What state of matter is least compressible?
solids are least compressible.
The least compressible state of matter is a solid. But even solids may be compressed slightly. A Neutron Star consists of matter so compressed that it is now composed only of neutrons. And of course, in a Black Hole, things are more compressed again. But both neutron Star and Black Hole are degenerate matter - they are no longer considered ordinary matter.
The state of matter than has the least internal kinetic energy (the kinetic energy of all the internal particles relative to the center of mass of the system), or the least internal + macrosopic kinetic energy, is the same state as "Which state of matter has the least thermal energy?". (hint: it's not the gaseous state). However, if you are asking what state of matter has the least macroscopic kinetic energy: Every state of matter…
Of the various states of matter (solid, liquid, and gas being the most common here on Earth; if we include stars, plasma is the most common state, and then there are exotic states such as degenerate matter in neutron stars) gas is the most compressible. In a gas, the particles are relatively far apart, they are not connected to each other or in contact with each other in any way, and they can all move…
No state of matter is incompressible. Solids and liquids tend to be sparingly compressible at common pressures. When you get to pressures found in the core of a neutron star, nothing can withstand the force and the nuclei merge and the electrons are stripped away and the material becomes unimaginably dense--even denser than Sean Penn...whoops, did I say that?
A change in volume is a change in volume - there is no difference. The question, as asked, is therefore meaningless. However if you try to compress air, its volume will decrease (because the gaseous state of matter is compressible). On the other and if you try and compress a liquid the volume will not change as the liquid state of matter is incompressible (that is why/how hydraulic machines work).