While deriving ideal gas equation - we take gas molecules to be contained in a cubical container (convinent shape) , but how do we derive it for a gas inside some arbitarily shaped container ? i think this has 2 answers 1) Using maths - but it will be mostly impossible 2) or it will be a therotical proof (this is what i am intrested to know) i could think of the ''therotical'' proof - Check it wheather its right inside an arbitarily shaped container we can assume an imaginary cube shaped container (with imaginary boundaries , of course ! ) and i think that, the existence of those imaginary boundaries can be justified owing to large number of intermolecular collisions , in sense - the place where we have assumed the imaginary boundaries of the cube-shaped container , right there the randomly moving molecules are colliding so fast and so much that , resultantly we can assume a wall existing right there. And hence again do the same cubical container proof So is this right ? And some other ideas of anybody ?