CPRT/51da

< Inhaltsverzeichnis - CPRT

Energie F (eine neue Variable)

$S$ kommt, $t$ geht.

$(01)$	$dE(N,S,V)$	$=$	$+\mu dN+tdS+pd(-V)$
$(02)$	$dF(N,t,V)$	$=$	$+\mu dN-Sdt+pd(-V)$
$(02)$	$dF(N,S,V)$	$=$	$+{\mu }_E^{F}dN+t_E^{F}dS+p_E^{F}d(-V)$
$(03)$	$F(N,t,V)$	$=$	$+\mu N+p(-V)$
$(03)$	$F(N,S,V)$	$=$	$+{\mu }_E^{F}N+t_E^{F}S+p_E^F(-V)$

Variante a)

(04a) folgt aus (03) und (03a). (05a) folgt aus (02a) und (03a).

$(01a)$	$-Sdt(N,S,V)$	$=$	$+[0-S\frac{\partial t}{\partial N}]dN+[0-S\frac{\partial t}{\partial S}]dS+[0-S\frac{\partial t}{\partial (-V)}]d(-V)$
$(02a)$	$dF(N,S,V)$	$=$	$+[\mu -S\frac{\partial t}{\partial N}]dN+[0-S\frac{\partial t}{\partial S}]dS+[p-S\frac{\partial t}{\partial (-V)}]d(-V)$
$(03a)$	$F(N,S,V)$	$=$	$+[\mu -S\frac{\partial t}{\partial N}]N+[0-S\frac{\partial t}{\partial S}]S+[p-S\frac{\partial t}{\partial (-V)}](-V)$
$(04a)$	$0(N,S,V)$	$=$	$+[0-S\frac{\partial t}{\partial N}]N+[0-S\frac{\partial t}{\partial S}]S+[0-S\frac{\partial t}{\partial (-V)}](-V)$
$(05a)$	$0(N,S,V)$	$=$	$-Nd[\mu -S\frac{\partial t}{\partial N}]-Sd[0-S\frac{\partial t}{\partial S}]-(-V)d[p-S\frac{\partial t}{\partial (-V)}]$

Variante b) (am einfachsten zu merken)

(04b) folgt aus (03) und (03b). (05b) folgt aus (02b) und (03b).

$(01b)$	$-Sdt(N,S,V)$	$=$	$+[0-S\frac{\partial \mu }{\partial S}]dN+[0-S\frac{\partial t}{\partial S}]dS+[0-S\frac{\partial p}{\partial S}]d(-V)$
$(02b)$	$dF(N,S,V)$	$=$	$+[\mu -S\frac{\partial \mu }{\partial S}]dN+[0-S\frac{\partial t}{\partial S}]dS+[p-S\frac{\partial p}{\partial S}]d(-V)$
$(03b)$	$F(N,S,V)$	$=$	$+[\mu -S\frac{\partial \mu }{\partial S}]N+[0-S\frac{\partial t}{\partial S}]S+[p-S\frac{\partial p}{\partial S}](-V)$
$(04b)$	$0(N,S,V)$	$=$	$+[0-S\frac{\partial \mu }{\partial S}]N+[0-S\frac{\partial t}{\partial S}]S+[0-S\frac{\partial p}{\partial S}](-V)$
$(05b)$	$0(N,S,V)$	$=$	$-Nd[\mu -S\frac{\partial \mu }{\partial S}]-Sd[0-S\frac{\partial t}{\partial S}]-(-V)d[p-S\frac{\partial p}{\partial S}]$

Variante c)

(04c) folgt aus (03) und (03c). (05c) folgt aus (02c) und (03c).

$(01c)$	$-Sdt(N,S,V)$	$=$	$+[0+N\frac{\partial \mu }{\partial N}+V\frac{\partial \mu }{\partial V}]dN+[0+N\frac{\partial t}{\partial N}+V\frac{\partial t}{\partial V}]dS+[0+N\frac{\partial p}{\partial N}+V\frac{\partial p}{\partial V}]d(-V)$
$(02c)$	$dF(N,S,V)$	$=$	$+[\mu +N\frac{\partial \mu }{\partial N}+V\frac{\partial \mu }{\partial V}]dN+[0+N\frac{\partial t}{\partial N}+V\frac{\partial t}{\partial V}]dS+[p+N\frac{\partial p}{\partial N}+V\frac{\partial p}{\partial V}]d(-V)$
$(03c)$	$F(N,S,V)$	$=$	$+[\mu +N\frac{\partial \mu }{\partial N}+V\frac{\partial \mu }{\partial V}]N+[0+N\frac{\partial t}{\partial N}+V\frac{\partial t}{\partial V}]S+[p+N\frac{\partial p}{\partial N}+V\frac{\partial p}{\partial V}](-V)$
$(04c)$	$0(N,S,V)$	$=$	$+[0+N\frac{\partial \mu }{\partial N}+V\frac{\partial \mu }{\partial V}]N+[0+N\frac{\partial t}{\partial N}+V\frac{\partial t}{\partial V}]S+[0+N\frac{\partial p}{\partial N}+V\frac{\partial p}{\partial V}](-V)$
$(05c)$	$0(N,S,V)$	$=$	$-Nd[\mu +N\frac{\partial \mu }{\partial N}+V\frac{\partial \mu }{\partial V}]-Sd[0+N\frac{\partial t}{\partial N}+V\frac{\partial t}{\partial V}]-(-V)d[p+N\frac{\partial p}{\partial N}+V\frac{\partial p}{\partial V}]$