Vander waals方程 p+aln (V-nb)=nRT 不可压缩项 分子间吸引力项
Vander Waals 方程 V nb nRT V n p a − = + ( ) 2 不可压缩项 分子间吸引力项 1
p+a (V-nb)=nRT nRT →p= C V-nb b nRT + 2an o丿(-mb)2 a2 2nrt -ban av2(V-nb
4 2 2 3 2 3 2 2 2 2 1 6 ( ) 2 1 2 ( ) ( ) V an V nb nRT V p V an V nb nRT V p V n a V nb nRT p V nb nRT V n p a T T − − = + − = − − − = − = + 1
临界点K处2 0 ap 0 nrT K-t2an 0 (K -nb K 2nRTK 6an 0 (K-nb) 4 K 2 2an(vx-nb) K RV K 3H(~hb)3 K RV K
− = − = − = − + = − − = = = = 4 3 3 2 4 2 3 3 2 2 2 2 3 ( ) 2 ( ) 0 1 6 ( ) 2 0 1 2 ( ) 0; 0 K K K K K K K K K K K K T T T T RV an V nb T RV an V nb T V an V nb nRT V an V nb nRT V p V p K K K 临界点 处, 1
两式相除得:3/x-nb)=2Vk = 3nb 8a K=27Rb227b2 (人=°,普适临界系数) pxk 3
) 3 8 ( 27 ; 27 8 3 两式相除得: 3 2 2 = ,普适临界系数 = = = − = K K K K K K K K p V RT b a p Rb a T V nb (V nb) V 1
取兀 ,代入 Vander waals方程 K K m K+a/、々 oVk -nb=nRtlk K →丌 (o3nb-nb)=nRt 27b o3nb 27 R6 →x+2(30-1)=8,无量纲普适方程
,无量纲普适方程 取 ,代入 方程 (3 1) 8 3 27 8 ( 3 ) 27 3 ( ) , , Vander Waals 2 2 2 2 − = + − = + − = + = = = Rb a nb nb nR nb n a b a V nb nR T V n p a T T V V p p K K K K K K K 1