Question

(p+a/v2) (v-b)=rt,find the dimensions of a and b?

Answer 1

it is given that, $\left(P+\frac{a}{V^2}\right)(V-b)=RT$

we have to find the dimension of a and b.

we know, dimension of Pressure, P = [ML-¹T-²]

dimension of volume , V = [L³]

from dimensional analysis,

dimension of P = dimension of (a/V²)

or, dimension of P = dimension of a/dimension of V²

or, dimension of P × dimension of V² = dimension of a

or, dimension of a = [ML-¹T-²][L³]² = [ML^5T^-2]

hence, dimension of a = $[ML^5T^{-2}]$

again, dimension of V = dimension of b

or, [L³] = dimension of b

hence, dimension of b = [L³]

[ note : dimension of universal gas constant, RT = [ML²T-²]

dimension of universal gas constant, RT = [ML²T-²] [ here R is universal gas constant and T is temperature. you should keep in mind that dimension of product of R and T = dimension of energy ]