$390.$ The Maxwell relation derived from the differential expression for the Helmholtz free energy $($dA$)$ is

$($T$/$V$)$S $=-($P$/$S$)$V

$($S$/$P$)$T $=-($V$/$T$)$P

$($V$/$S$)$P $=($T$/$P$)$S

$($S$/$V$)$T $=($P$/$T$)$V