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KDS4

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Moved from a technical forum, so homework template missing

The question I'm stuck on is:

P = NK

Re-arrange variables in the Van Der Waals equation of state, Eq. (1), so that V always appears in the equation as V/(3Nb) and P appears as 27b2P/a. Then T should appear in the combination 27b k

I managed to get P to appear as 27b

Any insight would be greatly appreciated!

P = NK

_{B}T/(V-Nb) - aN^{2}/(V^{2}) -----> (1)Re-arrange variables in the Van Der Waals equation of state, Eq. (1), so that V always appears in the equation as V/(3Nb) and P appears as 27b2P/a. Then T should appear in the combination 27b k

_{B}T/(8a). Call these dimensionless combinations v, p, and t (also called reduced variables), and express the van der Waals equation in terms of v, p, and t.I managed to get P to appear as 27b

^{2}P/a and T to appear as 27bK_{b}T/8a using algebra and getting some pretty ugly terms along the way that are floating around but with V appearing multiple times in the initial equation I can't for the life of me get it to appear the way the question wants me to.Any insight would be greatly appreciated!