CPRT/9cdc

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Energie H (eine neue Variable)

$V$ kommt, $p$ geht.

$(01)$	$dE(N,S,V)$	$=$	$+\mu dN+tdS+pd(-V)$
$(02)$	$dH(N,S,p)$	$=$	$+\mu dN+tdS-(-V)dp$
$(02)$	$dH(N,S,V)$	$=$	$+{\mu }_E^{H}dN+t_E^{H}dS+p_E^{H}d(-V)$
$(03)$	$H(N,S,p)$	$=$	$+\mu N+tS$
$(03)$	$H(N,S,V)$	$=$	$+{\mu }_E^{H}N+t_E^{H}S+p_E^H(-V)$

Variante a)

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

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

Variante b) (am einfachsten zu merken)

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

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

Variante c)

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

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