国際物理オリンピック 研修用テキスト Ⅲ 熱物理 相対論 量子力学 特定非営利活動法人物理オリンピック日本委員会
1 1.1 1 1. 1.3 3 1.4 4 1.5 6 1.6 7 1.7 9 11.1 11. 0.3 1 6 3.1 6 3. -9 3.3 - -- 31 3.4 --33 39 4.1 39 4. 40 4.3 4 4.4 44 4.5 47 5 5.1 5 5. 5 5.3 54 5.4 55 5.5 57 5.6 57 i
5.7 58 5.8 61 63 6.1 63 6. 63 6.3 65 6.4 66 6.5 68 6.6 69 6.7 71 74 7.1 74 7. 80 84 8.1 84 8. 85 8.3 87 A 91 A.1 91 A. 93 B 95 C 96 D 98 101 1.1 101 1. 103 1.3 104 107.1 107. 11.3 118 ii
13 3.1 13 3. 17 3.3 134 3.4 137 140 4.1 140 4. 141 4.3 144 4.4 146 4.5148 155 5.1 ()155 5. 157 5.3 161 5.4 163 5.5 165 173 6.1 173 6. 176 6.3 178 1 181 1.1 181 1. 186 1.3 188 1.4 191 1.5 197 1.6 0 1.7 06 1.1 1 iii
. 16.3 0.4 7.5 3 1,,47 3,8 iv
1
macroscopic thermodynamicsmicroscopic statistical mechanics temperature thermal equilibrium state quantity variable of state ABBCA C the zeroth law of thermodynamics AB BC AC -1-
empirical temperature 0 100 100 Celsius temperature pressure p V Boyle s law 1 1 C 1g Avogadro s constant one mole N N A 6. 0 10 3 1/mol p V pv RT (1.1) T K R gas constant 0 100 pv (pv ) 0 (pv ) 100 0 100 T 0 T100 T0 100 ( pv ) 0 RT 0 ( pv ) 100 RT100 ( pv ) 100 ( pv ) R 0 100 pv -1-1 R 8.31 J mol K ( pv ) 0 RT0 T 0 73. 15 K 1 1K 1 A 3 --
T 73. 15 1 85 15 K 1. pv n p V T n pv nrt (1.) (1.)ideal gas(1.) equation of state of ideal gas T T absolute temperature thermal expansion coefficient of linear expansion coefficient of volume expansion L T 1 dl (1.3) L dt V T 1 dv (1.4) V dt L T V 3 L 3 V L 1 dv V dt 1 3 L dl dt 3 (1.5) 4-3-
T T0 L L0 1 dl 0 L 0 dt T L L0 1 0( T T0) (1.6) (1.6)T 0 0 1.101l 30 1 cc 3. 5 10 4 1/ K 5. 5 10 6 1/ K 1.1 T V G G VG V0 1 G ( T T0 ) T 0 V 0 T V W T 0 V 0 W VW V0 1 W ( T T0 ) V V V 4 W / W W W V ( )( T T ) V W 3. 5 10 1 K 5. 5 10 1 K T 93 K T 303 K G 6 G / V 0 1000 cc V W 3.4 cc T p V p, V, T f ( p, V, T ) 0 (1.7) equation of state(1.7)v T p p V T G 0 0 0 5-4-
p, V, T dp dt dv V V dv dp dt p (1.8) T p T V (1.8)V p, T V V ( p, T ) (1.4) V 1 (1.4a) V T V (1.8) p T isothermal compressibilityk T 1 V kt V p (1.9) T (1.8) 0 k T V p T p (1.10) T V V kt p thermal pressure coefficient k T k T (1.) 1 V V T p 1 nr 1 1 V 1 nrt k T V p T V p V p 6-5- p T T 1 p
(1.10) kt p T V nr V p T (1.) van der Waals equation of state a p V b RT (1.11) V V 1a, b (1.) A B A B heat heat quantity J 1K heat capacityc 1 kg 1K specific heatc c m C C mc c m t Q mct J/K J/(kg K) 0.10 kg 15 18 0.50 kg 160 J/K 3 4. 10 J/(kg K) 4. 5 10 J/(kg K) 7-6-
t 18 15 18 0. 10 4. 5 10 ( t 18) ( 0. 50 4. 10 160) ( 18 15) t 169 3 heat conduction 1. L T 1 T T 1 S T T1 Q L T T1 Q S L thermal conductivity 1.1 L 1. 1.1 () W/(mK) 0 04 0 95 0 418 0 386 0 67 10 0.58 0.550.75 0 0.048 1-7-
1.3 x x x dx A, B A x q A T 1.3 x T q (1.1) x T T T B T dx dx B dt x x x x x T T dx dt x x A B AB c AB dt AB c dx dt T T T dt x dx dt c dx dt x x T T (1.13) t c x (1.13)heat conduction equation 1.4 L 1, L 1, C A T 1 B T T1 T C T 1.4-8-
A B q q T1 T T T q 1 q L L T 1 T T L L L 1 1 1 1 L1 heat convection heat radiation P thermal emissivity T P S T 4 P 4 P ST (1.14) Stefan-Boltzmann law Stefan-Boltzmann constant 8 5. 7 10 W/(m K ) emissivity 0 1 black body 1 1.5 T E T S 5770 K 10-9- 4 1.5
5 8 RS 6. 96 10 km a 1. 50 10 km H R E R E 4 4R S H A TS R 4a H H E A T 4 E E 4R H H T E A T S E E E RS 78 K 5 a 11-10-