Question

Find out the dimensions of the constants a and b in the Vander Waal's equation $[p+\frac{a}{v^2}](V-b)=RT$

where p is pressure, v is volume, R is gas constant and T is temperature.

$\begin{array}{cc}Column-I& Column-II\\ a& \left(i\right)\left[M{L}^5{T}^{-2}\right]\\ b& \left(ii\right)\left[M^2{L}^3{T}^{-1}\right]\\ & \left(iii\right)\left[M^0{L}^3{T}^0\right]\\ & \left(iv\right)\left[M^0{L}^2{T}^{-1}\right]\end{array}$

• A. a - (i); b - (iii)
• B. a - (ii); b - (iv)
• C. a - (iii); b - (i)
• D. a - (iv); b - (ii)

Answer 1

The correct option is A

a - (i); b - (iii)

We can add and subtract only like quantities

$\Rightarrow$ Dimensions of P = Dimensions of $\frac{a}{V^2}(\because p+\frac{a}{v^2})$ ................(1)

And dimensions of v = Dimensions of b ( ∵ v - b) .................(2)

From (1) Dimensions of a = Dimensions of P × Dimensions of $V^2$

$\left[a\right]=\left[M^1{L}^{-1}{T}^{-2}\right]\times [L^3{]}^2=[M^1{L}^5{T}^{-2}]$

From (2) $\left[b\right]=\left[v\right]=\left[M^0{L}^3{T}^0\right]$