Задачі з фізики. Молекулярна фізика і термодинаміка
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11 FHE?DMEYJG: N1ABD: 1 L?JFH>BG:F1D:
J1<GYGGY KL:GM 1>?:EVGH=H =:AM JHAIH>1E FHE?DME =:AM A: R<B>DHKLYFB
Hkgh\g• nhjfmeb
J•\gyggy klZgm •^_Zevgh]h ]Zam j•\gyggy DeZi_cjhgZ – F_g^_e}}\Z
S9 = Pμ 57 ,
^_ P – fZkZ ]Zam μ – ch]h fheyjgZ fZkZ S – lbkd ' – h[¶}f 7 – l_fi_jZlmjZ ]Zam 5 – mg•\_jkZevgZ ]Zah\Z klZeZ
AZdhg ;hcey – FZj•hllZ
(7 = FRQVW , P = FRQVW )
S 9 = S 9 .
AZdhg =_c – ExkkZdZ
( S = FRQVW , P = FRQVW )
9 = 7 .
9 7
AZdhg RZjey
(9 = FRQVW , P = FRQVW )
S = 7 .
S 7
H[¶}^gZgbc ]Zah\bc aZdhg
( P = FRQVW )
p1V1 = p2V2 . T1 T2
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AZdhg >ZevlhgZ ^ey lbkdm kmf•r• •^_Zevgbo ]Za•\
S = S + S + + SQ ,
^_ S – lbkd kmf•r• ]Za•\ 5L – iZjp•Zevgbc lbkd •-€ dhfihg_glb kmf•r•
AZe_`g•klv lbkdm ]Zam \•^ dhgp_gljZp•€ fhe_dme • l_fi_jZlmjb
S = QN7 ,
^_ N – klZeZ ;hevpfZgZ
FheyjgZ fZkZ kmf•r• ]Za•\
μ= P + P + + PN ,
ν+ν + +νN
^_ P |
– fZkZ •-€ dhfihg_glb kmf•r• |
ν |
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mi |
– d•evd•klv j_qh\bgb •-€ |
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dhfihg_glb kmf•r• N – d•evd•klv dhfihg_gl kmf•r•
K_j_^gy d\Z^jZlbqgZ r\b^d•klv fhe_dme •^_Zevgh]h ]Zam
<υd\ >= 3RTμ ,
^_ 5 – mg•\_jkZevgZ ]Zah\Z klZeZ
Hkgh\g_ j•\gyggy fhe_dmeyjgh-d•g_lbqgh€ l_hj•€ •^_Zevgh]h ]Zam p = 31 ρ < υd\ >2 ,
^_ ρ – ]mklbgZ ]Zam
GZc•fh\•jg•rZ r\b^d•klv fhe_dme ]Zam
υ•f = 2RTμ .
K_j_^gy Zjbnf_lbqgZ r\b^d•klv
<υ >= 
8πμRT .
AZdhg jhaih^•em fhe_dme aZ r\b^dhklyfb aZdhg FZdk\_eeZ Z d•evd•klv fhe_dme yd• fZxlv r\b^d•klv \ f_`Zo \•^ υ ^h
υ+ Gυ
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dN (υ) = N f (υ)dυ = 4πN |
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2kT υ |
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dυ, |
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2πkT |
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^_ |
1 – aZ]ZevgZ d•evd•klv fhe_dme f(v) – nmgdp•y jhaih^•em fhe_dme aZ |
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Z[khexlgbfb agZq_ggyfb r\b^dhkl_c |
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[ d•evd•klv fhe_dme yd• fZxlv \•^ghkg• r\b^dhkl• \ f_`Zo \•^ |
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υ ^h υ + Gυ : |
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G1 X = 1 I X GX = |
1H−X X GX |
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π |
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– \•^ghkgZ r\b^d•klv f(u) – nmgdp•y jhaih^•em aZ |
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υ•f |
2RT |
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\•^ghkgbfb r\b^dhklyfb |
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14 ;Zjhf_ljbqgZ nhjfmeZ |
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p = p0 e− |
μgh |
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RT , |
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S – lbkd ih\•ljy gZ \bkhl• K = , μ – fheyjgZ fZkZ ih\•ljy |
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K_j_^gy _g_j]•y l_ieh\h]h jmom fhe_dmeb
<Æ >= 2i kT ,
^_ L – d•evd•klv klmi_g•\ k\h[h^b \•evghkl• fhe_dmeb
<gmlj•rgy _g_j]•y •^_Zevgh]h ]Zam
U = ν 2i RT .
8.1. |
Ihkm^bgZ h[¶}fhf 9 |
f3 aZih\g_gZ dbkg_f fZkhx P d] |
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ijb lbkdm j dIZ <bagZqblb k_j_^gx d\Z^jZlbqgm r\b^d•klv |
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<vd\> fhe_dme ]Zam ]mklbgm ]Zam ρ • d•evd•klv fhe_dme N dbkgx |
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sh } \ ihkm^bg• f k d] f3; 2,82 1024) |
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8.2. |
Kmf•r \h^gx fZkhx m1 ] lZ g_hgm fZkhx m2 ] i_j_[m\Z} |
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ijb l_fi_jZlmj• L |
D lZ lbkdm j dIZ AgZclb ]mklbgm |
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kmf•r• d] f3) |
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8.3. |
Ihkm^bgZ aZih\g_gZ |
kmf•rrx Zahlm • ]_e•x ijb l_fi_jZlmj• |
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L D • lbkdm j |
103 IZ FZkZ Zahlm ^hj•\gx} 70 % \•^ |
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aZ]Zevgh€ fZkb kmf•r• <bagZqblb dhgp_gljZp•x fhe_dme dh`gh]h |
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•a ]Za•\ (8 1022f-3; 24 1022 f-3) |
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8.4. Kmf•r ]_e•x lZ g_hgm fZkhx P |
d] aZcfZ} h[¶}f V = e • |
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i_j_[m\Z} ijb l_fi_jZlmj• L |
D lZ lbkdm j |
dIZ. |
<bagZqblb ijhp_glgbc \f•kl h[ho ]Za•\ (20 %; 80 %) |
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8.5.Kmo_ Zlfhkn_jg_ ih\•ljy f•klblv dbkgx Zahlm •
Zj]hgm \•^ aZ]Zevgh€ ch]h fZkb QZkldZ •grbo ]Za•\ fZeZ AgZclb fheyjgm fZkm kmoh]h Zlfhkn_jgh]h ih\•ljy d] fhev
8.6. Kmf•r ]Za•\ kdeZ^Z}lvky a Zahlm fZkhx m1 |
] • ^_ydh€ d•evdhkl• |
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\m]e_dbkeh]h ]Zam FheyjgZ fZkZ kmf•r• |
μ |
d] fhev. |
<bagZqblb fZkm m2 \m]e_dbkeh]h ]Zam \ kmf•r• ]
8.7.>\• ihkm^bgb a ih\•ljyf h[¶}fb ydbo ^hj•\gxxlv V1 = 0,25 10-3 f3 •
V2 = 0,4 10-3 f3, a¶}^gZg• \mavdhx ljm[dhx a djZgbdhf L_fi_jZlmjb \ h[ho ihkm^bgZo \•^ih\•^gh ^hj•\gxxlv T1 • L2 D • i•^ qZk ^hke•^m i•^ljbfmxlvky klZebfb Ydsh djZg aZdjblbc lbkdb ih-
\•ljy \ ihkm^bgZo ^hj•\gxxlv \•^ih\•^gh j1 |
dIZ • j2 |
dIZ |
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Ydbc lbkd j mklZgh\blvky \ ihkm^bgZo |
ydsh \•^djblb djZg" |
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dIZ
8.8.I•^ qZk gZ]j•\Zggy ^\hZlhfgh]h ]Zam \ aZiZyg•c Zfime• \•^ l_fi_-
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jZlmjb L1 D ^h l_fi_jZlmjb L2 D ch]h lbkd ajhklZ} \•^ |
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j1 dIZ ^h j2 dIZ IjbimkdZxqb sh ijb l_fi_jZlmj• |
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L1 ^bkhp•Zp•y fhe_dme ]Zam \•^kmlgy \bagZqblb klmi•gv ^bkhp•Zp•€ |
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]Zam ijb l_fi_jZlmj• L2. (0,5) |
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8.9. |
M [Zehg• agZoh^blvky •^_Zevgbc ]Za ]mklbgZ ydh]h ρ |
d] f3 • |
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lbkd j dIZ <bagZqblb k_j_^gx Zjbnf_lbqgm r\b^d•klv v> |
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fhe_dme ]Zam f k |
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8.10. |
;Zehg aZih\g_gh •^_Zevgbf ]Zahf |
]mklbgZ ydh]h ρ |
d] f3 • |
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lbkd j dIZ H[qbkeblb gZc•fh\•jg•rm v• r\b^d•klv fhe_dme |
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]Zam f k |
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8.11. |
K_j_^gy d\Z^jZlbqgZ r\b^d•klv v d\> fhe_dme dbkgx [•evrZ \•^ |
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€o gZc•fh\•jg•rh€ r\b^dhkl• v• gZ |
v f k <bagZqblb l_fi_- |
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jZlmjm L ]Zam D |
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8.12. |
L_fi_jZlmjZ Zahlm N2 L D YdZ qZklbgZ fhe_dme Zahlm |
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fZ} r\b^d•klv \ f_`Zo Z \•^ v1 |
f k ^h v2 f k [ \•^ |
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v1 f k ^h v2 f k \ \•^ v1 f k ^h v2 f k?
(1,38 %; 2,90 %; 2,76 %)
8.13.M kd•evdb jZa•\ d•evd•klv fhe_dme •a r\b^dhklyfb \ •gl_j\Ze• <vd\> ” v1 ” <vd\> + dv f_grZ \•^ d•evdhkl• fhe_dme r\b^dhkl• ydbo e_`Zlv \ •gl_j\Ze• vi ” v2 ” vi + dv, ^_ vi – gZc•fh\•jg•rZ r\b^d•klv fhe_dme ijb l•c kZf•c l_fi_jZlmj• ]Zam" (1,1)
8.14.M kd•evdb jZa•\ d•evd•klv fhe_dme •a r\b^dhklyfb \ •gl_j\Ze• <v> ” v1 ” v> + dv f_grZ \•^ d•evdhkl• fhe_dme r\b^dhkl• ydbo e_`Zlv \ •gl_j\Ze• vi ” v2 ” vi + dv ^_ vi – gZc•fh\•jg•rZ r\b^d•klv fhe_dme ijb l•c kZf•c l_fi_jZlmj• ]Zam" (1,03)
8.15.M kd•evdb jZa•\ d•evd•klv fhe_dme •a r\b^dhklyfb \ •gl_j\Ze• <vd\> ” v1 ” <vd\> + dv f_grZ \•^ d•evdhkl• fhe_dme r\b^dhkl• ydbo e_`Zlv \ •gl_j\Ze• <v> ” v2 ” v> + dv? (1,06)
8.16.Ydbc \•^khlhd fhe_dme ]Zam fZ} r\b^dhkl• sh \•^j•agyxlvky \•^ gZc•fh\•jg•rh€ g_ [•evr_ g•` gZ 1 %? (1,66 %)
8.17.L_fi_jZlmjZ ih\•ljy klZeZ • ^hj•\gx} t = 21 0K GZ yd•c \bkhl• h lbkd j ih\•ljy ^hj•\gx} \•^ lbkdm j0 gZ j•\g• fhjy" f
8.18.L_fi_jZlmjZ ih\•ljy ih \k•c \bkhl• k\_j^eh\bgb klZeZ • ^hj•\gx}
M kd•evdb jZa•\ lbkd j ih- \•ljy gZ ^g• k\_j^eh\bgb [•evrbc \•^ lbkdm j0 gZ ih\_jog• A_fe•" (2,1)
9. I?JRBC A:DHG L?JFH>BG:F1DB L?IEH/FG1KLV 1>?:EVGH=H =:AM :>1:;:LGBC IJHP?K
Hkgh\g• nhjfmeb
I_jrbc aZdhg l_jfh^bgZf•db
4 = 8 + $ ,
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^_ Q – l_iehlZ ydZ gZ^ZgZ kbkl_f• U – af•gZ \gmlj•rgvh€ _g_j]•€ kbkl_fb A – jh[hlZ ydZ \bdhgZgZ kbkl_fhx ijhlb ah\g•rg•o kbe
Jh[hlZ jharbj_ggy ]Zam Z ^ey •ah[Zjgh]h ijhp_km
$ = S(9 − 9 ), |
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[ ^ey •ahl_jf•qgh]h ijhp_km |
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\ \ aZ]Zevghfm \biZ^dm |
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$ = |
9∫ SG9 . |
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Iblhf• l_ieh}fghkl• ]Zam ijb klZehfm h[’}f• lZ ijb klZehfm lbkdm
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A\’yahd f•` fheyjghx & • iblhfhx k l_ieh}fghklyfb ]Zam
C = μc.
J•\gyggy FZc}jZ
&S − &9 = 5
J•\gyggy ImZkkhgZ
S9 γ = FRQVW
^_ γ = &S = L + – ihdZagbd Z^•Z[Zlb
&9 L
7 A\’yahd f•` ihqZldh\bfb • d•gp_\bfb agZq_ggyfb iZjZf_lj•\ klZg•\ ]Zam ijb Z^•Z[Zlghfm ijhp_k•
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8 Jh[hlZ •^_Zevgh]h ]Zam ijb Z^•Z[Zlghfm ijhp_k• |
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38
9.1. |
<h^_gv fZkhx m = 0, d] agZoh^blvky ijb l_fi_jZlmj• L1 |
D. AZ |
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jZomghd gZ]j•\Zggy h[¶}f \h^gx a[•evrm}lvky \ n = 2 jZab ijb |
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klZehfm lbkdm <bagZqblb jh[hlm : jharbj_ggy ]Zam af•gm |
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\gmlj•rgvh€ _g_j]•€ U ]Zam • d•evd•klv l_iehlb Q ydZ gZ^ZgZ ]Zam |
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>` >` >` |
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9.2. |
I•^ qZk •ah[Zjgh]h gZ]j•\Zggy \•^ l_fi_jZlmjb L1 |
D ^h |
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L2 |
D fhev •^_Zevgh]h ]Zam hljbfm} Q d>` l_iehlb |
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AgZclb agZq_ggy γ = Kj KV af•gm \gmlj•rgvh€ _g_j]•€ |
U ]Zam • |
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jh[hlm : \bdhgZgm ]Zahf >` >` |
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9.3. |
;Zehg h[¶}fhf V |
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f3 gZih\g_gbc dbkg_f ijb l_fi_jZlmj• |
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L1 |
D • lbkdm j1 |
dIZ I•key gZ]j•\Zggy lbkd \ [Zehg• |
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a[•evrb\ky ^h j2 dIZ <bagZqblb l_fi_jZlmjm L2 dbkgx i•key gZ]j•\Zggy • d•evd•klv l_iehlb Q ydZ gZ^ZgZ ]Zam D d>`
f3 f•klblvky dbk_gv ijb l_fi_jZlmj•
L1 D • lbkdm j1 FIZ GZ]j•\Zxqbkv i•^ khgyqgbfb ijh- f_gyfb dbk_gv hljbfm} Q >` l_iehlb <bagZqblb l_fi_jZ-
lmjm L2 • lbkd j2 dbkgx i•key gZ]j•\Zggy D FIZ
9.5.:ahl fZkhx P d] jharbjy}lvky •ahl_jf•qgh ijb l_fi_jZ-
lmj• L1 D ijbqhfm h[¶}f Zahlm a[•evrm}lvky \ n = 3 jZab <bagZqblb af•gm \gmlj•rgvh€ _g_j]•€ U ]Zam \bdhgZgm i•^ qZk
jharbj_ggy ]Zam jh[hlm : d•evd•klv l_iehlb Q sh hljbfZ\ ]Za
>` >`
9.6. >_ydbc ]Za fZkhx P d] agZoh^blvky ijb l_fi_jZlmj• L D •
lbkdm j1 FIZ <gZke•^hd •ahl_jf•qgh]h klbkdZggy lbkd ]Zam a[•evrb\ky \ n = 2 jZab Jh[hlZ ydZ \bdhgZgZ i•^ qZk klbkdZggy ]Zam : – d>` JhajZom\Zlb fheyjgm fZkm μ ]Zam • ihqZldh- \bc iblhfbc h[¶}f V1/m ]Zam d] fhev f3 d]
9.7. I_\gZ d•evd•klv Zahlm ijb lbkdm j1 dIZ aZih\gx\ZeZ h[¶}f V1 e Z ijb lbkdm j2 dIZ – h[¶}f V2 e I_j_o•^ \•^ i_jrh]h klZgm ^h ^jm]h]h \•^[m\Z\ky \ ^\Z _lZib kihqZldm •ahohjgh Z ihl•f •ah[Zjgh H[qbkeblb af•gm \gmlj•rgvh€ _g_j]•€ U ]Zam d•evd•klv l_iehlb Q, • jh[hlm : \bdhgZgm ]Zahf m pvhfm
ijhp_k• >` >` – >`
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3 • agZoh^blvky i•^ lbkdhf |
dIZ |
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9.8. :ahl aZcfZ} h[¶}f V1 f |
j1 |
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=Za gZ]j•eb ijb klZehfm lbkdm ^h h[¶}fm V2 |
f3 Z ihl•f ijb |
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klZehfm h[¶}f• ^h lbkdm j2 dIZ <bagZqblb af•gm \gmlj•r- gvh€ _g_j]•€ U ]Zam \bdhgZgm gbf jh[hlm : • d•evd•klv l_iehlb Q, ydm i_j_^Zeb ]Zam F>` F>` F>`
9.9.Dbk_gv fZkZ ydh]h P d] agZoh^blvky ijb l_fi_jZlmj•
LD <gZke•^hd •ahohjgh]h hoheh^`_ggy lbkd ]Zam af_grb\ky
\ n = 4 jZab Z ihl•f \gZke•^hd •ah[Zjgh]h jharbj_ggy l_fi_jZlmjZ
dbkgx ^hj•\gx\ZeZ ihqZldh\•c L1 <bagZqblb jh[hlm : ydm \bdhgZ\ ]Za • af•gm \gmlj•rgvh€ _g_j]•€ U ]Zam >`
9.10. H[¶}f ν fhev •^_Zevgh]h ]Zam sh agZoh^b\ky ijb l_fi_jZlmj• L1 D ijb •ahl_jf•qghfm jharbj_gg• a[•evrb\ky \ n = 5,0 jZa•\
Ihl•f i•key •ahohjgh]h gZ]j•\Zggy lbkd ]Zam ^hj•\gx\Z\ ihqZldh\hfm AZ \_kv ijhp_k ]Za hljbfZ\ d•evd•klv l_iehlb Q d>` <bagZqblb
γ = Kj KV ^ey pvh]h ]Zam (1,4)
9.11.fhev •^_Zevgh]h ]Zam f•klblvky \ pbe•g^j• ijb l_fi_jZlmj• L1 =
D =Za •ah[Zjgh gZ]j•\Zxlv ^h l_fi_jZlmjb L2 D ihl•f
•ahohjgh hoheh^`mxlv ^h l_fi_jZlmjb L3 |
D i•key qh]h |
•ah[Zjgh klbkdZxlv ^h ihqZldh\h]h h[¶}fm |
• ihl•f •ahohjgh |
i_j_\h^ylv m ihqZldh\bc klZg H[qbkeblb ydm jh[hlm : \bdhgZ\ ]Za aZ pbde >`
9.12.J•agbpy iblhfbo l_ieh}fghkl_c kj – kV ^_ydh]h ^\hZlhfgh]h ]Zam ^hj•\gx} 296,8 >` d] D <bagZqblb fheyjgm fZkm ]Zam • ch]h iblhf• l_ieh}fghkl• kj • kV. >` d] D >` d] D
9.13.FheyjgZ fZkZ ^_ydh]h ]Zam μ d] fhev <•^ghr_ggy fheyj-
gbo l_ieh}fghkl_c Kj KV = 1,4 AgZclb iblhf• l_ieh}fghkl• kj • kV pvh]h ]Zam >` d] D >` d] D
9.14. |
>_ydbc ]Za aZ ghjfZevgbo n•abqgbo mfh\ J0 dIZ L0 D) |
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fZ} ]mklbgm ρ d] f3 <bagZqblb ch]h iblhf• l_ieh}fghkl• |
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kj • kV. >` d] D >` d] D |
9.15. |
Ijb l_fi_jZlmj• L D ^_ydbc ]Za fZkhx P d] aZcfZ} |
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h[¶}f V = 0,8 f3 IblhfZ l_ieh}fg•klv ]Zam kj = 519 >` d] D Z |
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Kj KV = 1,66 <bagZqblb lbkd j ]Zam dIZ |
40
9.16. >_ydbc ]Za ijb lbkdm j dIZ • l_fi_jZlmj• L |
D fZ} |
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iblhfbc h[¶}f v |
f3 d] IblhfZ l_ieh}fg•klv |
]Zam kj = |
= >` d] D AgZclb \•^ghr_ggy γ Kj KV. (1,4) |
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9.17.Kmf•r ]Za•\ kdeZ^Z}lvky •a g_hgm • \h^gx FZkh\• qZkldb g_hgm •
\h^gx k1 = 80 % • k2 = 20 % \•^ih\•^gh H[qbkeblb iblhf• l_ieh-
}fghkl• kj • kV kmf•r• ]Za•\ >` d] D >` d] D
9.18. |
Kmf•r ]Za•\ kdeZ^Z}lvky |
•a Zj]hgm d•evd•klv |
j_qh\bgb ydh]h |
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ν1 |
dfhe• • Zahlm d•evd•klv j_qh\bgb ydh]h ν2 |
dfhe• <bagZqblb |
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iblhfm l_ieh}fg•klv kj ]Zah\h€ kmf•r• >` d] D |
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9.19. |
:ahl fZkhx P d] ijb l_fi_jZlmj• L |
D aZcfZ} h[¶}f |
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V |
f3. <gZke•^hd |
Z^•Z[Zlgh]h jharbj_ggy l_fi_jZlmjZ |
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Zahlm af_grbeZkv ^h L2 |
D Z lbkd ^h j2 |
dIZ H[- |
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qbkeblb \•^ghr_ggy γ = Kj KV. (1,4) |
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9.20. |
K•jdh\h^_gv H2S fZkhx P |
d] ydbc aZcfZ} h[¶}f V1 f3 ijb |
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l_fi_jZlmj• L1 D Z^•Z[Zlgh klbkgmeb lZd sh ch]h lbkd a[•evrb\ky \ n = 2 jZab <bagZqblb d•gp_\bc h[¶}f V2 l_fi_jZ-
lmjm L2 • af•gm \gmlj•rgvh€ _g_j]•€ ]Zam U FheyjgZ fZkZ k•jdh-
\h^gx μ d] fhev. f3 D d>`
9.21. |
1^_Zevgbc ^\hZlhfgbc ]Za sh fZ} lbkd j1 |
dIZ • h[¶}f V1 = |
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f3 •ahl_jf•qgh klbkdZ}lvky ^h h[¶}fm V2 |
f3. I•key pvh]h \•g |
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jharbjy}lvky Z^•Z[Zlgh ^h ihqZldh\h]h h[¶}fm V1. GZ kd•evdb |
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af•gblvky lbkd ]Zam \gZke•^hd Z^•Z[Zlgh]h jharbj_ggy" dIZ |
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9.22. |
Ih\•ljy fZkZ ydh]h P |
d] l_fi_jZlmjZ L1 |
D • lbkd |
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j1 dIZ Z^•Z[Zlgh jharbjy}lvky γ |
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LZdZ kZfZ fZkZ |
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ih\•ljy jharbjy}lvky •ahl_jf•qgh \•^ ihqZldh\h]h klZgm a iZjZf_l- jZfb p3 dIZ, V3 f3 <bagZqblb iZjZf_ljb klZgm L2, V2, j2, sh \•^ih\•^Zxlv i_j_lbgm Z^•Z[Zlb lZ •ahl_jfb FheyjgZ fZkZ ih\•ljy μ d] fhev (2 D f3 dIZ
9.23. <gZke•^hd Z^•Z[Zlgh]h jharbj_ggy lbkd ]Zam af_grm}lvky \•^
j1 dIZ Ihl•f ]Za gZ]j•\Z}lvky ijb klZehfm h[¶}f• ^h ihqZldh\h€ l_fi_jZlmjb Z lbkd ]Zam ajhklZ} ^h j3 =
dIZ JhajZom\Zlb \•^ghr_ggy γ = Kj / KV ^ey pvh]h ]Zam (1,4)
41
9.24. M pbe•g^j• i•^ ihjrg_f agZoh^blvky \h^_gv fZkhx P d]
ijb l_fi_jZlmj• L1 D <h^_gv kihqZldm jharbjb\ky Z^•Z[Zlgh a[•evrb\rb k\•c h[¶}f n1 = 4 jZab Z ihl•f [m\ klbkgmlbc •ahl_jf•qgh ijbqhfm h[¶}f ]Zam af_grb\ky \ n2 = 4 jZab <bagZqblb l_fi_jZlmjm
L2 \ d•gp• Z^•Z[Zlgh]h jharbj_ggy • jh[hlm : ydm \bdhgZ\ ]Za i•^ qZk pbo ijhp_k•\ D d>`
9.25. |
Dbk_gv sh fZ} l_fi_jZlmjm L1 |
D • lbkd j1 |
dIZ, |
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kihqZldm jharbjy}lvky Z^•Z[Zlgh \•^ h[¶}fm V1 f3 ^h h[¶}fm |
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V2 |
f3 Z ihl•f •ah[Zjgh ^h h[¶}fm V3 |
f3 <bagZqblb jh- |
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[hlm : ydm \bdhgZ\ ]Za af•gm ch]h \gmlj•rgvh€ _g_j]•€ |
U • d•evd•klv |
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l_iehlb Q, ydZ i•^\_^_gZ ^h ]Zam d>` d>` d>` |
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9.26. |
>\hZlhfgbc •^_Zevgbc ]Za ydbc ijb lbkdm j1 |
dIZ aZcfZ} h[¶}f |
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V1 |
e kihqZldm jharbjy}lvky Z^•Z[Zlgh ^h h[¶}fm V2 |
e Z ihl•f |
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•ahohjgh ch]h lbkd ihgb`m}lvky ^h j2 |
dIZ <bagZqblb \bdhgZgm |
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]Zahf jh[hlm : af•gm ch]h \gmlj•rgvh€ _g_j]•€ |
U • d•evd•klv l_iehlb |
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Q , ydm hljbfZ\ ]Za (450 >` – >` – >`
9.27. fhev •^_Zevgh]h h^ghZlhfgh]h ]Zam gZ]j•\Zxlv \•^ l_fi_jZlmjb
L1 D ^h L2 D lZd sh i•^ qZk gZ]j•\Zggy j V = const. <bagZqblb fheyjgm l_ieh}fg•klv K • jhajZom\Zlb d•evd•klv l_iehlb Q,
ydZ ih]ebgZ}lvky ]Zahf i•^ qZk gZ]j•\Zggy >`
Y<BS: I?J?G?K?GGY
Hkgh\g• nhjfmeb
K_j_^gy d•evd•klv a•ldg_gv h^g•}€ fhe_dmeb ]Zam aZ h^bgbpx qZkm
< z >= 2π d 2n < υ >,
^_ G – _n_dlb\gbc ^•Zf_lj fhe_dmeb
K_j_^gy ^h\`bgZ \•evgh]h ijh[•]m fhe_dme ]Zam
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kT |
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2π d 2n |
2π d 2 p |
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42