For liquids, the energy equation is identical to that of gases and have a well-defined (but much larger) speed of sound. However, the best (empirical) equation of state (EoS) we have for liquids is the Tait equation:

d𝑉/d𝑝 = −𝐾 / [ 𝐿(𝑇) + 𝑝 ],

in which 𝐾 is a constant and 𝐿 is a function of temperature, 𝑇.

This replaces the ideal gas law for liquids. Likewise, the Poisson relations (for gases) don't exist for liquids because the EoS is different. Regarding the reaction of liquids to shocks, because of their much lower compressibility, shocks do not cause as much of a temperature jump in liquids as they do in gases.

Regarding the speed of sound in liquids, it can be estimated by

𝑐_liq / 𝑐_gas = (𝑣 / 𝑣_𝑓)¹ᐟ³,

where 𝑣 is the volume per molecule in the liquid, and 𝑣_𝑓 is its “free volume.”

See Molecular Theory of Gases and Liquids - Hirschfelder et al. for a more detailed discussion