[[Thermodynamics]] ## Maxwell Relationships | $dU = TdS- PdV$ | $(\frac{\partial T}{\partial V})_S = -(\frac{\partial P}{\partial S})_V$ | $T = (\frac{\partial U}{\partial S})_V = -(\frac{\partial H}{\partial S})_P$ | | ------------------ | -------------------------------------------------------------------------- | ------------------------------------------------------------------------------- | | $dH = TdS+ VdP$ | $(\frac{\partial T}{\partial P})_S = (\frac{\partial V}{\partial S})_P$ | $P = -(\frac{\partial U}{\partial V})_S = -(\frac{\partial A}{\partial V})_T$ | | $dG = -SdT+ VdP$ | $(\frac{\partial S}{\partial P})_T = -(\frac{\partial V}{\partial T})_P$ | $V = (\frac{\partial H}{\partial P})_S = (\frac{\partial G}{\partial P})_T$ | | $dA = -SdT+ PdV$ | $(\frac{\partial S}{\partial V})_T = (\frac{\partial P}{\partial T})_V$ | $S = -(\frac{\partial A}{\partial T})_V = (\frac{\partial G}{\partial T})_P$ | |