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Maxwell's Relations of Thermodynamic Functions

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The following are Maxwell's Relations right?

[itex]\left(\frac{\partial s}{\partial v}\right)_{T}[/itex] = [itex]\left(\frac{\partial p}{\partial T}\right)_{v}[/itex]

[itex]\left(\frac{\partial s}{\partial p}\right)_{T}[/itex] = [itex] - \left(\frac{\partial v}{\partial T}\right)_{p}[/itex]

Are these all? And BTW, these are derived from the thermodynamic POTENTIALS. Are thermodynamic POTENTIALS also called thermodynamic FUNCTIONS? Sorry for this dumb question. I just want to be sure. I'm reviewing and all the different notations from different books are really mixing up in my head.

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