Задачі з фізики. Молекулярна фізика і термодинаміка
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10.1. |
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(4,82 109 k-1; 6,39 1029 k-1) |
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10.2. |
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10.3. |
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^h\`bgm \•evgh]h ijh[•]m <λ> fhe_dme Zahlm dh_n•p•}gl ^bnma•€ D • |
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10.4. |
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\•evgh]h ijh[•]m <λ> Zlhf•\ pvh]h ]Zam fdf
10.5.M ihkm^bg• h[¶}fhf 9 f3 f•klblvky N = 2 1022 fhe_dme ^\h- Zlhfgh]h ]Zam Dh_n•p•}gl l_iehijh\•^ghkl• ]Zam æ = 0,0 <l f k . <bagZqblb dh_n•p•}gl ^bnma•€ D ]Zam (4,06 10-4 f2 k
10.6. AgZclb dh_n•p•}gl l_iehijh\•^ghkl• æ \h^gx, \¶yad•klv ydh]h
η fdIZ k. f<l f k
10.7.Dh_n•p•}gl ^bnma•€ • \¶yad•klv \h^gx ijb ^_ydbo mfh\Zo ^hj•\gx-
xlv D = 1,42 10-5 f2 k • η = 8 fdIZ k <bagZqblb d•evd•klv fh- e_dme n \h^gx \ h^bgbp• h[¶}fm (1,80 1025 f-3)
10.8. :ahl agZoh^blvky ijb l_fi_jZlmj• L D K_j_^gy ^h\`bgZ \•ev- gh]h ijh[•]m fhe_dme Zahlm <λ! fdf AgZclb fZkm Zahlm ydbc ijhcrh\ \gZke•^hd ^bnma•€ q_j_a iehsbgm iehs_x S f2 aZ qZk t k ydsh ]jZ^•}gl ]mklbgb m gZijyfdm i_ji_g^bdmeyjghfm ^h
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10.9. :ahl aZih\gx} ijhkl•j f•` ^\hfZ ieZklbgZfb \•^klZgv f•` ydbfb
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10.10. Ijhkl•j f•` ^\hfZ dhgp_gljbqgbfb kn_jZfb a jZ^•mkZfb R1 |
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10.11. L_ieh\bc Z]j_]Zl h[fmjh\Zgbc \h]g_ljb\dhx p_]ehx Lh\sbgZ |
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h[fmjm\Zggy d f l_fi_jZlmjb ih\_johgv h[fmjm\Zggy L1 = |
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D • L2 |
D Dh_n•p•}gl l_iehijh\•^ghkl• \h]g_ljb\dh]h |
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h[fmjm\Zggy af•gx}lvky aZ aZdhghf æ = æ0 < L ^_ æ0 = |
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10.12.L_ieh\bc ihl•d • l_fi_jZlmjb ah\g•rg•o ih\_johgv kl•gb gZ]j•\Zevgh€ i_q• lh\sbghx d f ydZ ih\g•klx ajh[e_gZ •a \h]g_ljb\dh€ p_]eb a dh_n•p•}glhf l_iehijh\•^ghkl• æ1 = <l D f , lZd• kZf• yd m ^\hrZjh\h€ kl•gb i_jrbc rZj ydh€ \b]hlh\e_gbc •a \h]g_ljb\dh€ p_]eb lh\sbghx d1 f Z ^jm]bc rZj a g_\h]g_ljb\dh]h Ze_ fZehijh\•^gh]h fZl_j•Zem a æ2 = 0, <l D f AgZclb lh\sbgm d2 ^\hrZjh\h€ kl•gb f
10.13.Sh[ \bf•jylb dh_n•p•}gl l_iehijh\•^ghkl• æ Zahlm gbf aZih\-
gxxlv ijhkl•j f•` ^\hfZ ^h\]bfb dhZdk•Zevgbfb pbe•g^jZfb a jZ^•mkZfb R1 kf • R2 kf <gmlj•rg•c pbe•g^j j•\ghf•jgh gZ]j•\Z}lvky ki•jZeex ih yd•c ijhoh^blv kljmf kbehx , :.
Hi•j ki•jZe• sh ijbiZ^Z} gZ h^bgbpx ^h\`bgb pbe•g^jZ ^hj•\-
gx} RΩ Hf L_fi_jZlmjZ L2 D ah\g•rgvh]h pbe•g^jZ i•^ljbfm}lvky klZehx Ydsh ijhp_k klZp•hgZjgbc l_fi_jZlmjZ \gmlj•rgvh]h pbe•g^jZ L1 D <bagZqblb dh_n•p•}gl l_ieh- ijh\•^ghkl• æ Zahlm f<l f k
10.14.GZ \bkhl• h f gZ^ ]hjbahglZevgh jhaf•s_ghx ljZgkf•k•cghx klj•qdhx klj•qdhx ljZgkihjl_jZ ydZ jmoZ}lvky a• r\b^d•klx
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v1 = 70 f k i•^\•r_gZ ieZklbgdZ iehs_x S kf2 hj•}glh\ZgZ iZjZe_evgh ^h klj•qdb Ydm kbem ihlj•[gh ijbdeZklb ^h ieZklbgdb sh[ dhfi_gkm\Zlb kbem \¶yadhkl• a [hdm ih\•ljy • i•^ljbfm\Zlb €€
g_jmohfhx" AZ ghjfZevgbo mfh\ L D j Zlf dh_n•p•}gl \¶yadhkl• ih\•ljy η0=1,7 105 G f k fdG
PBDE D:JGH ?GLJHI1Y J?:EVG1 =:AB
Hkgh\g• nhjfmeb
L_jf•qgbc dh_n•p•}gl dhjbkgh€ ^•€ pbdem
η= 4 −4 4
^_ Q1 – d•evd•klv l_iehlb hljbfZgh€ jh[hqbf l•ehf aZ pbde \•^ gZ]j•\- gbdZ Q2 – d•evd•klv l_iehlb i_j_^Zgh€ jh[hqbf l•ehf oheh^bevgbdm
Dh_n•p•}gl dhjbkgh€ ^•€ pbdem DZjgh
η= 7 −7 7
^_ L1 – l_fi_jZlmjZ gZ]j•\gbdZ L2 – l_fi_jZlmjZ oheh^bevgbdZ
Oheh^bevgbc dh_n•p•}gl η ^ey fZrbgb sh ijZpx} aZ h[hjhlgbf pbdehf
η = QA2 .
^_ Q2 – d•evd•klv l_iehlb ydZ \•^^Z}lvky hoheh^`m\Zgbf l•ehf
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6= ∫ δ4
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^_ L – Z[khexlgZ l_fi_jZlmjZ kbkl_fb sh hljbfm} d•evd•klv l_iehlb δQ.
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11.1. |
1^_ZevgZ l_ieh\Z fZrbgZ, \ yd•c jh[hqhx j_qh\bghx } •^_Zevgbc |
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11.2. |
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ijZpx} aZ pbdehf DZjgh L_fi_jZlmjb gZ]j•\gbdZ • oheh^bevgbdZ |
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\•^ih\•^gh L1 D • L2 |
D <bagZqblb DD> η pbdem DZjgh GZ |
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kd•evdb ihlj•[gh a[•evrblb l_fi_jZlmjm gZ]j•\gbdZ sh[ DD> pbdem |
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11.3. IZjh\Z fZrbgZ ihlm`g•klx J d<l kih`b\Z} aZ qZk t ]h^ jh[hlb fZkm m d] \m]•eey a iblhfhx l_iehlhx a]hjyggy
q = 33 F>` d] L_fi_jZlmjZ m dhle• T1 = 473 K l_fi_jZlmjZ oheh^bevgbdZ hlhqmxqh]h k_j_^h\bsZ T2 = 331 K <bagZqblb DD> η p•}€ iZjh\h€ fZrbgb • η′ •^_Zevgh€ l_ieh\h€ fZrbgb sh
ijZpx} aZ pbdehf DZjgh a lZdbfb kZfbfb l_fi_jZlmjZfb gZ]j•\- gbdZ • oheh^bevgbdZ (19,92 %; 30,02 %)
11.4. >h\_klb sh af•gZ l_fi_jZlmjb T2 oheh^bevgbdZ \ieb\Z} kbevg•r_ gZ DD> l_ieh\h€ fZrbgb ydZ ijZpx} aZ pbdehf DZjgh g•` lZdZ kZfZ af•gZ l_fi_jZlmjb T1 gZ]j•\gbdZ <dZa•\dZ agZc^•lv
qZkldh\• iho•^g• ih T1 • T2 \•^ η • ihj•\gycl_ €o)
11.5. < •^_Zevg•c l_ieh\•c fZrbg• ydZ ijZpx} aZ pbdehf DZjgh • jh[hqhx
j_qh\bghx ydh€ } •^_Zevgbc ]Za gZcf_grbc lbkd j3 |
dIZ, Z lbkd |
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dIZ Z \ d•gp• |
•ahl_jf•qgh]h klbkdZggy j4 dIZ Ydbf [m\ lbkd j1 ]Zam gZ ihqZldm •ahl_jf•qgh]h jharbj_ggy? FIZ
11.6.L_ieh\bc ^\b]mg jh[hqbf l•ehf \ ydhfm } •^_Zevgbc ]Za ijZpx} aZ pbdehf sh kdeZ^Z}lvky •a •ahl_jf•qgh]h •ah[Zjgh]h lZ Z^•Z[Zlgh]h
ijhp_k•\ Ydsh ijhp_k •ah[Zjgbc jh[hq_ l•eh gZ]j•\Z}lvky \•^ l_fi_jZlmjb L1 = D ^h L2 = D <bagZqblb DD> η pvh]h l_ieh\h]h ^\b]mgZ • ^\b]mgZ sh ijZpx} aZ pbdehf DZjgh ydbc
fZ} lZd• kZf• l_fi_jZlmjb L1 gZ]j•\gbdZ • L2 oheh^bevgbdZ
(38,91 %; 60,00 %)
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Z^•Z[Zlg• Klmi•gv Z^•Z[Zlgh]h klbkdm |
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= 70 Z klmi•gv ihi_j_^gvh]h jharbj_ggy |
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11.8.Sh[ i•^ljbfZlb \ ijbf•s_gg• l_fi_jZlmjm t2 = 20 0K dhg^b- p•hg_j sh ijZpx} aZ pbdehf DZjgh sh]h^bgb \bdhgm} jh[hlm
:F>` Oheh^bevgbc dh_n•p•}gl η* = 12,7 <bagZqblb l_fi_-3 2
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jZlmjm t1 hlhqmxqh]h k_j_^h\bsZ • d•evd•klv l_iehlb ydZ \•^\h- ^blvky a ijbf•s_ggy (45 0K F>`
11.9.M dZj[xjZlhjghfm ^\b]mg• \gmlj•rgvh]h a]hjyggy ^\hZlhfgbc
•^_Zevgbc ]Za \bdhgm} pbde sh kdeZ^Z}lvky a ^\ho Z^•Z[Zl • ^\ho •ahohj Klmi•gv Z^•Z[Zlgh]h klbkdm ε = V1/V2=10 H[qbkeblb DD>
ηpvh]h pbdem (60,19 %)
11.10.Oheh^bevgZ fZrbgZ jh[hqbf l•ehf ydh€ } ]Za Zahl fZkhx m =
d] ijZpx} aZ a\hjhlgbf pbdehf DZjgh \ •gl_j\Ze• l_fi_jZ-
lmj L1 = D • L2 D . <•^ghr_ggy fZdkbfZevgh]h h[¶}fm
]Zam ^h f•g•fZevgh]h n <bagZqblb d•evd•klv l_iehlb Q2 sh aZ[bjZ}lvky \•^ l•eZ yd_ hoheh^`m}lvky • jh[hlm : ah\g•rg•o kbe
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11.11. E•^ fZkhx m d] sh fZ\ l_fi_jZlmjm L D [m\ ihke•^h\gh i_j_l\hj_gbc m \h^m Z ihl•f ijb Zlfhkn_jghfm lbkdm – \ iZjm Qhfm ^hj•\gx} af•gZ _gljhi•€ S i•^ qZk dh`gh]h a pbo ijhp_k•\" IblhfZ
l_ieh}fg•klv evh^m ke |
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\h^b l_fi_jZlmjZ ydh€ L2 |
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11.13. IblhfZ l_ieh}fg•klv l\_j^h]h l•eZ ijb l_fi_jZlmj• L > D
fh`_ [mlb jhajZoh\ZgZ aZ _fi•jbqghx nhjfmehx k |
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11.14. H[¶}f dbkgx fZkZ ydh]h m |
d] \gZke•^hd •ahl_jf•qgh]h |
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jharbj_ggy a[•evrb\ky \ n = 3 jZab <bagZqblb af•gm _gljhi•€ S i•^ qZk pvh]h ijhp_km >` D
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11.15. <h^_gv fZkZ ydh]h m d] i_j_oh^blv •a klZgm a iZjZf_ljZfb
V1 e • j1 dIZ \ klZg a iZjZf_ljZfb V2 e • j2 = dIZ. AgZclb af•gm _gljhi•€ S i•^ qZk pvh]h ijhp_km >` D
11.16. Dbk_gv fZkZ ydh]h m d] i_j_oh^blv •a klZgm L1 D \
klZg a l_fi_jZlmjhx L2 D i_jrbc jZa \gZke•^hd •ah[Zjgh]h jharbj_ggy Z ^jm]bc jZa – •ahl_jf•qgh]h jharbj_ggy a ih^Zev-
rbf •ahohjgbf gZ]j•\Zggyf <bagZqblb af•gm _gljhi•€ S i•^ qZk h[ho ijhp_k•\ >` D >` D
11.17. M [Zehg• h[¶}fhf V f3 f•klblvky ν |
fhev ^_ydh]h ]Zam |
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Ydsh L1 D lbkd ]Zam ^hj•\gx} j1 |
FIZ Z ydsh L2 = |
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FIZ H[qbkeblb ihijZ\db Z • b <Zg-^_j <ZZevkZ |
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^ey pvh]h ]Zam IZ f6 fhev2 f3 dfhev |
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11.18. Ijb lbkdm j dIZ \m]e_dbkebc ]Za KH2 fZkhx m |
d] |
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aZcfZ} h[¶}f V |
f3 IhijZ\db \ j•\gygg• <Zg-^_j-<ZZevkZ |
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Z G f4 fhev2 • b f3 dfhev. H[qbkeblb l_fi_jZlmjm |
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L ]Zam dhjbklmxqbkv j•\gyggyfb DeZi_cjhgZ – F_g^_e}}\Z • <Zg- |
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^_j-<ZZevkZ D D |
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11.19. >_ydbc ]Za d•evd•klx j_qh\bgb ν |
fhev aZcfZ} h[¶}f V1 |
f3. |
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I•^ qZk jharbj_ggy ]Zam ^h h[¶}fm V2 |
f3 [meZ \bdhgZgZ jh- |
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[hlZ : |
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f•`fhe_dmeyjgh]h ijbly]Zggy |
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<bagZqblb ihijZ\dm Z sh \oh^blv m j•\gyggy <Zg-^_j-<ZZevkZ
G f4 fhev2)
11.20. Djblbqg• lbkd • l_fi_jZlmjZ ih\•ljy \•^ih\•^gh ^hj•\gxxlv jd =
D AgZclb ihijZ\db Z • b \ j•\gygg• klZgm <Zg- ^_j-<ZZevkZ ^ey ih\•ljy IZ f6 fhev2 f3 dfhev
11.21. >ey ^_ydh]h ]Zam ihijZ\dZ \ j•\gygg• <Zg-^_j-<ZZevkZ Z
= 0,453 G f4 fhev2 Z djblbqgZ l_fi_jZlmjZ Ld D <bagZ- qblb _n_dlb\gbc ^•Zf_lj fhe_dmeb ]Zam gf
50