In van der Waals' gas equation (p + a/V^2) (V - b) = RT, the dimensional formula for constants a and b respectively are

Question

In van der Waals' gas equation \(\left(p +\frac{a}{V^2}\right)(V-b) = RT\), the dimensional formula for constants a and b respectively are 

(A) [ML³T^-2], [ML^-1]

(B) [ML⁵T^-2], [L³]

(C) [L³], [ML⁵T^-2]

(D) [ML^-1], [ML³T^-2]

Answer 1

Correct option is (B) [ML⁵T^-2], [L³]

Given, \(\left(p +\frac{a}{V^2}\right)(V-b) = RT\)

Dimension of b = Dimension of V

= [L] x [L] x [L]

= [L³]

Dimension of p = Dimension of a/V²

⇒ Dimension of a = p x V²

⇒ Dimension of F/A x V²

⇒ Dimension of a = \(\frac{[MLT^{-2}]}{[L^2]}\times [L^3]^2\)

= [ML⁵T^-2]