Why doesn any substance have zero volume at zero kelvin?
I doubt this is the answer you are looking for, but physically a substance is made of matter, and matter by definition has to take up space no matter how minute that that space maybe. Therefore nothing can occupy a space consisting of measurements of 0 units. Also despite what the second answer said, it would not be a gas, liquid or solid as it nears 0 kelvin, it would be entering one of the other states of matters in this case Bose-Einstein Condensate (the 7 states of matter in increasing energy level: Bose-Einstein Condensate, Solid, Liquid, Gas, Plasma, Super heated Plasma, Ray, and finally Wave).