Question

Why an ideal gas cannot be liquefied?

Answer 1

he concept of liquefaction of gases works on the principle 
of inter molecular forces of attraction between the gas molecules.Gases liquefy when these forces increase between the molecules , binding them together. But an ideal gas is one where the molecules do not influence each other. the explanation comes from joule Thompson effect. when a gas is passed through a narrow tube, and allowing to expand in the available volume, the molecules lose their kinetic energy to overcome the forces of attraction . this causes them to come together. But such a thing doesn't work with ideal gases because they obey all the laws at all conditions ( especially boyle's law in this case). So that's the reason you cant liquefy an ideal gas. mathematically speaking the compressibility factor is 1.So that's another reason.(Also ideal gases don't exist anyway!).

Answer 2

Gases can be liquified under extreme pressure. but ideal gases are assumed to be incompressible hence they cannot be compressed and liquified