If the vander waal equation has only one root, what is the relation between a and b?(a) 729a = pb^2(b) 243a = pb^2(c) 81a = pb^2(d) 9a = pb^2The question was asked in unit test.I'm obligated to ask this question of Equations of State topic in chapter Real Gases: Equations of State, Single Component Two Phase Systems, Saturation & Condensation of Basic Chemical Engineering

If the vander waal equation has only one root, what is the relation be

1.	If the vander waal equation has only one root, what is the relation between a and b?(a) 729a = pb^2(b) 243a = pb^2(c) 81a = pb^2(d) 9a = pb^2The question was asked in unit test.I'm obligated to ask this question of Equations of State topic in chapter Real Gases: Equations of State, Single Component Two Phase Systems, Saturation & Condensation of Basic Chemical Engineering
Answer» The correct option is (a) 729a = pb^2 To elaborate: Vander WAAL equation, V^3 – (NB + nRT/p)V^2 + (N^2a/p)V – n^3ab/p = 0, comparing with (V – Vc)^3 = 0, => 3n(a/p)^1/2 = n(ab/p)^1/3, => 729a = pb^2.

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