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Compressibility under isentropic   (constant entropy 

LaTeX Math Inline
bodyS = \rm const
) compression/decompression thermodynamic process:

LaTeX Math Block
anchor1
alignmentleft
c_S = \frac{1}{\rho} \left( \frac{\partial \rho}{\partial p} \right)_TS = - \frac{1}{V_m} \left( \frac{\partial V_m}{\partial p} \right)_TS


Isentropic Compressibility is material property and is inverse to Isentropic bulk modulus 

LaTeX Math Inline
bodyK_S
:

LaTeX Math Block
anchorEWCN5
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\beta_S = \frac{1}{K_S}

See also

...

Physics / Mechanics / Continuum mechanics /  Continuum body / Compressibility

[ Isentropic bulk modulus (KS) ]