Why are W and V interchangeable in the Boltzman formula?

[Leo_Navejas_3B]

In lecture we saw that
So why is that the same as ?

[mikezargari]

I believe because W is simply the number of different ways or combinations in which atoms can in a sense exist. Using that definition of W we can assume that if the volume has doubled then so have the number of different ways in which the atoms can orient themselves. If V2/V1 = 2/1 then W2/W1 = 2/1.

[Sophia Rawson 1C]

I don't know that they will always be interchangeable but in the example given during lecture the degeneracy (W) was interchangeable with volume because he said that the volume doubled. Doubling the volume therefore making 2x the available positions. This means that V2/V1=2 and W2/W1 are both equal to 2.