol K
= = = = . 1 1 1 1 1 1 1 1
2 2 2 2 2 12 1
P V n RT P V n RT
5P V n RT P 2Vn R T
4
= = = 1
2 1
2
4n1 8
n n 0,8mol2 5n 5 = = = 0,3mol He . 1,2g He
. : 3 323 3
2 1 11
P PP 0,82atm 4P 0,82atm P 0, 656atm
5T T T 5T
4
= = = =
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18. 3
4. ,
,
. = 3 3
AV 3 10 m
2mol
R
= 5A 2
NP 2 10
m.
= 3 3B
V 4 10 m 3
molR
= 5B 2NP 3 10 m .. .
.
= 52
NP 2, 25 10
m. -
.
: R 8, 314 S.I.
:
. :A A
A A A A AA
P V
P V n RT T 300Kn R
= = = : B B
B B B B B
B
P VP V n RT T 400K
n R
= = =. -
, , .
' ' A BA B A B A B
P V P Vn n n n n n
R T R T
+ = + + = +
( )( )
A B
A B
P V VT 315K
R n n
+= =+
5. 4mol
0P
0T .
0
2P . -
04T ,
0
4T .
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19. 3
. N mol -
-
04T .
.
= 01 VV10
= 0P P = 0T T ;:
. ( )0 0 0P V 4RT 1 x mol
( )x 4 x mol 02P , 0V , 04T :( ) ( )0 0 02P V 4 x R4T 2
(1), (2)
( )0 0 00 0 0P V 4RT
2P V 4 x R4T=
1 4 1 42 x 2
2 4 x 4 4 x
= = = x 4 2 2mol = =
. 0V
10 mol
1n :
1y n 2 mol= 1 2ny
= (y) 0V10
. -
: ( )00 1 0VP n RT 410
= (1) (5)
0
00
1
0 0 0
VP n RT10
P V 4RT= 0
0
2RT
1 2 4yy 5
10 4RT y 10 = = =
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20. 3
6. = 5 3V 10 m .
K 10J
3 0, 5kg / m .
. .
.
34 1 0 m / s
.
.
: R 8, 3 J / mol
4g/mol .
:
. 2 2 2
1 1K m m
K V2 2N mm N m 2
VV V
= = = == 22K
V= 2
2K
V = =
5
2 10 m / s
0,5 10
= 6 4 10 m / s= ( )3 2 10 m / s 1. :
2
r r
3RT 3RT
2 M= ( )T 4T 2 . Gay - Lussac ( )V 4V 2 .
Charles -
. :
4 2
2 2= = = V V 4V=
.
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21. 3
:
3
r
3RT 2 10 m / sM
= = ( )6r
3RT 4 10 S.I.M
= 6
r4 10 MT3 8,3
= 6 34 10 4 10
T K24,9
=3
16 10T K
24,9
= T 642,5K T 2 1285 =
7. =V 1L e = 6
2
NP 10
m.
= 3
m 2 10
s :
.
. mol
.
.
.
.
3
He
kgM 4 10
mol
= He .
:
. ( )6
2 2 3
223
1 1 3P 3 10P P kg / m
3 3 2 10
= = = = 6
3
6 3
3 10 kg kg / m 0,75
4 10 m
= =. 3 5
m m V m 0,75 1 10 kg m 75 10 kg
V
= = = =
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22. 3
52
3
r
m 75 10n n n 18,75 10 mol
M 4 10
= = = .
A A
3 3 R 3 N 3 3K k T R T nRT P V
2 2 N 2 N 2 2= = = = = = =
6 3 33 310 1 10 J 10 J 1500 J
2 2
= = =.
( )'
'r
r r
r
rr
3R 3R
23R
' 2 4:
3R 1 13R3R
= = = = ==
8. = 3n molR
( R
)
.
. -
.
.
. .
. -
-
.
: = 25 JR 3 mol K = gM 2
mol.
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23. 3
:
. - .
2 2m1 1
P P 3 3 V
= = .
y x .
m1
3 V= m1 .
3 V =
m . -
V . .
2
,
.
. :
5 52 6 2 2 2 6A 62 2 2
P 10 4 10 4 10 m / s 4 10 m / s
10
= = = =
( )3
m 2 10
s=
.5
2 3AA A 6 32
3P1 3 10 kgP kg / m 0,3
3 10 m
= = = =3 3
m 3 3n m n M m 2 10 kg m 2 10 kg
25M R
3
= = = =
3 3
O O
18m 10 kg m 0,72 10 kg
25
= = 3
3 3 3 A A A A
A A
m m 0,72 10 V V m V 2,4 10 m
V 0,3
= = = =
AV 2, 4 L
B AV V 2, 4 L=
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24. 3
. ( )2 2
B2 6B BB B
622A2
A
1 1K m
m K 4 102 2: 411 10K m K m 22
= = = = =
9. -
=AP 8atm , =AV 3 L =AT 300K . :
.
-
. -
. -
.
i. P, V,
T , .
ii. P V , P T V T .:
i. : , -
3
K kT2
= K , ()
: 3
K kT2
= K T O
m
V= m -
, .
: m
V
=
m
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25. 3
V
r
3RT
M=
,
: AP 8atm , AV 3 L , AT 300K
: :B A
P P 8atm=
( )B B BB A B BA A
A AA
3 3K k T k T
TK 2K2 2: T 2 300K 600K33 300K Kk TK k T
22
= = = = = = A B B
B
A B
V V V3LV 6 L
T T 300 600= = =
: BP 8atm , BV 6 L , BT 600K
: : B
T T 600K=O
B
B
B
m
V
m m m 1 2 2 V 2V 2 6L 12 L
V V V V V
2
= = = = = = = Boyle
B B
48P V P V 8 6atm P 12 P atm P 4atm
12 = = = =
:
P 4atm ,
V 12 L ,
T 600K
: :
V V 12 L=( )
( )( ) ( )
( )( )( )
r r r
r
rr
3R 3R
3R 600: 2
3R 3R3R
2
= = = = =
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26. 3
600 6004 K 150
4
= = =
4atm 600 atm 1atm
600 150 600= = = =
:
P 1atm ,
V 12 L ,
T 150K
ii.
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27. 4
1.4
n molR
= 2L 5 21 8 1 0 N / m . : -
, -
, -
.
.
P V , P T V T .
. :
i.
P P
= ii. V V = : R 8, 314 S.I.
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
2. 1200mL (He) 123 C .
o 10atm. mol ;
.
: 5 21atm 1,013 10 N / m , R 8, 314 ( S.I.) - He 4 g / mol .
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28. 4
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
3.
2
2V V 10 m= = -
2
1V 10 m= . -
-
. - ()
() , ,
2 . -
5 2
10 / m h 1m .
mol 1 22
n nR
= = R S.I. :
.
. ..
T 700 .
i. ;
ii. mol ;
( (ii) R).
............................................................................................................................
............................................................................................................................
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29. 4
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
4. .
. .
. B
V ,
V ,
.
. ,
V .
. -
3
kg0, 3
m, -
.
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
5. 4
n mol3
=
AV 6 L 5
A 2
N 2 10
m= . -
B
T 400K , -
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30. 4
-
.
. A
T ,B
V
.
. V , , V .
.
. :J
R 8, 31mol K
= ............................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
6. V 2L He 5
2
NP 2 10
m
=
3
kg 0, 2
m= . :
.
.
.
. .
:J
R 8, 31mol K
= , He grM 4 mol= 23A N 6 10 mol= ............................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
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31. 4
7. -
-
. 2
6g H
2
1,5molO .
T 350 K .
. 1
2
.
. 2
O 2
T 800 K
2
H 1
T -
. 1
T .
. 2
H
2
O .
:2H
grM 2
mol=
2O
grM 32
mol= .
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
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32. 5
1
.1. -
. :
.
.
.
.
2. -
. :
.
.
.
.
3.
:
.
.
.
.
4. :
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33. 5
. :
.
A A B BP V P V =
.
. -
.
. () mol.
. PV n R T= - .
( 25)
20
1. V
. V
2 2.
:
.
.
2.
. .
3. P V T . ;
( 25)
30
()
5 2
AP 10 N / m= AT 400K= .
3
kg 0,3
m= , :
.
.
. , -
.
: 265
m 10 kg3
= .
( 25)
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34. 5
40
-
.
AT 200K=
-
,
.
P V V T.
.
. .
( 25)
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-
:
[ -.
[ .[ .[ .[
.
[ T .
[ (W) (Q) (U) .
[ P-V .
[ -.
[ 1 .
[ .
[ .[ U 0 .[ .
taexeiola.blogspot.com
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36. - -
[ 2 .[ Carnot.[
, Carnot.
[ .[ (Q) (U)
.
[ 1 .[ .[ .
N : -
, ,
vnC 0 vnC
W
B A
A B
B A
nRTlnV /V
nRTln P / P
P V l n V / V0
pnC P V n R T = vnC
0 2 2 1 1P V P V
1
vnC
Q W 0
Q W U
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37. - -
1o /: Q WU+
-
.
2o /: Kelvin - Planck
-
.
Clausius
.
( )V 0> W 0> ( )V 0<
W 0< .
( )T 0> U 0> ( )T 0<
U 0< . Q 0> ,
Q 0< .
Q Q QWe 1
Q Q Q
= = =
Carnot c
h
QTT Q
=
c
h
Te 1
T= .
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38. 1
1 . .
. P
C V
C .
.
() .
.A
3 R 3 3U N K N T nRT PV
2 N 2 2
= = = =
. 1
:
P VQ W U n C T P V n C T= + = +
P Vn C T n R T n C T = +
P VC R C = +
.3 3
U nRT U nR 2 2= =
:VU nC = V
3C R
2=
,P V P
5C C R C R
2= + =
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39. 1
P
V
5R
c 52 3c 3
R2
= = =
2
V
W PV .
.
-
. x
: W F x= F P A= F . W P A x P V= = V .
* 3 c 2
h 1
Q
Q =
(. Boyle):1 1 2 2
P V P V =
(. Poisson): 2 2 3 3
P V P V =
(. Boyle): 3 3 4 4P V P V = (. Poisson):
4 4 1 1P V P V =
, :
( )
1 1 2 2 3 3 4 4 2 2 3 3 4 4 1 1
1 1 1 13 32 4 1 2
2 4 3 1
2 4 3 1 1 4
P V P V P V P V P V P V P V P V
V VV V V VV V V V 1
V V V V V V
=
= = =
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40. 1
: 2h 11
VQ nRT ln
V
=
: 4c 23
VQ nRT ln
V=
3c 2 4 3 c 2 3 4 c 2
4
3c 2
4
VQ nRT ln V ln V Q nRT ln V ln V Q nRT ln
V
VQ nRT ln
V
= = =
=
:( )
32 1
c c4 2
2h h 11
1
VnRT ln
Q QV
VQ Q nRT ln
V
= =
.
. : 2 2 1 1P V P V
W1
=
1 .. ( Q = 0 )
( ) 2 2 1 1v 2 1 vP V P V
W U nC T T W nCnR nR
= = =
( ) ( )v 2 2 1 1C
W P V P V 1R
=
( )v vpp v
v
C C 1 12
CR C C 11C
= = =
(1) (2) : ( ) 2 2 1 12 2 1 1P V P V1
W P V P V W 1 1
= =
.
. N.Poisson P, V, T.
i. : 1 1 2 2P V P V =
ii. V, T:
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41. 1
1 11 21 1 2 2 1 2 1 1 2 21 2
nRT nRTP V P V V V V V
V V
= = =
iii. P, T:
1 1 1 21 1 2 2 1 2 1 1 2 2
1 2
nRT nRTP V P V P P P P
P P
= = =
.
. ;
: ( )
( )Q 0= 10 . W U W 0 ,
U 0 .
-
-
, -
( ) .
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42. 2
. 2003.
.. 68 - 71: 2.10, 2.11, 2.13, 2.14, 2.15, 2.16, 2.17,
2.18, 2.19, 2.27, 2.28
. 76 - 79: 2.57, 2.60, 2.63, 2.64, 2.65, 2.66, 2.70,
2.71, , 2.72
.
.. 51 - 56: 2.3, 2.4, 2.5,
2.6, 2.7, 2.8
.. 68 -75: 2.9, 2.10, 2.11,
2.12, 2.13, 2.14
. 61: 1
. 69: 1.. 59 - 61: 2.3, 2.4, 2.5, 2.7, 2.8,
2.9, 2.10
.. 77, 78: 2.12, 2.14
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43. 3
1. .
-
.
.
:
:
U ( )
( ). W ( )
( ).
Q
(), ().
Q 1
( ).
:
U W Q
A BB
+ + +
- - -
+ - 0
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44. 3
2. -
1
W .
1
T
1
V . -
2
W
. 2
V . -
:
.
.
. .
P , V3
C R2
= .:
:
( )11 WP P 1A
= +
:
( )1 22 W W
P P 2A
+= +
: 1 1 2 2 2 2 12
1 2 1 1
P V P V P V TT
T T P V
= =
: V3
U nC nR2= =
( ) ( )1 1 1 1 2 2 12 1 1 2 2 1 11 1 1 1
P V P V P V T3 3 3U T T T P V P V
2 T 2 T P V 2
= = =
( )Q 0= W U=
( )2 2 1 13
W P V P V2
= 1P 2P (1) (2).
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45. 3
3. ( )0 0 0P , V , T - . -
,
.
. (P) -
(V).
.
.
. .
: n3 1,1:
.
.
0
AB 0 0 0 0 0 0 0
0
V
13W n R T ln P V ln P V ln 3 1,1 P VV 3
= = = =
0 0B 0 0 0 0 0
V 2VW 3P V 3P 2P V
3 3
= = =
W 0=
o AB 0 0W W W W 0,9 P V= + + =
. :
p 0 0 0 0 0 0
5 5 5 1Q n C n R T 3P V 3P V V 5P V
2 2 2 3
= = = = =
:
0 0
0 0
W 0,9P Ve 0,18 18%
Q 5P V
= = = =
P
3P0
P0
0 V /30 V0 V
A
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46. 3
4.
V
RC 3
2= ,
. A
V 2V ,
5
AU 4, 5 10 J 5
U 9 10 J ,
-V, P-V,
, ,
.
: R 8, 314 S.I.
:
, -V :
:
U 2 2
U = = = =
:
2 2
= = = =
-V :
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47. 3
:
B AP 2P P
AV B AV V AV 2V
AT 2 2=():
ABW 0
(): B B A
A
VW n R T ln 2n R T ln 2
V= =
(): ( ) ( ) A A A A A AW V V V 2V P V n R T = = = , : ( ) ( )o AB B AW W W W n R T 2ln 2 1 I+ + =
, ( ) V A U nC T T ( ) ( )5 5A A A A3R 3U U n T 2T 4,5 10 9 10 J n R T
2 2
= = 5
An R T 3 10 J = ., () : ( )5oW 3 10 2ln 2 1 J 5.
.
:V
C 3 R / 2
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48. 3
:
, C
h
Q 1Q
= ,
C Q Q Q= +
, h AB Q Q Q= + .
:
AB 2
2VQ nRT n 2nRT n2
V= =
( )B V VQ nC T 2T nC T= =
VQ nRT n nRT n 2
2V= =
( ) V VQ nC 2T T nC T= =
, ( )c V c VQ nC T nRT n 2 Q nT C R n 2= = +
( )h V h VQ 2nRT n 2 nC T Q nT 2R n 2 C= + = +
V
V V
C R n 2 R n 2 R n 2 n 2 1
3RC 2R n 2 C 2R n 2 1,5 2 n 22R n 22
+ = = = =
+ + + +
6. , 5
3
= , . -
6000J, -
:
.
.
. ,
100 / s.
:
.
:
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49. 3
( ) ( )0 0 0 00 0
5P P 2V VW 2P V
2
= = ( ) ( ) ( ) p A A 0 0 0 0 0 05 5 5Q nC T T nR T T P V 2P V P V
2 2 2= = = =
( )
0 0 0 0
2 6000 J2QP V P V 2400J
5 5
= = =, W 4800 J
. :
( ) ( ) ( )AB V B A B A 0 0 0 03 3U n C T T n R T T 5P V P V2 2
= = = =0 06P V 6 2400J 14400 J= =
( ) ( ) ( )B V 0 0 0 03 3U n C T T n R T T 2P V 5P V2 2
= = = =0 04, 5P V 4, 5 2400J 10800 J = =
.
.
5OW N W 100 4800 Watt 4,8 10 Wattt t
= = = =
7. Carnot 300
1200 4500 J. -
.
: :
2
1
1 1 0, 25 0,75
= = =
( ). hQ Q= :
h h
h
W W 4500J Q Q 6000 J
Q 0,75
= = = =
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50. 3
8. -
, .
ABQ 60 J :
.
;
. -
;
.
Carnot -
.
: VC 3 R / 2 , ln 2 0, 7 .
:
. P V P P
3 5C C R C R R C R
2 2= + = + = ,
P V n R = P V n R = .
AB
Q
:
( )AB P 0 0 0 0 0 05 5 5
Q n C n R 2P V 2P 2V V 5P V2 2 2
= = = = =
AB0 0
Q 60P V J 12 J
5 5 = = =
,( ) ( )0 0 0 0 0 02P P 2V V P V 12 JW 6 J
2 2 2
= = = = =
. A 0 0
V P V 2 V = = A T T= U 0= . 1 ..:
0 0
3Q W U W V 18J
2= + = = = =
. :
W 6 Je 0,1 10%
Q 60 J= = = =
Carnot :
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51. 3
0 0C A
2P VT T T
n R
= = =
0 0h B
4P VT T
n R
= =
0 0
CC
0 0h
2P VT 1 1n Re 1 1 1 50%
4P VT 2 2
n R
= = = = =
.
9. - (0 0
P , V ) -
(0 0
P / 2, 4V ) .
. -
(0 0
P , 2V )
(0 0
P /2, 4V ).
. - (
0 0P / 2,V )
(0 0
P / 2, 4V ).
. - .
.
.
:V
C 3 R / 2, ln 2 0,7= .:
.
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52. 3
. p V p p
3 5C C R C R R C R
2 2
= + = + = ,
P V n R = P V n R T = .
Q
:
( ) p 0 0 0 05 5 5
Q n C T n R P V P 2V V2 2 2
= = = = =
0 0 0 0
5P V 2,5 P V
2= =
Q :
0B 0 0
0
4VVQ W n R T ln P 2V ln
V 2V= = =
0 0 0 02 ln 2 P V 1, 4 P V= =
( 0 0
P V n R T P 2V n R T = = )
0 0 0 0 0 0
Q Q Q Q 2,5 P V 1, 4 P V 3,9 P V= + = + =
Q
:
0 V 0 0 0
P3 3 3Q U n C n R T P V P V
2 2 2 2
= = = = = =
00 0 0
P3 3V P V
2 2 4
= =
Q
:
( )0 0 p 0 0P P5 5 5Q n C n R V 4V V2 2 2 2 2
= = = = =
00 0 0
P5 153V P V
2 2 4= =
0 0 0 0 0 03 15
Q Q Q Q P V P V 3 P V4 4
= + = + =
Q Q> .
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53. 3
10. 2n molR
= ( )3A A AA P , V 2m , T 200K= -
- . B A
V 2V V
3RC
2= ( R 8, 314 S.I.)
. .
. P-V.
. AB
B
U
U .
. B -
214, 157 10 J ..
.
: n2 0, 7 .
:
. ,
, . -
U
. -
, = .
.
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54. 3
.( )( )
V B AAB
B V A B
nC T TU1
U nC T T
= = . : 5 2
A A A A
2R 200P V n R T P 2 10 N / m
R 2
= = = . Gay-Lussac :
A BB
A B
V VT 400K
T T= =
. Charles :5 2
10 N / m
= = .
B B
3K kT
2= , A A3K kT
2= B 21B B
A A
TKK 8,314 10 J
TK
= = .
c B
h B
Q Q Qe 1 1
Q Q
+= = ( )AB p B A 2 5Q nC T T R 200 1000 J
R 2= = =
( ) ( )B V 2 3Q nC T T R 200 400 600 JR 2
= = = A
A
VQ nRT n 400 n2 J 280 J
V= = = . 880Je 1 0,12 12%
1000J= =
11. - -
.
-
.
5
3
= 2 1
4 .
.
P-V ()
. :B
P 16P
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55. 3
. : ( ) ( ) 2.
.
: n2 0, 7 .
:
. -
. m
V
= m . - V . .
. .
:
R TP V n R T P
M
= =
.
:
. Boyle -
: ( )B 2 0 1P V P V 1= ( ) 1 0 2P V P V 2= . (1) (2) : ( )
2
1
2
V3
V
= .
2
2
m
V= 1
1
m
V= .
2 1 1 2
2 1
m m 4 4 V 4V
V V= = = (3) : B
16 P 16P
= =
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56. 3
. ( ) ( )20 2 1 43
= ( ) ( )20 1 1 53= . (4) (5) :
( ) ( )2 22 1 A 1 1
3 3
= ( ) ( ) ( ) ( )2 2 A 4 2 = .
2 =
1 = = ( ) ( ) ( ) ( ) .
: ( ) ( ) 2 .
. ( ) ( ) 2 ( )2 1 2 13kT 3kT1 T 4T 6m m= = .: ( )AB V 2 1 AB V 1Q n C T T Q 3n C T =
1 2B 2 1 1
2 2
V 4VQ n R T n 4nRT n 8nRT n2
V V = =
h AB B V 1 1
Q Q Q 3nC T 8nRT n2+ = + : ( ) V 1 2 V 1Q nC T T Q 3nC T =
2 2 1 1 1
1 2
V VQ n R T n nRT n 2nRT n2
V 4V = =
: C V 1 1Q Q Q 3nC T 2nRT n2+ = :
C V 1 1 V
h V 1 1 V
Q 3nC T 2nR T n2 3C 2R n 2e 1 1 1
Q 3nC T 8nR T n 2 3C 8R n2
+ + = = = + +
5
3
= V
3C R
2= :
33 R 2R n2
9 4 n2 12 n22e 1 1 0, 423 9 16 n2 9 16 n2
3 R 8R n22
+ + = = = + + +
p V
V V
C C R
C C
+= = =
V
R1
C+
V
R 1
C=
VC 1R 1=
V
R R 3C R
5 1 21
3
= = =
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57. 4
1. , 1 4 3 , -
143Q 100 J
143W 83,6 J . -
1 2 3 , 123
Q 110 J ;
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
2. -
. - ,
,
P V.
............................................................................................................................
............................................................................................................................
............................................................................................................................
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58. 4
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
3. -
Q 7/2 W.
.
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
4.
( )A A AA P , V , T ::
B AV 4V .
:
T 4 .
. : P V
. Q, U W.
A
P ,A
V 5
3
= .............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
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59. 4
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
5. 2R
mol He , -
A
V , A
P 2atm A
T 300K .
,
. R 8, 314 (S.I.) :
. P V .
. ,
, .
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
6. 2n75 R
= mol , - ,
AV 16 L ,
AP 0, 5atm -
A
T . ,
BV 2 L .
. .
. .
. P V .
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60. 4
.
.
:5
3
= R 8, 314 ( S.I.)...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
7. 1
V 10 L , -
.
, -
. .: n2 0, 7 ............................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
8.
,
.
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61. 4
4 , 2V
1T,
4 V. N
.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
9.3
Rmol -
-
.
. P T - .
. P, V
-
, AP 1atm 3
AV 0, 2m
. ,
. : R 8, 314 ( S.I.) P, V.......................................................................................................................................................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
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62. 4
10.
V 6 2
10
m= .
, :
. -
B A
V 4V ,
3
A BW 3 10 J = .. -
V
.
. .:
. () -
- ( P V ).
.
V .
.
/
.
. , -
-
e 0, 538 .
:p
5C R
2=
V
3C R
2= .
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
11.O 1e
2e . -
;
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63. 4
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
12. -
-
, -
.
-
1
T 600K
, -
. .
: n2 0, 7 5
3
= ............................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
13. .
: AB
TT
4=
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64. 4
:
T
:
. P V .
. V
3C R
2= , n2 0, 7 .
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
14.
AT 400K , 5 2
AP 4 10 N / m 3 3AV 10 m= . :
. ,
3 3BV 2 10 m= . ,
3 3
V 3, 2 10 m= 5 2
P 10 N / m .
. ()
P V .
. .
. .
.
.
:5
3
= V 3C R2
= ............................................................................................................................
.........................................................................................................................
.........................................................................................................................
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65. 4
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
15. -
:
. 1, 5 2
1P 3 10 N /m 3 31V 4 10 m= 2, 2 1V 3V ,. 2 3 ,
. 3 1T ,
1.
3
n molR
= , R - ( )J / m o l K , :.
- ( )P V ..
1 2
2 3
U
U
-
.
. Carnot
.
.
-
, -
3 1W 1318 Joule = .
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
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66. 5
1
.1. 5
3
=
Q 10J= . (W) - (U) :
. W 6J= , U 4J= ,. W 4J= , U 6J= ,. W 8J= , U 2J= ,
. W 5J= ,U 5J
= .2. :.
.
.
. .
3. :
. 2P V 3U =. 3P V 2U =
. P V U =. P V 3U =
4. 50%
Carnot ,
1e
4= ( ) -
:
. ch
T1
T= . c
h
T 1
T 4= . c
h
T 1
T 2= . c
h
T 1
T 3=
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67. 5
5.
.
( 25) 20
. P VC C R= + , P
5C R
2= ,
V
3C R
2=
5
3= .
. Carnot - -
.
. P V , V T .
( 25) 30
.
:
:
:
W 300J=
W 200J= . :
. 1. U W=
. 2. Q U W= +
. 3. Q U=
. 4. Q W=.
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68. 5
. AB
Q . W . AB
A
U
U
.
( 25)
40
( )5 3 32A ANP 4 10 , V 5 10 mm= =
:
: ( )B AP 2P=:
: .
: n2 0, 7= 5
3
=
. P-V.
. , -
, , .
.
.. .
( 25)
taexeiola.blogspot.com
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-
:
[ Coulomb.
[ - .
[ .
[ .
[ , .( Q q 0 U 0, Q q 0 U 0 > > < < ).
[ .[
.
[ .[ -
.... ( .).
[
.
[ .
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70. -
[ g - .
[ .
: -
1 2c
Q QU Kr
=
:
Q
CV
= 0
SC =
S, -
.
V
E =
21U CV
2=
.
xx yy
xF 0= yF E q=
x 0= yE q
m
=
x 0 = y y t=
0x t= 2
y
1y t
2=
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71. 1
1 - .
q AV , -
V , ( )A A A W q V q V V = =
A W 0 > .
A W 0 <
.
2
.
+q -
-
. ,
( )F E q 1= .
-
( )W F L 2= .
(1) (2) ( )W E q L 3= .
( )W q V 4=
(3), (4) E q L q V = , V
E
L
=
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72. 1
3
-
, .
(-
) ()
, :
, ,E + =
-
. :
1 :
. -
.
2 : - -
.
.
Q
. :
. ,
.
.
. 1
:
A,B B, ,U U U U= + +
.U = A B B AQ Q Q Q Q Qk k k
+ +
.U =
2Q
3k
.
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73. 1
2
Q .
Q -
:2
1 B B
Q QW W W Q.k k
= = = =
Q .
2 W W W Q V = = = .
B
Q Q QV V V k k 2k
= + = + = . :
2
2
QW W 2k
= = .
:2 2 2
1 2Q Q QW W W k 2k 3k
= + = + =
:2
.
QU 3k
= .
:
.
. , , , E U U+ = + =
2 2
Q Q0 3k 3k + = =
4 -
.
i.
E : q
m
= , 0 t ,
2
0
1
y t t2= ii. -
ii. m +q
V0
0. -
.
L.
taexeiola.blogspot.com
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74. 1
d V.
. 0
.
. -
. -
.
. .
. .
. - -
.
. -
.
. S .. .
.
:
i. ,
ii. y
iii. Vy,
.
.
.
.
:
. .
= W K
-
= qV0 201 m
2 - 0 = qV
0 00 2qV
m=
.
.
.
xx 0
-
yy
taexeiola.blogspot.com
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75. 1
. xx x L .
( ) ( )0 0
L2 L t t 4
= =
. x y.
(2) (1) .
( )0
x2 t
= ( ) 2 22 2
0 0
1 x 1 y y x
2 2 = = 2
2
0
1 qV xy
2 md =
. (1) (4) 0
Lt t
= = :
( )22 20
1 1 qV Ly t y 5
2 2 md = = (5)
2
2
0
1 qV Lx L y
2 md = =
.y
y, o
V
E V yy= = (5)
( )2 2 2y, y, 2 2 20 0
V 1 qV L qV LV V 6
d 2 md 2md = =
. S
. :
2 2 2 2 2
S L y S L y+ + (5) 2 2 42 2 2 40
q V LS L
4m d = + .
xx yy
xF 0= yF E q=
x 0= yE q qV
m md
= =
x 0 = ( )y y t 3=
( )0x t 2= ( )2
y
1y t 1
2=
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76. 1
. x 0 y o y
0
qV L t
md
= = . :
y 0
2
x 0 0
qVL
md qVL
md= = = .
. i..2 2 2
2 2 2 2 2 2x y 0 0 2 2 2
0
q V L t
m d = + + = + .
ii. -
.
2 2
o 0 o
1 1 W K F y m m qEy
2 2= = =
2 2 2 2
0 o 0
V qVm m 2q y 2 y
d md = = 20 2qV y
md= +
iii. -
.
o y W K q V =
2 2 2 20 y, y,
1 1m m qV m m 2qV
2 2 = =
0
y, y, 2 2 20 0
2qV 2qV
m m = = +
.
0 0
P L V LF P Ft P qE P q
t d
= = = =
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77. 3
.
2003.
.. 126 - 127: 3.17, 3.18, 3.19, 3.20, 3.21, 3.22
. 138: 3.90, 3.91, 3.92, 3.93
. 139: 3.94, 3.95, 3.97
. 140: 3.98, 3.99, 3.100
.
.. 89 - 102: 3.1, 3.2, 3.3,
3.4, 3.6, 3.7, 3.9, 3.10, 3.12
. 109: 1 (
:
2
c
20
K qx
6m
= )
.. 105 - 108: 3.2, 3.4, 3.5, 3.6,
3.10, 3.12
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78. 2
1. 0,36cm -
Q, 2Q, Q 2Q Q 2C .
.
.
. Q -
. m 2g ,
.
: 9cK 9 10 ( SI). .:.
3AB B 3,6 10 m
= = = = 3A B 2 3,6 2 10 m= = = . :
2 2
c c c
Q 2Q Q 4QU 4 K
2 2
= + +
2 2 2 9 12c c c
3
8K Q 5K Q K Q 5 9 10 4 10 5U 8 8 J
2 2 3, 6 10 2
= + = + = +
510 8 J
2= +
. ,
.
..: ( ) ( )2 2 2
2 c c c
2Q 2Q 2Q 1U K m
2 2
= + + =
22 c2K Q 2
4
m 2
= +
100 4 2 / 2m / s 217m / s = +
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79. 3
2. Q 20C
q 1C m 4g . U 3,6 J .
. .
. q . -
-
.
. q.
: 9cK 9 10 ( SI):
. 9 6 6
2cc
K QqQq 9 10 20 10 10U K r m 5 10 m
r U 3, 6
= = = =
. q
Coulomb.
. ,
( ) .
r 2r: 2
1E U U m
2
= = +
2 cc c
K QqQq Qq 1K K m 30m / s
r 2r 2 mr = + = =
. . r :
2c c
K Qq 2K Qq1 m 30 2 m / s
r 2 mr= = = = .
3. = 91q 10 C = 92q 4 10 C =r 20cm .
1q 2q , -
22 2 10 m / s= . 1q - 2q ,
21 6 10 m / s= .
.
. ;
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80. 3
. 1m , 2m ;
. ;
:
. :
9 991 2
c 1
q q 10 4 10U K 9 10 J
r 2 10
= =
8U 18 10 J=
.1.
I IIE E= 2 c 1 21 2
c 2 2 2 22
2K q qq q 1K m m
r 2 r
= =
84
2 4
36 10m kg 9 10 kg
4 10
= =
.
.2.
V
21 2III IV c 1 1
q q 1E E K m
r 2
= =
( )
8 84c 1 2
1 12 2 42
1
2K q q 2 18 10 36 10m kg kg m 10 kg
r 36 106 10
= = = =
.
. ( ).
..: 1 1 2 2P P 0 m m
= =
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81. 3
( )21 2 1 21
m 9 1
m
= =
..:( )1
2 21 2 c 1 1 2 2
q q 1 1E E K m m
r 2 2
= = +
2 21 2c 1 2 2 2
q q 1 1K m 81 m
r 2 2
= +
21m
m9
= 2 21 2c 2 2 2 2q q 1 1
K m 9 m r 2 2
= +
2 c 1 21 2c 2 2 2
2
K q qq q 1K 5m
r 5m r
= =
9 182
2 4 1
9 10 4 10 m / s 0,4 10 m / s
5 9 10 2 10
= =
(1): 21 9 0,4 10 m / s=
4. = 8m =Q 2C M 200 g . Q q 1mC =m 20g - 0 5m / s .
. h
q.
. q
Q .
.
:2g 10m / s
29
c 2
N mK 9 10
C
= :
. q ,
( ). q () () :
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82. 3
2, , , c 0 c
Qq 1 QqU U U K m mgh
2 h
+ = + + = +
h <
9 6 339 10 2 10 10 1 1820 10 25 0, 2h
8 2 8 h
+ = +
(h m)
2 20m . 20 m 8m2h 41h 20 0 h
0,5m
> = + = =
. () Q q
( ) c 2 2
Q q 18F N
7,5h
= =
B Mg 2N= = .
B F> Q , . q -
x
F B= ( ) : cc 2K QqQq
K Mg x 3mMgx
= = =
Q () (): , , , , U U U U + = + +
( )2
c c max
Qq Qq 1
K Mg K Mg h x Mh x 2 + = + + +
21816 6 2 3,5 0,1
7,5 + = + + 25,4 0,1 54 m / s 3 6 m / s = = =
5. o30
= 4Q 2 10 C . =h 6m Q
= 4q 10 C =m 50g 0 40m /s . - .
2g 10m / s
9cK 9 10 (SI).
:
, q
. q -
, r Q.
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83. 3
2h 30= .
K U U U U+ + = +
2 c c0
K Qq K Qq1 rm mgh mg
2 2h 2 r + + = +
r 18040 15 3
4 r + + = + (r m)
2 228,85mr 232r 720 0 r
3,15m
+ = =
m inr 3,15 m= maxr 228,85m= .
6. A =d 10cm =V 100Volt ,
=q 5C .
. ;
. ;.
0 .
. 0 ;
. ;
: 11m 10 kg= .:
. ... :
2
1
V 10 VE
d m10= = 3E 10 V / m=
63 2
11
F q E 5 10 10 m / s
m m 10
= = = 8 2 5 10 m /s=
g .
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84. 3
. .
12
8
1 2d 2 10d t t s2 5 10
= = = =
104 10 s 5t 2 10 s=
.
.
. 0 t= 00 t= 0 t= 0t
=
2 22 0 0
0
1d t t d
2 2= =
20
0
d 2 d
2= = 8 1 40 25 10 10 m / s 10 m / s= =
4
50
8
10t s 210 s
510= = = .
. :
20
1y 0 t t 0
2= = 02t
=
0 t= 0 = - ( ).
7. 19q 1, 6 10 C= 31m 9 10 kg= -
=L 10 cm = 4 NE 10C
. =S 10 cm - . 0
0 2 . -
. :
.
. ,
. ,
. .
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85. 3
:
.. .
:
. 0 2= 0 0
0
2
2 2= = = . 45= .
.. :
0 0
x L Lt
x t
= ==
y 7
2 020 0 00
qt E q L E q L q Lm 445 1 10 m / s
m m 3m
45 1
= = = = = = =
xx yy
xF 0= yF E q=
x 0= yE q
m
=
x 0 = y y t=
0x t= 2
y
1y t
2=
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86. 3
8
0
L 3t 10 s
4
= = 2 2yE q1 1
t t 0, 05m2 2 m
= = = .
..
V V= (
AEV 0= ) A
V V V E 500V
= = = =
. ... A : W =
( ) ( )19A q V 1,6 10 C 500V= = 17 8 10 J=
. 2 15
F t E q 1,6 10 N
tF E q
= = = =
15 8 233 E q t 1,6 10 N 10 s 1, 2 10 N s
4
= = =
. S 10cm= = = .
ZH 5cm= = H 15cm= + = .
8. m 20 kg 10C -
2
T 10 ,
-
. -
..
( )77
10 t S.I. 0 t 2s
2 10 N / C t 2s
= >. ;
. -
0 t 4s. 2s;
. 2s 4s. .
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87. 3
:
. .
e F T q E T
5 7 210 10 t 10 t 1s .
.
:
5 7F qE 10 10 t
m m 2 10
= = =
5t= 1 t 2s .
t 1s= t 2s= -
25 m / s 210m/s .
210m/s .
. -
t 1= t 2= ( ).
5 10 1m / s 7,5m / s
2
+= =
0
7,5 m / s 7,5 m / s = = .
. 2 sec -
t 2s= ( 2 4 sec)
20
1x t t
2= + 21x 7,5 2 10 2 m x 35m
2
= + =
.
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88. 4
1. , 0, 1m ,
9Aq 1 10 C= 9q 2 10 C= . -:
. -
.
.
.
: 9 2 2cK 9 10 N m / C .............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
2.
0 m +q.
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89. 4
+Q.
, :
.
. .
cK
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
3. ... - . -
0 50m / s m 6g q 1,5C . t 4s .
... : 2g 10m / s .
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
4. 4cm .
4
m 2 10 kg=
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90. 4
7q 2 10 C= .. -
.
.
;
. -
; : 2g 10m / s .
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
5. 24 10 g q 20C
0 100m / s -
-
-
-
d 5cm -
12,5kV . -
h 4, 5 cm -
. L 8cm b 10 cm
-
. :
. t 0, 2ms
.
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91. 4
.
.
. .
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
6. q 1C
r 1m
Q 100C .
5E 4 10 N / C .
q .
. .
. Q q
; ;
. .
: 9cK 9 10 ( S.I.)............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
............................................................................................................................
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92. 5
1
.1. -
. :
. .
. .
. .
. .
2. 1Q+ 2Q+ -
r. 1Q 2Q
:
. .
. .
. .
. .
3. -
0 . :
. 0 .
. 0 .. -
0 .
4.
U 20J= . - :
. U 40J= .. U 10J= .
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93. 5
. U 10J= ,
. U 40J= .. .
. -
, -
, . ( )
.
. ( )
.
, , -
. ( )
.
-
. ( )
( 25)
20
1.
, .
: p eq q= , p em m>
. -
p e.
. ;
. .
.
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94. 5
2.. m q -
.
;
. ,
. ,
.
. .
3.
45
-.
F.
( 25) 30
0 200m / s
= . - 14t 10 s
= .
E=100N C . :
. .
. q
m .
.
.
( 25)
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95. 5
40
6m 10 kg= 6q 10 C= -
0V =200V .
-
. -
1 8cm= .
V=100V 20cm= d 40cm= , : ( )
. .. .
. ,
.
. -
.
( 25)
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:
[ Lorentz. - .
[ .
[ Lorentz 0 0 180 .
[
, , -
T.
[ -
.
[ 90= - -
t
s N 2R , tNT
= - ( ).
[
:
, -
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98. -
: -
[ .
[ ,
LF
. 2
R
= .
[ LF -
.
Lorentz, :
LF B q =
A ,
:m
R q
=
: 2mTB q
=
,( ),
= :m
Rq
=
: =
Lorentz . Lorentz
.
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99. 1
1 . K
.
. -
. q Lorentz
-
.
, -
:
2
L KENTm mF F Bq R
R qB= = =
m2
2R 2mqBT
qB= = = .
-
.
. +q
.
.
:
, x .
:
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100. 1
( )x 1=
( ) 2=
x
Lorentz x
.
Lorentz :L F q q= =
(
FL
)
R :
( )m m
R 3q B q B
= =
,
, ,
.
R
.
,
x,
,
.
( )
( )1
x T 4= =
:2m
Tq B
=
(4) :2m
q
=
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101. 2
.
2003.
.. 171 - 173: 4.14, 4.15, 4.17, 4.18, 4.22, 4.23, 4.24,
4.25, 4.26, 4.27
. 176: 4.46, 4.47, 4.48
. 179: 4.59, 4.60, 4.64
.
.. 116 - 124: 4.2, 4.3, 4.6,
4.7, 4.9,
. 128: 4.2, 4.5
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102. 3
1. 191, 6 10 C 319 10 kg
= 3B 2 10 T 26p 28, 8 10 kg m / s= . :
.
. -
. -
.
.
:
. ... -