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1 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

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8 macroscopic thermodynamicsmicroscopic statistical mechanics temperature thermal equilibrium state quantity variable of state ABBCA C the zeroth law of thermodynamics AB BC AC -1-

9 empirical temperature Celsius temperature pressure p V Boyle s law 1 1 C 1g Avogadro s constant one mole N N A /mol p V pv RT (1.1) T K R gas constant pv (pv ) 0 (pv ) T 0 T100 T0 100 ( pv ) 0 RT 0 ( pv ) 100 RT100 ( pv ) 100 ( pv ) R pv -1-1 R 8.31 J mol K ( pv ) 0 RT0 T K 1 1K 1 A 3 --

10 T 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-

11 T T0 L L0 1 dl 0 L 0 dt T L L0 1 0( T T0) (1.6) (1.6)T l 30 1 cc / K / 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 K K T 93 K T 303 K G 6 G / V 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

12 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

13 (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 kg 160 J/K J/(kg K) J/(kg K) 7-6-

14 t ( t 18) ( ) ( 18 15) t heat conduction 1. L T 1 T T 1 S T T1 Q L T T1 Q S L thermal conductivity 1.1 L () W/(mK)

15 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

16 A B q q T1 T T T q 1 q L L T 1 T T L L L 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 W/(m K ) emissivity 0 1 black body T E T S 5770 K

17 5 8 RS km a 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

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