Question

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^2

The 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 1

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.