The dimensional formula of constant a in van der Waals gas equation (p+(a/V2))(V-b)=R T is :

Question

The dimensional formula of constant a in van der Waals gas equation (p+(a/V2))(V-b)=R T is : (A) [M L3 T-2] (B) [M L5 T-2] (C) [M L2 T-1] (D) [M L-2 T5]

Tardigrade Admin · Accepted Answer

Pressure P and (a/V2)(V= volume) must have same dimensions ∴ dimensions of [ P ]= dimensions of [(a/V2)] ⇒ dimensions of [a] = dimensions of [P V2] =[M L-1 T-2] ×[(L3)2] =[M L5 T-2]

Q. The dimensional formula of constant a in van der Waals gas equation $(p + \frac{a}{V ^{2}}) (V - b) = RT$ is :

$[M L^{3} T^{- 2}]$

$[M L^{5} T^{- 2}]$

$[M L^{2} T^{- 1}]$

$[M L^{- 2} T^{5}]$

Pressure $P$ and $\frac{a}{V ^{2}} (V =$ volume) must have same dimensions
$∴$ dimensions of $[P] =$ dimensions of $[\frac{a}{V ^{2}}]$
$\Rightarrow$ dimensions of $[a] =$ dimensions of $[P V^{2}]$
$= [M L^{- 1} T^{- 2}] \times [(L^{3})^{2}]$
$= [M L^{5} T^{- 2}]$

Q. The dimensional formula of constant a in van der Waals gas equation (p+V2a​)(V−b)=RT is :

[ML3T−2]

[ML5T−2]

[ML2T−1]

[ML−2T5]