Question

how can we demonstrate that interparticular spaces are present in a matter

Answer 1

A matter is defined as anything that has mass, which occupies space and may be perceived by senses. There are three states of matter, viz. (a) solid, (b) liquid and (c) gaseous states.
Historical Perspective of States of Matter:

Ancient Indian philosopher suggested that all the forms of matter are made up of five basic elements (they called it tatva) they called these five basic elements as ‘panch maha bhoota’. These elements are sky (Akash), air (vayu), fire (teja), water (ap) and earth (soil).
Ancient Greek philosophers considered that all for of matter are made of fire, water, air and the earth.
Thales (640-546 BC) suggested that all things arose from the water.