# Need credible source on proof that Van der Waals equation coefficient b if 4 times of the sum of molecular volume [duplicate]

Van der Waals equation coefficient b is approximately 4 times of the sum of the molecular volume. There are different kind of proofs for this. What I am interested in is a very simple one: the centers of two molecules must be at least twice of their radius away. Thus there is a co-volume of 4 Pi (2r)^3/3. And this divided by 2, results in 4 Pi (r)^3/3. I see this kind of argument/proof on the internet everywhere, but I want to find a credible source.

This is a paragraph I found on the Wikepedia page on Van Der Waals equation:

"The excluded volume b is not just equal to the volume occupied by the solid, finite-sized particles, but actually four times the total molecular volume for one mole of a Van der waals' gas. To see this, we must realize that a particle is surrounded by a sphere of radius 2r (two times the original radius) that is forbidden for the centers of the other particles. If the distance between two particle centers were to be smaller than 2r, it would mean that the two particles penetrate each other, which, by definition, hard spheres are unable to do."

Please tell me in which book I can find similar argument.

• Do not post a new question when the old one has been closed for the reason. This will be closed as well. Instead of that, edit the old one, address the objections and request its reopening. / Old closed question Nov 3 at 19:30
• I edited the old one but nothing happened, sorry, didn't know there is a mechanism for reopening a closed one. Nov 3 at 19:36
• There should be reopen link below the post. That should bring the question to reopen voting queue. Nov 3 at 19:44