Fisiki katefthinsis g Lykeiou

7/29/2019 Fisiki katefthinsis g Lykeiou

1/144

-

:

[ .

[ .

[ .[ ,

, .

[ (mol), (), Avogadro ( ) .

[ T Kelvin K.[

.

[ P -V, P-T, V-T.[ (, , -

).

[ -

L atmR 0, 082

mol K

= J

R 8, 314mol K

= .[ .

taexeiola.blogspot.com


2/144

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

=



3/144

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)



4/144

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



5/144

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= =



6/144

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



7/144

15. 3

1. .

. .

. .

. P V P T .:

. :

: ()

:

: ()

. : A BA B

P P

T T=: B

B

V V

T =

:

V V= :

V V

T =

.



8/144

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

= =



9/144

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

= = = =



10/144

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 .



11/144

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 = = =



12/144

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=

.



13/144

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

= = = =



14/144

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.



15/144

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=



16/144

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



17/144

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

= = = = =



18/144

26. 3

600 6004 K 150

4

= = =

4atm 600 atm 1atm

600 150 600= = = =

:

P 1atm ,

V 12 L ,

T 150K

ii.



19/144

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 .



20/144

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).

............................................................................................................................

............................................................................................................................



21/144

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 , -



22/144

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= ............................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................



23/144

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= .

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................



24/144

32. 5

1

.1. -

. :

.

.

.

.

2. -

. :

.

.

.

.

3.

:

.

.

.

.

4. :



25/144

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)



26/144

34. 5

40

-

.

AT 200K=

-

,

.

P V V T.

.

. .

( 25)



27/144

-

:

[ -.

[ .[ .[ .[

.

[ T .

[ (W) (Q) (U) .

[ P-V .

[ -.

[ 1 .

[ .

[ .[ U 0 .[ .



28/144

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



29/144

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= .



30/144

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= + =



31/144

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

=

= = =



32/144

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:



33/144

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 .

-

-

, -

( ) .



34/144

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



35/144

43. 3

1. .

-

.

.

:

:

U ( )

( ). W ( )

( ).

Q

(), ().

Q 1

( ).

:

U W Q

A BB

+ + +

- - -

+ - 0



36/144

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).



37/144

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



38/144

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 :



39/144

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



40/144

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.

:

.

:



41/144

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

= = = =



42/144

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 :



43/144

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= .:

.



44/144

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> .



45/144

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

. -

, = .

.



46/144

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



47/144

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

= =



48/144

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

= = =



49/144

57. 4

1. , 1 4 3 , -

143Q 100 J

143W 83,6 J . -

1 2 3 , 123

Q 110 J ;

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

2. -

. - ,

,

P V.

............................................................................................................................

............................................................................................................................

............................................................................................................................



50/144

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

= .............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................



51/144

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 .



52/144

60. 4

.

.

:5

3

= R 8, 314 ( S.I.)...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

7. 1

V 10 L , -

.

, -

. .: n2 0, 7 ............................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

8.

,

.



53/144

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.......................................................................................................................................................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................



54/144

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 . -

;



55/144

63. 4

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

12. -

-

, -

.

-

1

T 600K

, -

. .

: n2 0, 7 5

3

= ............................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

13. .

: AB

TT

4=



56/144

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

= ............................................................................................................................

.........................................................................................................................

.........................................................................................................................



57/144

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 = .

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................



58/144

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=



59/144

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=.



60/144

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)



61/144

-

:

[ Coulomb.

[ - .

[ .

[ .

[ , .( Q q 0 U 0, Q q 0 U 0 > > < < ).

[ .[

.

[ .[ -

.... ( .).

[

.

[ .



62/144

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=



63/144

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

=



64/144

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

.



65/144

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.



66/144

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



67/144

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=



68/144

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

= = = =



69/144

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



70/144

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 = +



71/144

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= .

.

. ;



72/144

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

= =



73/144

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 () () :



74/144

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.



75/144

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 .



76/144

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 . -

. :

.

. ,

. ,

. .



77/144

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=



78/144

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. .



79/144

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

= + =

.



80/144

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.



81/144

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=



82/144

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

.



83/144

91. 4

.

.

. .

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

6. q 1C

r 1m

Q 100C .

5E 4 10 N / C .

q .

. .

. Q q

; ;

. .

: 9cK 9 10 ( S.I.)............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................



84/144

92. 5

1

.1. -

. :

. .

. .

. .

. .

2. 1Q+ 2Q+ -

r. 1Q 2Q

:

. .

. .

. .

. .

3. -

0 . :

. 0 .

. 0 .. -

0 .

4.

U 20J= . - :

. U 40J= .. U 10J= .



85/144

93. 5

. U 10J= ,

. U 40J= .. .

. -

, -

, . ( )

.

. ( )

.

, , -

. ( )

.

-

. ( )

( 25)

20

1.

, .

: p eq q= , p em m>

. -

p e.

. ;

. .

.



86/144

94. 5

2.. m q -

.

;

. ,

. ,

.

. .

3.

45

-.

F.

( 25) 30

0 200m / s

= . - 14t 10 s

= .

E=100N C . :

. .

. q

m .

.

.

( 25)



87/144

95. 5

40

6m 10 kg= 6q 10 C= -

0V =200V .

-

. -

1 8cm= .

V=100V 20cm= d 40cm= , : ( )

. .. .

. ,

.

. -

.

( 25)



88/144



89/144

:

[ Lorentz. - .

[ .

[ Lorentz 0 0 180 .

[

, , -

T.

[ -

.

[ 90= - -

t

s N 2R , tNT

= - ( ).

[

:

, -



90/144

98. -

: -

[ .

[ ,

LF

. 2

R

= .

[ LF -

.

Lorentz, :

LF B q =

A ,

:m

R q

=

: 2mTB q

=

,( ),

= :m

Rq

=

: =

Lorentz . Lorentz

.



91/144

99. 1

1 . K

.

. -

. q Lorentz

-

.

, -

:

2

L KENTm mF F Bq R

R qB= = =

m2

2R 2mqBT

qB= = = .

-

.

. +q

.

.

:

, x .

:



92/144

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

=



93/144

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



94/144

102. 3

1. 191, 6 10 C 319 10 kg

= 3B 2 10 T 26p 28, 8 10 kg m / s= . :

.

. -

. -

.

.

:

. ... -

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