10.10: J- Thermodynamic Master Equations

$E(S, V, N)$

$d E=T d S-p d V+\mu d N$

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$F(T, V, N)=E-T S$

$d F=-S d T-p d V+\mu d N$

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$H(S, p, N)=E+p V$

$d H=T d S+V d p+\mu d N$

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$G(T, p, N)=F+p V$

$d G=-S d T+V d p+\mu d N$

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$\Pi(T, V, \mu)=F-\mu N=-p V$

$d \Pi=-S d T-p d V-N d \mu$

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$p(T, \mu) \text { [intensive quantities only } ]$

$d p=\mathcal{S} d T+\rho d \mu \quad[\mathcal{S}=S / V, \quad \rho=N / V]$

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