Prove that where [ left(frac{partial beta}{partial P} ight)_{T}=-left(frac{partial alpha}{partial T} ight)_{P} ] (alpha=) Isothermal compressibility (beta=) Volume

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Prove that where

\[ \left(\frac{\partial \beta}{\partial P}\right)_{T}=-\left(\frac{\partial \alpha}{\partial T}\right)_{P} \]

\(\alpha=\) Isothermal compressibility

\(\beta=\) Volume expansivity.

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