Question

. In Vander Waals corrected gas equation (P + a / V²) (V – b) = n R T, where a and b are the constants. Calculate the dimensional formulae of a and b.

Answer 1

(P + a / V ² ) (V – b) = n R T

from the principal of dimensional homogeneity, Pressure p can be added to pressure term only, therfore

a / V ² should have the dimensions of pressure ie, [ M L^-1 T^-2]

here V is volume, therefore

a / V ² ---------> [ M L^-1 T^-2]

a/ [ L³ ] -----------> [ M L^-1 T^-2]

a -----------> [ M L^-1 T^-2] [ L³ ]

--------------> [ M L² T^-2]

similarly in (V-b), V is volume so 'b' needs to have dimensions of volume ie, [ L³]