Water: Bulk Modulus and compressibility

Bulk Modulus of Liquids: The bulk modulus K of a substance is a measure of how resistant to compression that substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume

The bulk modulus of a liquid is related to its compressibility. It is defined as the pressure required to cause a unit change of volume of a liquid. Since most liquids are practically incompressible, they require very large pressures to cause any significant volume change. For most liquids, the bulk modulus is approximately in the range of 250,000–300,000 psi. The fairly high number demonstrates the incompressibility of liquids. 1gpa = 145038 psi. The inverse of the bulk modulus (K) is called the compressibility. Water has a bulk modulus of approximately 300,000 psi (2.1 GPa) and therefore compressibility of 3.3 × 10^6 (psi). 

Change in thermodynamic properties of saturated water with pressure

dH = dU  + PdV [ H is enthalpy, U is internal energy, P pressure and V is volume.

Non-compressibility of water explains why for all practical purposes when water is compressed dV = 0 and therefore dH = dU , in other words, water’s enthalpy is its internal energy. The above table is showing a dramatic increase in internal energy and therefore enthalpy as both are the same and entropy.

Internal energy and entropy increase

The reason is when water is pressurized as in the above case, because of the close molecular proximity to one another, the liquid would experience intermolecular forces resulting in more collisions and a rise in temperature. Since dV =0  there is no work component in this compression. The increase in thermal energy, therefore, gets added to the internal energy of water and that explains why the internal energy of water increases when water is compressed. More energy gives greater entropy and randomness of the atoms and molecules and increases entropy.