(Heat) ??y Ba ￡Dù?`# = ? 1.` ￡ ?D"d ·?v s0e0F? ·"d?￥t8? ?? 2. = ? D ￡C`μ1￥?é?? p ￡C`té?v s0 ￡?￥ "8VCb =a ￡D￥ù?ZE =a ￡D￥ù?ZE 1.±4 í ?ZE ±4 í ?ZE ---d9t ?ZE d9t ?ZE ·Vté￥±42?¨ Vté￥±42?¨ d9 ü ( d9 ü ( ￥ZEù? ￡C`#? p￥±4'éb ￥ZEù? ￡C`#? p￥±4'éb 2.?4 í ?ZE ?4 í ?ZE --- ￡ ?DZE ￡ ?DZE ·[ L Y L1$V ? 4?? [ L Y L1$V ? 4?? , ù? ￡?D￥1"?Hqa ￡C` ￥?4+??? p L¨N′úb ￥?4+??? p L¨N′úb ·"dé??8 í ?b "dé??8 í ?b ?a+?à Q ?a+?à Q 1.?4 D±4  ?4 D±4  (1)?4  ?4  (macroscopic quantity) ·V?"d?8?é V?"d?8?é ( ?? ??  ?? ?? )￥t ?  ￥t ?  · V°¤?  V°¤?  ( ?8aa < ?8aa < ) (2)±4  ±4  (microscopic quantity) · í??±4 ì0? ?￥t ?  í??±4 ì0? ?￥t ?  ·B?? ?°¤?  B?? ?°¤?  ( ?s0é a ?  ?s0é a ?  ) ·?4  ^±4 ￥d9 ü (′ ?4  ^±4 ￥d9 ü (′ ( ?a <?v s0 C H? M? ?a <?v s0 C H? M? q￥d9 ü (′μ1 q￥d9 ü (′μ1 ) 2. ü? ? ü? ? (equilibrium state) ·? s???Y￥Hq/ ? s???Y￥Hq/ "d?4?é? ? HW?M￥ ? "d?4?é? ? HW?M￥ ? ( ￡? ü? ￡? ü? )b · ü? ? ^B?Hq/ L= f ?￥ ü? ? ^B?Hq/ L= f ?￥ à ??`b 3. ??   ??  (quantity of state) · í ?"d ü? ?￥?4?  í ?"d ü? ?￥?4?  ·è¨ è¨ PaVaT · ü? ?/ ?? ? ? HWM? ü? ?/ ?? ? ? HWM? 4. ?Z?  ?Z? (equation of state) · ?? -W￥f ?1"  ?? -W￥f ?1" 0),,( =VTpf (Kinetic Theory of Gases) ±4 ? ? ±4 ? ?   ¨d9ZEy ??4 ¨d9ZEy ??4 DM?±4  ü (′-W￥1" DM?±4  ü (′-W￥1" ?6-1 s0 ￡?Dd9? p s0 ￡?Dd9? p B B . 8? ? ?'4? 8? ? ?'4? 1s0￥4? s0￥4? ?4té?v ? ?? ?4té?v ? ?? ￥±4 ì0 ￥±4 ì0 (s0e0 s0e0 )F? F? 2s0?￥4? s0?￥4? s0??T1T s0??T1T í?5￥? í?5￥? 3s0 ?￥4? s0 ?￥4? s0-WμMoT s0-WμMoT ¨ ? ¨ ? ----? ?? ? ? ?? ? 2006-3-22 10 d 0 r  ?  ? ? ? ? ? ? ? ? ? f r r o   ü?  ? ~10 -10 m d  s0μr°? s0μr°? r=d H ?M1íK v?? ? V ? l? db ----N H? ?1 , N H? ?1 , m10 9? >r Hs0 ? Hs0 ? V- { V- { = = . 8s0￥+? 8s0￥+? (laa ya y ) l ??s0￥°??1 ??s0￥°??1 10 -10 m   S ?/ ? : 8?μ S ?/ ? : 8?μ 6×10 23 ?s0 ?s0 y y S ?/￥ ü ( ? q?1 ? S ?/￥ ü ( ? q?1 ? e+? ü e+? ü y y  yíca §￡M￥?  yíca §￡M￥? ? ? .d9? p d9? p ?:e L ?:e L l? l o ? '? l o ? '? ￠ ^ } ? Yq ? z ? z .￠ ￠ ^ } ? Yq v l oB?B?g ?BQ v l oB?B?g ?BQ g ?s? f ?váM] g ?s? f ?váM] d9? p d9? p B?￥Hq/v ￥ B?￥Hq/v ￥ } ? Yqi"B?A ?? p? } ? Yqi"B?A ?? p? 1.à q à q B?Hq/  } ? YqC B?Hq/  } ? YqC ￥ V ??￥vlb ! ! N1 L9Q ? 1 L9Q ? N A 1 Yq 1 Yq A C￥Q ?5 C￥Q ?5 N N W A N A ∞→ = lim N N W A A =e1 e1   nq Yq q Yq ∑∑ = N N W i i 1= N N i ∑ = ----BB?Hq BB?Hq ?B Yq￥+ q ?@ ?B Yq￥+ q ?@ 10 ≤≤ i W 2.d9 ü (′ d9 ü (′ ? t ?  ? t ?  x  x 1 ax 2 aL L x n CQ ? CQ ? sY1 sY1 N 1 aN 2 aL L N n x ￥ ? ? ü (′1 ￥ ? ? ü (′1 n nn NNN NxNxNx x +++ +++ = L L 21 2211 N Nx ii Σ = N NxNxNx x nn N +++ = ∞→ L 2211 lim N Nx x ii Σ = nn WxWxWx +++= L 2211 ii WxΣ= ii Wxx Σ= [ è è ]d9 &ú d9 &ú &ú z ^ Bú &ú z ^ Bú h ( ? ? 1.815m) ￥ ￥ | ?+?1 , | ?+?1 , &úo? &úo? 1.700~1.800m-W￥ | ? -W￥ | ? μB? \? Oμil￥s? μB? \? Oμil￥s? m100.0=?h hhh ii ?+~ &úo? &úo? ￥ | ?1 ￥ | ?1 i N N N W i i = hN N f i i ?? = úo? úo? uW uW ￥ | ?]9 | ?￥?s1 ￥ | ?]9 | ?￥?s1 hhh ii ?+~  &ú  &ú ?í?êúW? ?í?êúW? =￥ | ?]9 | ?￥?s1 =￥ | ?]9 | ?￥?s1 i h i f i h hfW ii ??= 2006-3-22 19 ? ? 0? } ? t?;á wL 0? } ? t?;á wL0→?h hfW ii ??= )(hf ¨ ¨ }9 }9 i f )(hf h hhfW hhh d)( d~ = + hhNfN d)(d = ∫ =1d)( hhf 2006-3-22 20 )(hf h hhNfN d)(d = N Nh h ∫ = d N hhhNf ∫ = d)( N Nx x ii Σ = ∫ = hhhf d)( ?6-2 ?X 8 ?Z? ?X 8 ?Z? B B . ￡ ?D? ,? p ￡ ?D? ,? p 1 T 1 p 2 T 2 p A B ' ￡ ' ￡ C C   "dsYr ü? ? "dsYr ü? ? A B i ￡C i ￡C A B 1 p T 2 p T   "d ￡ ü? "d ￡ ü? "dMoT¨ "dMoT¨ ?Mo)? ￡ ü ?Mo)? ￡ ü ?￥"d?M] ?￥"d?M] C A B A B C ? "d?D? ?"d ￡ ü? ? "d?D? ?"d ￡ ü? 5 "d9 ￡ ü? 5 "d9 ￡ ü? ---- ￡ ?D? ,? p ￡ ?D? ,? p ` ü?V? ü?V? V?? ? V?? ? B?W ?? V B?W ?? V í ? í ? AT1 ü? ?￥V? AT1 ü? ?￥V? dè? ¤1a ê dè? ¤1a ê (1) ü?V?￥ ü?V?￥ ?B? ?B? W ? V¨ ?  W ? V¨ ?  paVaT í ? í ? 2006-3-22 25 (2) ü?V? pVm ¨B m ¨B H wLV U H wLV U p V a b ),,( ccc TVpc = = . ?X 8￥ ?Z? ?X 8￥ ?Z? 1.?S ?S ?? f?S ? f?S 1714 M? § ? ~Z+ ? ~Z+ y ?[ ￡2b￥?1 y ?[ ￡2b￥?1 32 o F  ￡m-￥?1 ￡m-￥?1 212 o F ?  f?S  f?S 1742 M ???óD M ???óD E E :? ? :? ? y ?[b￥ ??? y ?[b￥ ??? 1 1 0 o C  ￡￥m??1 ￡￥m??1 100 o C )32( 9 5 ?= Ft ? ￡ ?D? ￡ ?D? S S DyTtéí1 DyTtéí1 ￥?S??S￥ ￥?S??S￥ 7:ó 7:ó y ? y ? D  f?￥1"1 D  f?￥1"1 15.273+= tT ?ê 7 ?ê 7 (K)  ?1 ￡ ?D? ?1 ￡ ?D? 2. ?X 8 ?Z? ?X 8 ?Z? C T pV = S ? S ? )(N/mPa10013.1 25 0 ×=p atm1 C0 0 K15.273 0 =T /molm104.22 33 mol,0 ? ×=V C T pV =   m kg￥ ?X 8 ￥ ?X 8 0 00 T Vp T pV =∴ mol,0 mol0 0 V M m T p = R M m mol = 0 mol,00 T Vp R = KJ/mol31.8 ?= ---- ? a 8è  RT M m pV mol =∴ [ è è 1]  T ?1   T ?1 3.2?10 -2 m 3   ? ? a ?1 a ?1 1.3?10 7 Pab ì??a ?  ì??a ? ?? ?? 10 6 Pa Hü1×? b !  L i Hü1×? b !  L i ??¨ ??¨ 1atm￥  ￥  0.2m 3 ,ù??M ù??M ￥ f ?/B T  ?¨ ? ￥ f ?/B T  ?¨ ? ? 3 3 ! P¨ -a T? é sY1 ! P¨ -a T? é sY1 m 1 am 2   ?? P¨ é 1 ?? P¨ é 1 m 3 RT M m pV mol = RT pVM m mol = RT pVM m mol = RT VpM m 1mol 1 = RT VpM m 2mol 2 = RT VpM m 33mol 3 = V¨? ? V¨? ? 3 21 m mm N ? = 33 21 )( Vp Vpp ? = 2.010013.1 102.3)10103.1( 5 267 ×× ××?× = ? ?(19= [ è è 2] ! b ?cμ ! b ?cμ 23.6 % ? ? 76.4 % ? ? , pa < pa < p = 10 5 Pa ?? ?? T = 17 o C H b ￥ áb 3 3 ! b ???￥é sY1 ! b ???￥é sY1 m 1 a m 2   :é sY1 :é sY1 M 1 aM 2 RT M m pV mol = ρ 21 mm V + = ??:sa? ? ??:sa? ? L++= 21 ppp V RT M m V RT M m 2 2 1 1 += 221 2 121 1 M RT mm m M RT mm m p ρρ + + + =∴ 21 %4.76%6.23 M RT M RT ρρ ×+×= 21 %4.76%6.23 M RT M RT p ×+× =ρ 21 %4.76%6.23 M RT M RT p ×+× =ρ 33 5 1028 29031.8 %4.76 1032 29031.8 %6.23 10 ?? × × ×+ × × × = 3 kg/m20.1= ` ?6-3 ?X 8￥a < 8￥a < B B . ?X 8￥±4 ? ?X 8￥±4 ? (1) |s0 AT1é? |s0 AT1é? (2) " ·?s0-W#s0D ? " ·?s0-W#s0D ? CWMoT¨ ? V- {?9 CWMoT¨ ? V- {?9 (3) |s0 AT ^? ???l o |s0 AT ^? ???l o (4) s0?NVü? ?D? pb s0?NVü? ?D? pb (1) ??s0) ?  bW = ?B?￥ ??s0) ?  bW = ?B?￥ + qM] ?B??ís0 ? á + qM] ?B??ís0 ? á (M?b (2) ??s0_ò?Z_?￥+ qM ??s0_ò?Z_?￥+ qM ] ] ' ' 8s0￥ ?ò?Z_ 8s0￥ ?ò?Z_ ￥s ￥ò? ü (′M?b ￥s ￥ò? ü (′M?b = = .d9L ! d9L ! ? ? 222 zyx vvv == ` 1 l 2 l 3 l 1 A 2 A B?s0D C B?s0D C A 1 · óí óí A 1 ￥ 1 ￥ 1 x mv2 B e =B?s0￥ B e =B?s0￥ Q ·óí Q ·óí A 1 ￥ ￥  1  1 1 2 1 /2 1 2 l mv vl mv x x x =? ? ? .a < T a < T y x z v v x v y v z v N?s0B e =óí ?s0B e =óí A 1 ￥ 1 ￥ 1 1 2 1 2 2 1 2 1 l mv l mv l mv tF Nxxx +++=?? L ∑ = i ix v l m 2 1 ∑ =∴ i ix v l m F 2 1 1=?tQ A 1 ￥a < ￥a < 32 ll F p = N vvv V Nm Nxxx 22 2 2 1 +++ ?= L 2 x vnm?= ∑ = i ix v lll m 2 321 222 zyx vvv ==Q 2 3 1 v= ∑ = i ix v l m F 2 1 2 3 1 vnmp =∴ 2 2 1 vm t =ε ?l ?l s0￥ ü s0￥ ü ( ü?? ? ( ü?? ? 1 1 ? ? ? ? ? ? = 2 2 1 3 2 vmnp t nε 3 2 = 5 5 ` ! ! N 1 1 M kg 8￥s0 ? 8￥s0 ? N o 1 1 1 mol 8￥s0 ? 8￥s0 ? m 1B?s0￥é  1B?s0￥é  ?6-4 ?X 8￥? ?X 8￥? NmM =Q mNM 0mol = V RT M M p mol =∴ T mN R V Nm o ??= nkT= nkTp =' ' 0 N R k= nkTp = t np ε 3 2 = t np ε 3 2 = nkT= kT t 2 3 =∴ε ?￥'é ?￥'é ? ^s0 ? ^s0 ü ( ü?? ?￥  ü ( ü?? ?￥  ?6-5 ? ?1? (s? ? ? ?1? (s? ? (Principle of the equipartition of energy) s0? ? ü?? ? = ?? ? + ??? ? + B B .1? (degree of freedom) ??B?t8 bW￥ê? ?3 ??B?t8 bW￥ê? ?3 ￥? ?US￥ ? " ￥? ?US￥ ? "   ?Q? ? ?Q? ? ￥1??b ú ú $K?E?  $K?E?  ?1?1 ?1?1 1 }/ }/ B ￡ ü ?  B ￡ ü ?  ?1?1 ?1?1 2 f f  b?f?1  b?f?1 ?1 3 1.D8￥1? D8￥1? x y z C 'x 'y 'z α β γ A θ 6?1? ?1? 3??1? ??1? 3? ü?1? ),,( zyx D8 ? D8 ? CAà? à? θ γβα ,, CA￥Zê ￥Zê ? ? ? ? ^? ?￥ ^? ?￥ ? ? ? ?? ?? C￥ê? ￥ê? 2. 8s0￥1? 8s0￥1? è?/ V? I ns0￥?? è?/ V? I ns0￥?? ü?1? ?1? ?1? 99 99 ?e0s0 ?e0s0 ?e0s0 ?e0s0 ?e0[ s0 ?e0[ s0 30 3 3 2 5 3 3 6 kT t 2 3 =ε = = . ? ?1? (se ? ? ?1? (se ? 2 2 3 x vm= kT 2 3 = 2 2 1 vm t =εQ 222 2 1 2 1 2 1 zyx vmvmvm ==∴ kT 2 1 = ?? ü?1?￥? ?1 ?? ü?1?￥? ?1 2 kT 8s0 ?B 8s0 ?B ü?   ? ? 1? ￥ ü (? ???? ￥ ü (? ???? 2 kT ---- ? ?1? (s? ? ? ?1? (s? ? kT i k 2 =ε 1?1 i￥ ?? ￥ ?? s0￥ ü (9? ?1 s0￥ ü (9? ?1 ? ? . ?X 8￥ ?X 8￥ = ? (Internal energy of ideal gases ) 8 = ? = + s0WMoT¨ ] ? s0WMoT¨ ] ? s0? ? s0? ? 1mol ?X 8￥ = ? ?X 8￥ = ? kT i NE 2 0mol ?= RT i 2 = 0 N R k = M kg ?X 8￥ = ? ?X 8￥ = ? RT i E 2 mol = RT i RT i M M E ν 22 mol =?= ---- ?X 8 = ? ^ ?X 8 = ? ^ ?￥?′f ? ?￥?′f ? [ è è 3] ?  =?μ ?  =?μ 1 mol￥ ? 8? ￥ ? 8? V?? { ? V?? { ? ￥ ￡ ?¤ ￥ ￡ ?¤ ? 6 ? 6 10K  p? 8s0￥1?b p? 8s0￥1?b J1009.2 2 × TR i M M EQ ??=?= 2 mol 3 3 { ?￥ ￡ ?1 8 = ?￥9  { ?￥ ￡ ?1 8 = ?￥9  TMR QM i ?? = mol 2 1031.8 1009.22 2 × ×× = 5= [ è è 4]é  é  0.1 Kga? ? T=300K￥? ￥?   ?   ? V=0.01m 3 ￥ ? ? ￥ ? ? ? [ ? q ? [ ? q T ?°L T ?°L ? ? ? l ?T/ ?s0?_ ? ? ? l ?T/ ?s0?_ ?￥? ? ???1s0 ￡?￥ ?￥? ? ???1s0 ￡?￥ ? ?5 ü?a? ￥??a <ò ? ?5 ü?a? ￥??a <ò 9F $ 9F $ m/s100=v 3 3 s0?_?￥? ?YV · s0?_?￥? ?YV · ?1s0 ￡?￥? ? ?1s0 ￡?￥? ? TR i M M E ???=? 2 mol ? ? 22 1001.0 2 1 2 1 ××==? MvE RT i M M E 2 mol ?= J500= 531.81.0 10285002 3 ×× ××× = ? MRi EM T mol 2? =? C7.6 °= ? 8?M ? 8?M RT M M pV mol =Q T VM MR p ? ? =?∴ mol 7.6 01.01028 31.81.0 3 × ×× × = ? Pa100.2 4 ×= ?6-6 ? X ?3 ? qs? p ? X ?3 ? qs? p B B .s0 ? qs?￥?? s0 ? qs?￥?? l v v ω ? á ? á ? ?  ?  ? ? à ?+6 L ?+6 L v l t =Q ω ? = lv ω ? =∴ ---- VYV ? VYV ? = = . 8s0 8s0 ? qs?f ? ? qs?f ? (function of distribution of speeds) ? q ? q v ?í?ê ? q uW =￥s ?í?ê ? q uW =￥s 0 ?]9s0 ?￥?s1 0 ?]9s0 ?￥?s1 vN N vf v d d )( = ' ' ----Q?s0 ? qs? Q?s0 ? qs? v ?í? ?í? ê ? q uW =￥à qvl ê ? q uW =￥à qvl   v 1 --v 2 uW uW ∫ = ? 2 1 d)( v v vvf N N )(vf v O vd 1 v 2 v   v--v+dv uW￥s0 ? uW￥s0 ? ]9s0 ?￥?s11 ]9s0 ?￥?s11 vvf N N v d)( d = ∫ ∞ = 0 1d)( vvf ----BB?Hq BB?Hq vN N vf v d d )( =   0 -- ∞ uW uW ? ? . ? X ?3 ? qs?? p ? X ?3 ? qs?? p 2 2 2/3 2 2 4)( ve kT m vf kT mv ? ? ? ? ? ? ? = ? π π )(vf v O ? X ?3 ? ? X ?3 ? qs? wL qs? wL p v ` 1 1 . 8s0￥ ?? ? q 8s0￥ ?? ? q 1.Kà ? ? q Kà ? ? q v p   (the most probable speed) D D f(v)￥v′?￥ ? q ￥v′?￥ ? q 7 7 kT m b 2 = 2 2 2/3 2 2 4)( ve kT m vf kT mv ? ? ? ? ? ? ? = ? π π 5 5 2 2/3 2 4)( ve b vf bv ? ? ? ? ? ? ? = ? π π 2 2/3 2 4)( ve b vf bv ? ? ? ? ? ? ? = ? π π 0 d )(d = v vf 7 7 ( ) 0)22(4 22 2 2/3 =+?? ?? bvbv vevbveb ππ kT m b 2 = 0 N R k = 01 2 =?? bv b v p 1 =∴ mol 2 M RT = m kT2 = mol 41.1 M RT ≈ vN N vf v d d )( = N Nv v v ∫ ∞ = 0 d N vvvNf ∫ ∞ = 0 d)( ∫ ∞ = 0 d)( vvvf 2 2/3 2 4)( ve b vf bv ? ? ? ? ? ? ? = ? π π vve b v bv d4 2 2/3 0 2 ? ? ? ? ? ? ? ?= ? ∞ ∫ π π v 2. ü ( ? q ü ( ? q (average speed) vve b vv bv d4 2 2/3 0 2 ? ? ? ? ? ? ? ?= ? ∞ ∫ π π vev b bv d4 2 0 3 2/3 ? ∞ ∫ ? ? ? ? ? ? ? = π π 2 2 1 b = 2 2/3 2 1 4 b b v ? ? ? ? ? ? ? =∴ π π b? = π 2 mol 8 M RT π = m kT π 8 = b v ? = π 2 kT m b 2 = mol 41.1 M RT v p ≈ mol 60.1 M RT ≈ ∫ ∞ = 0 22 d)( vvfvv vve b v bv d4 2 2/3 0 2 2 ? ? ? ? ? ? ? ?= ? ∞ ∫ π π vev b bv d4 2 0 4 2/3 ? ∞ ∫ ? ? ? ? ? ? ? = π π ∫ ∞ = 0 d)( vvvfv 2 2/3 2 4)( ve b vf bv ? ? ? ? ? ? ? = ? π π 5 8 3 b π = 3.Z (? ? q Z (? ? q 2 v (root-mean-square speed) 5 2/3 2 8 3 4 b b v π π π ? ? ? ? ? ? = m kT3 = m kT v 3 2 =∴ mol 3 M RT = mol 73.1 M RT ≈ mol 60.1 M RT v ≈ mol 41.1 M RT v p ≈ kT m b 2 = )(vf v 0 v mol 60.1 M RT v ≈ p v mol 41.1 M RT v p ≈ 2 v mol 2 73.1 M RT v ≈ [ è è 5]μ μ 0 o C ü? ?/￥ 9 ü? ?/￥ 9 ? ? q ? ? q 300 -- 310m/s uW =s uW =s 0 ?￥?s q 0 ?￥?s q 3 3 vvf N N ?= ? )( ∫ = ? 2 1 d)( v v vvf N N ? q uW?l ? q uW?l )(vf v O vd 1 v 2 v 2 2 2/3 2 2 4)( ve kT m vf kT mv ? ? ? ? ? ? ? ? ? = ? π π 2 )( 3 2 4 p v v p e v v ? = π m kT v p 2 = vvf N N ?= ? )( p v v p v v e v v p ? ?= ? 2 )( 2 )( 4 π p v v p v v e v v N N p ? ?= ? ? 2 )( 2 )( 4 π ? q uW ? q uW ?l H ?l Hv? mol 2 M RT = sm377= m kT v p 2 = sm10=?vsm300=v p v v p v v e v v N N p ? ?= ? ? 2 )( 2 )( 4 π ) 377 10 () 377 300 ( 4 2 ) 377 300 ( 2 ? = e π %0.2≈ [ è è 6] ! _ ￥?1N ! _ ￥?1N 300 o Cb p p ? q ? q 3000--3010m/s uW =￥s0 uW =￥s0 ? ? D ? qvl D ? qvl ? ? - - W￥s0 ? W￥s0 ? -1b 1 n p v 10+ p v 2 n 3 3 ?? ? q uW?l ?? ? q uW?l p v v p v v e v v N n p ? ?= ? 2 )( 2 )( 4 π p v v p v v e v v Nn p 1 )( 2 1 1 2 1 )( 4 ? ?= ? π p v v p v v e v v Nn p 2 )( 2 2 2 2 2 )( 4 ? ?= ? π 2 1 )()( 2 2 1 2 1 2 2 2 1 )( v v e v v n n pp v v v v ? ? ?= +? 2 1 )()( 2 2 1 2 1 2 2 2 1 )( v v e v v n n pp v v v v ? ? ?= +? m/s10 1 =?v m/s3000 1 =v mol p M RT vv 2 2 == 3 102 57331.82 ? × ×× = m/s2182= m/s10 2 =?v 2 1 )()( 2 2 1 2 1 2 2 2 1 )( v v e v v n n pp v v v v ? ? ?= +? 10 10 ) 2182 3000 ( 1) 2182 3000 ( 2 2 ?= +? e 776.0= [ è è 7]?8?1?è0￥? ? ?? 8 ?8?1?è0￥? ? ?? 8 s0￥?b !?8? μ s0￥?b !?8? μ N ?1?è0 ?1?è0 è0￥Kv ? q è0￥Kv ? q (n ü ? q n ü ? q )1 1 ,è0￥ è0￥ ? q ? q -W￥à q1 -W￥à q1 F v vvv d~ + ? ? ? ? ? > << = F F vv vv N vAv N N ,0 0, d4 d 2 π A1 1 è ? è ? .(1)?BB?Hq p ?BB?Hq p Ab(2)￡ ü ￡ ü è0￥ ü (? ? è0￥ ü (? ? 2 10 3 Ft mv=ε 3 3 :(1)?5i? N Av vf 2 4 )( π = 1d 4 d)( 0 2 0 == ∫∫ FF vv v N Av vvf π 3 4 3 F v N A π =∴ 3 22 34 )( F v v N Av vf ==∴ π 3 2 3 )( F v v vf = vvfvv F v d)( 0 22 ∫ = (2) v v v v F v F d 3 3 2 0 2 ∫ = 2 5 3 F v= 22 10 3 2 1 Ft mvvm ==ε [ è è 8]μ μ N? ì0F?￥"d  ? q ? ì0F?￥"d  ? q s?f ? ?m Ub p s?f ? ?m Ub p (1) pè ? pè ? a  (2) ? q ? q 1.5v 0 ~2v 0 -W￥ ì0 ? -W￥ ì0 ? ; (3) ì0￥ ü ( ? qb ì0￥ ü ( ? qb )(vf a O 0 v 0 2v v 3 3 :(1) v v a vf 0 1 )( = avf =)( 2 0)( 3 =vf ∫ ∞ = 0 1d)( vvf ?BB? Hq Hq ∫∫ =+ 00 0 0 2 21 1d)(d)( vv v vvfvvf )(vf a O 0 v 0 2v v (2) ∫ =? 0 0 2 5.1 2 d)( v v vvfNN 32 d 0 2 5.1 0 0 N v Na vaN v v === ∫ ∫∫ =+ 00 0 0 2 0 1dd vv v vav v a 0 3 2 v a =∴ vN N vf d d )( = )(vf a O 0 v 0 2v v (3) ∫ ∞ = 0 d)( vvvfv ∫∫ += 0 0 0 2 2 0 1 d)(d)( v v v vvvfvvvf ∫∫ += 0 0 0 2 0 2 0 dd v v v vvavv v a v v a vf 0 1 )( = avf =)( 2 0 9 11 v= ?6-7 s0￥ ü ( · ? q s0￥ ü ( · ? q ü (1?? B B .à Q ü ( · ? q (collision frequency) B?s0?ê HW =D  es0 B?s0?ê HW =D  es0 ·Q ?￥ ü (′ ·Q ?￥ ü (′ ü (1?? ü (1?? (mean free path) B?s0 ?? Q · ?üV ^? B?s0 ?? Q · ?üV ^? ￥ ü (′ ￥ ü (′ ` = = .9 ? 9 ? (]B ?s0 ]B ?s0 ) s0 j1??l o s0 j1??l o   μr°?1 μr°?1 d  ? q1 ? q1 , ·a ? q ˉ1 ·a ? q ˉ1 b v v 1. I nB?s0?5L? I nB?s0?5L?  ?s0á?  ?s0á? ?s0 ?s0 1 e = D  ?s0￥ ü ( D  ?s0￥ ü ( ·Q ?1 ·Q ?1 d2 d nvdZ 2 π= 2. I n ?μ￥s0?? I n ?μ￥s0?? ü ( · ? q1 8s0￥ ü (M ? q 8s0￥ ü (M ? q D D ü ( ? q ü ( ? q ￥1"1 ￥1"1 u v vu 2= d2 d nvdZ 2 2π= 3.s0￥ ü (1?? s0￥ ü (1?? Z v =λ nd 2 2 1 π = nkTp = nvdZ 2 2π= pd kT 2 2π λ =∴ [ è è 9]9 ? S ?/￥s0 9 ? S ?/￥s0 ü ( · ? q? ü (1?? b ! ! s0￥μr°?1 s0￥μr°?1 2.9?10 -10 mb 3 3 S ? S ? K273=T Pa10013.1 5 ×=p mol 8 M RT v π =Q 3 103214.3 27331.88 ? ×× ×× = sm426= kT p n= 2731038.1 10013.1 23 5 ×× × = ? 325 m1069.2 ? ×= nvdz 2 2π=∴ 19 s1028.4 ? ×= z v =λ 9 1028.4 426 × = m1095.9 8? ×= %MC` {V? {V? (Transport process) 8 ??? ü? t_? ü?￥C` ?6-8 8 =￥ %MC` 1.?4C`#? p a @ ??] a @ ??] ? 3￥C` x y A u v B u v f v f v ? S? B A B B . = ?C` (TìC` ) (internal friction) LV ü LV ü 8s0?_ 8s0?_ ?  %M ?  %M η1Tì" ? 1Tì" ? ?μ|V U = ?μ|V U = ? ??C ? ??C x y S? A u v B u v f v f v ? B A )(mu? 2.±4'é ±4'é ?0 ?0 S y u f ?±= d d η y x S? A B BA TT > A T B T S x T t Q ??= ? ? d d λ LV ü LV ü λ1 ￡? q? ￡" ?μ|V U 1 ￡? q? ￡" ?μ|V U ￡ Vú?)._??) = = . ￡.? ￡.? (thermal conduct) 1.?4C`#? p 8 =? 8 =? ??] ??] 7? 3￥C` ?0 ?0 ￡ Vú?)._??) y x S? A B BA TT > A T B T ? ? . ? ? ? ? (diffusion) 1.?4C`#? p 8s0 8s0 ? á ? á ? ( ? ( 7? 3￥C` x A B S? BA ρρ > m? 2.±4'é ±4'é 8s0 ￡? 8s0 ￡? ? ? %M ? ? %M Q? LV ü LV ü S x D t M ??= ? ? d dρ á0 á0 8s0 8s0 é  %M é  %M D1 ? ?" ? 1 ? ?" ? μ|V UV á μ|V UV á ?v)_ á??) ? ? ?v)_ á??) ? ? x A B S? BA ρρ > 2.±4'é ±4'é m? 2006-3-22 92 [ a5  ¨ 5-1a5-2a5-3a5-4a5-5 5-6a5-7a5-8a5-9a5-10 5-11a5-12a5-13a5-14 [/ = ??? [/ = ??? ?6-9 j:% ￡s? p j:% ￡s? p B B .× ??? ì0?ú￥s? × ??? ì0?ú￥s? s0 ￡? s0 ￡? Ps0 t? ( s? Ps0 t? ( s? × ? × ? Ps0 t?_1 ?? ? Ps0 t?_1 ?? ? hh d+ h p 'p ppp ?= 'd hg dρ?= ! 8s0￥é 1 ! 8s0￥é 1 m hnmgp dd ?=∴ ü? ? H ü? ? H T))M?a < ))M?a < nkTp= nkTp dd =∴ h kT mg n n d d ?= μ μ s¤ s¤ kTmgh enn ? = 0 n 0   h = 0)￥s0 ? á )￥s0 ? á nkTp = kTmgh ep ? = 0 ú ú h) ) kTmgh kTen ? = 0 hnmgp dd ?= kTmgh enn ? = 0 = = j:% ￡s? p j:% ￡s? p p Emgh =Q ----s0￥× ? ] ? s0￥× ? ] ? kTE p enn ? =∴ 0   x--x+dx  y--y+dy  z--z+dz u× u× VnN dd = zyxen kTE p ddd 0 ? = ----j:% ￡s? p j:% ￡s? p ] ? V !Xs0? ?￥s?? ? ] ? V !Xs0? ?￥s?? ? ? %?iD %?iD ??1 ??1 2 2 mvE k = kTE k e ? ?1 ?1 T ￥ ü? 8 ￥ ü? 8 ),(d vrN vv zyxvvvCe zyx kTEE pk dddddd )( +? = ---- ? X ?3 -j:% ￡s? p j:% ￡s? p C  Dê?? ?í1￥1 èy0 Dê?? ?í1￥1 èy0 a <9 a <9 1869 M ?￡ Z ?   CO 2 é?ù?? é?ù??   CO 2 ?]?/ ?]?/ ￥??L ￥??L ?6-10 L= 8??L L= 8??L CO 2 ??a ê L a <9   A A A A  i  p v O CO 2 ??a ê L a <9   A A A A  i  p v O a <9   A A CO 2 ??a ê L A A  i  p v O a <9   A A CO 2 ??a ê L A A  i  p v O a <9   A A CO 2 ??a ê L A A  i  p v O a <9   A A CO 2 ??a ê L A A  i  p v O a <9   A A CO 2 ??a ê L A A  i  p v O CO 2 ??a ê L A A  i  p v O a <9   A A CO 2 ??a ê L A A  i  p v O a <9   A A CO 2 ??a ê L A A  i  p v O a <9   A A CO 2 ??a ê L A A  i  p v O a <9   A A  CO 2 ??a ê L A A  i p v O a <9   A A CO 2 ??a ê L A A  i  p v O a <9   A A a <9   A A CO 2 ??a ê L A A  i  p v O a <9   A A CO 2 ??a ê L A A  i  p v O A A   A A  i O L/mol)10( 3? m V atm/p   K K  "?? "?? 3.72 5.95