Bulk modulus under isothermal (constant temperature ) compression/decompression thermodynamic process:

K_T = \rho \cdot \left( \frac{\partial p}{\partial \rho} \right)_T

Isothermal bulk modulus is material property and is inverse to Isothermal Compressibility :

K_T = \frac{1}{\beta_T}

See also

Physics / Mechanics / Continuum mechanics /  Continuum body / Bulk modulus

[ Isothermal Compressibility ]