ÿþK a r t a w y b r a n y c h w z o r ó w i s t a "y c h f i z y c z n y c h
1
T e r m o d y n a m i k a F i z y k a w s p ó Bc z e s n a N i e k t ó r e s t a Be f i z y c z n e
2
m 0 c
2 m m
F
c i Ê n i e n i e p r z y s p i e s z e n i e z i e m s k i e g . 9 , 8 1 . 1 0
p = E = m c =
S 2 s 2 s 2
r ó w n o w a Ýn o Ê ç m a s y e n e r g i i
v
1 -
2
c
2 4
m
m a s a Z i e m i
g ´ s t o Ê ç t = M Z = 5 , 9 8 $ 1 0 k g
V
m 0 v
p =
2
p ´ d r e l a t y w i s t y c z n y
v
1 - p r o m i e ’ Z i e m i R Z = 6 3 7 0 k m
c i e p Bo Q = m c ” T 2
w
c
m 2
N $
Q = m L ”t '
s t a Ba g r a w i t a c j i G = 6 , 6 7 $ 1 0 - 1 1
” t =
c i e p Bo w p r z e m i a n i e f a z o w e j
d y l a t a c j a c z a s u k g 2
2
Q = m R
v
1 -
2
c
p V
Ba d u n e k e l e k t r o n u e = 1 , 6 $ 1 0 - 1 9 C
r ó w n a n i e s t a n u g a z u = c o n s t
T
e n e r g i a f o t o n u
E = h o
j e d n o s t k a m a s y
u = 1 , 6 6 $ 1 0 - 2 7 k g
a t o m o w e j
r ó w n a n i e C l a p e y r o n a p V = n R T
h
p ´ d f o t o n u
p =
m
m a s a e l e k t r o n u
m e = 9 1 1 $ 1 0 - 3 1 k g
,
c i e p Bo m o l o w e C = C V + R
p
f a l a d e B r o g l i e a h
m =
p
m a s a p r o t o n u m = 1 , 6 7 2 6 $ 1 0 - 2 7 k g
p
I z a s a d a t e r m o d y n a m i k i ” U = Q + W
h
z a s a d a n i e o z n a c z o n o Ê c i
” p x ” x H
4 r
m a s a n e u t r o n u
m n = 1 , 6 7 4 9 $ 1 0 - 2 7 k g
p r a c a ( p = c o n s t )
W = - p ” V
2
e f e k t f o t o e l e k t r y c z n y m v
p r z e n i k a l n o Ê ç
h o = W + e o
8 , 8 5 $ 1 0 - 1 2 C 2
2 f 0 =
W
e l e k t r y c z n a p r ó Ýn i
u Ý
m a x N $ m 2
h =
Q
w B
s p r a w n o Ê ç
t p r z e n i k a l n o Ê ç
r o z p a d p r o m i e n i o t w ó r c z y -
n 0 = 4 À $ 1 0 - 7 N
1
T
Q - Q N = N 0 $ 2 m a g n e t y c z n a p r ó Ýn i
2 A 2
1 2
h =
Q 1
s t a Ba P l a n c k a
h = 6 , 6 3 $ 1 0 - 3 4 J $ s
T - T
H y d r o s t a t y k a
1 2
h =
s p r a w n o Ê ç s i l n i k a C a r n o t a
T
1
s t a Ba R y d b e r g a
R = 1 , 0 9 7 $ 1 0 7 1
m
s i Ba p a r c i a F = p S
s t a Ba p r z e s u n i ´ ç
O p t y k a C = 2 , 9 0 $ 1 0 - 3 m $ K
W i e n a
p = t g h
c i Ê n i e n i e h y d r o s t a t y c z n e
r ó w n a n i e s o c z e w k i
1 1 1
= +
= 6 , 0 2 $ 1 0 2 3 1
x y l i c z b a A v o g a d r a N
z w i e r c i a d Ba f A
m o l
s i Ba w y p o r u F = t g V
w y p
n
1 s o c z 1 1
o b j ´ t o Ê ç 1 m o l a g a z u d m 3
s o c z e w k a
= - 1 + n
e o d
2 2 , 4 1
n
f R 1 R 2
o t o c z w w a r u n k a c h n o r m a l n y c h
m o l
A s t r o n o m i a
R
z w i e r c i a d Bo
f = s t a Ba B o l t z m a n n a k = 1 , 3 8 $ 1 0 - 2 3 J
2
2 K
T
= c o n s t
I I I p r a w o K e p l e r a
3
R Ê r
J
1
z d o l n o Ê ç s k u p i a j à c a R = 8 , 3
s t a Ba g a z o w a
Z =
m o l $ K
f
A t o m w o d o r u p r ´ d k o Ê ç Ê w i a t Ba
1
k à t g r a n i c z n y c = 2 , 9 9 7 9 3 $ 1 0 8 m
s i n a =
s
g r n w p r ó Ýn i
4
m e
e n e r g i a a t o m u w o d o r u e 1
p r ´ d k o Ê ç d ê w i ´ k u
E = - $ m
2 2 2
n
3 4 0
k à t B r e w s t e r a ( m o d e l B o h r a )
t g a B = n
8 f 0 h n w p o w i e t r z u s
A l f a b e t g r e c k i
A a a l p h a E f e p s i l o n I k i o t a N o n i Q t r h o U { p h i
B b b e t a F g d z e t a J l k a p p a N p k s i R v s i g m a X | c h i
C c g a m m a H h e t a K m l a m b d a O o o m i k r o n S x t a u W } p s i
D d d e l t a H i t h e t a M n m i P r p i T y y p s i l o n X ~ o m e g a
P r z e d r o s t k i
9 6 3 2 1 - 1 - 2 - 3 - 6 - 9 - 1 2
M n o Ýn i k
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
P r z e d r o s t e k g i g a m e g a k i l o h e k t o d e k a d e c y c e n t y m i l i m i k r o n a n o p i k o
O z n a c z e n i e G M k h d a d c m ¼ n p
K a r t a w y b r a n y c h w z o r ó w i s t a "y c h f i z y c z n y c h
2
R u c h p r o s t o l i n i o w y G r a w i t a c j a P r ´ d s t a By
m 1 m 2
” Q
F = G
p r ´ d k o Ê ç n a t ´ Ýe n i e p r à d u s t a Be g o
2 I =
v ^ t h = v 0 + a t s i Ba g
” t
r
2 "
a t F
n a t ´ Ýe n i e p o l a " g p r a w o O h m a
d r o g a s ^ t h = v 0 t + U = R I
c =
2
m
n
" m 1 m 2
"
Bà c z e n i e o p o r ó w
" ”v F R Z = R i
E = - G , !
e n e r g i a
p r z y s p i e s z e n i e a = , " = p o t r
a
m s z e r e g o w e
i = 1
” t
p o t e n c j a l n a
( d l a h <
< R Z )
E = m g h
n
p o t
1 1
Bà c z e n i e o p o r ó w
" "
!
p = m v
p ´ d R Z = R i
i = 1
G M Z k m r ó w n o l e g Be
p i e r w s z a p r ´ d k o Ê ç
v = . 7 , 9
I
k o s m i c z n a R Z s
l
F T = n F N o p ó r R = t
s i Ba t a r c i a
S
d r u g a p r ´ d k o Ê ç
2 G M Z k m
v = . 1 1 , 2
k o s m i c z n a I I f
"
p r a w o O h m a d l a o b w o d u
R Z s
I =
d
s
p r a c a W = F s c o s ] F , " n
R + R
z w
2
m o c
m v
P = I U
e n e r g i a k i n e t y c z n a E k i n =
F a l e
2
v
”W
d Bu g o Ê ç m = v T =
m o c
P = P r à d p r z e m i e n n y
f
” t
v 1 s i n a n 2
f = n B S ~ s i n ~ t
z a Ba m a n i e f a l i
v 2 = = n 1 = n 2 , 1 S E M p r à d n i c a
s i n b
R u c h p o o k r ´ g u
U
m a x
U =
n a p i ´ c i e s k u t e c z n e
s i a t k a d y f r a k c y j n a n m = d s i n a
1 s k
f = 2
c z ´ t o t l i w o Ê ç
T
I
m a x
I
I =
L = 1 0 l o g n a t ´ Ýe n i e s k u t e c z n e
s k
”a 2 r I 0
2
p r ´ d k o Ê ç k à t o w a ~ = = = 2 r f
” t T
p o z i o m n a t ´ Ýe n i a U 1 n 1 I 2
- 1 2
W t r a n s f o r m a t o r
d ê w i ´ k u
n 2
2
I 0 = 1 0 U 2 = = I 1
2
v
p r z y s p i e s z e n i e d o Ê r o d k o w e m
a d =
r
v
! u o b o p ó r i n d u k c y j n y R L = ~ L = 2 r f L
2
e f e k t D o p p l e r a
=
m v f f ê r v " u ê r
s i Ba d o Ê r o d k o w a
F d =
r
1
1
o p ó r p o j e m n o Ê c i o w y
R C = =
~ C 2 r f C
1
R u c h o b r o t o w y E l e k t r o s t a t y k a c z ´ s t o t l i w o Ê ç r e z o n a n s o w a
f =
o b w o d u L C 2 r L C
q 1 q 2 1
p r ´ d k o Ê ç k à t o w a ~ ^ t h = ~ 0 + f t 2
p r a w o C o u l o m b a F = k , k =
2 2
1
4 r f 0 z a w a d a
r Z = R + ~ L - l
b
~ C
2
"
f t "
F U
k à t n a t ´ Ýe n i e p o l a
a ^ t h = ~ 0 t +
E = , E =
=
2 q
d
P o l e m a g n e t y c z n e
"
" n e n e r g i a p o t e n c j a l n a E = k q 1 q 2
m o m e n t s i By d
M = F r s i n ] F , r
p o t r "
"
d n
F = q v B s i n ] v , B
s i Ba L o r e n t z a
E
M p o t
p o t e n c j a B e l e k t r o s t a t y c z n y
p r z y s p i e s z e n i e k à t o w e
f = V =
" "
q
I
e o
F = B I l s i n ] l , B
s i Ba e l e k t r o d y n a m i c z n a
2 Q
p o j e m n o Ê ç
I ~ C =
E k i n = U " " n
e n e r g i a k i n e t y c z n a
2 d
U = B S c o s ] B , S
s t r u m i e ’ p o l a
S
k o n d e n s a t o r p Ba s k i
C = f 0 f d
r
n 0 n r I
p r z e w ó d p r o s t o l i n i o w y B =
R u c h d r g a j à c y
2 r r
2
C U
e n e r g i a k o n d e n s a t o r a
W =
n 0 n r I
2
x ^ t h = A s i n ^ ~ t + { h
w y c h y l e n i e p o j e d y n c z y z w ó j
B =
2 r
n
1 1
Bà c z e n i e k o n d e n s a t o r ó w
=
= !
C C i I
s z e r e g o w e
z i = 1
B = n 0 n r n
p r ´ d k o Ê ç v ^ t h = A ~ c o s ^ ~ t + { h z w o j n i c a
x l
n
Bà c z e n i e k o n d e n s a t o r ó w
s i Ba w z a j e m n e g o
C = C i
!
2 n 0 n r I 1 I 2 l
z
r ó w n o l e g Be
o d d z i a By w a n i a
p r z y s p i e s z e n i e a ^ t h = - A ~ s i n ^ ~ t + { h i = 1
F =
x
m i ´ d z y p r z e w o d a m i 2 r r
2
”U
s i Ba F ^ t h = - m A ~ s i n ^ ~ t + { h f = -
S E M i n d u k c j i
x S p r ´ Ýy s t o Ê ç
”t
” I
l
w a h a d Bo m a t e m a t y c z n e s i Ba s p r ´ Ýy s t o Ê c i F = - k x S E M s a m o i n d u k c j i
f = - L
T = 2 r
g x
”t
2
m k x
m a s a n a s p r ´ Ýy n i e e n e r g i a p o t e n c j a l n a i n d u k c y j n o Ê ç z w o j n i c y L = n 0 n r n 2 S
T = 2 r E =
p o t l
k 2
S z y b k o Ê ç d ê w i ´ k u w w y b r a n y c h s u b s t a n c j a c h
p o w i e t r z e p o w i e t r z e p a r a w o d n a d w u t l e n e k w ´ g l a m e t a n w o d ó r w o d a e l a z o
p o w i e t r z e
- 2 0 % C 0 % C 3 0 % C 1 0 0 % C 0 % C 0 % C 0 % C 2 5 % C 2 0 % C
3 2 0 m 3 3 0 m 3 4 9 m 4 9 0 m 2 7 0 m 4 3 0 m 1 2 7 0 m 1 5 0 0 m 5 1 0 0 m
s s s s s s s s s