Question

find the dimensions of a and b from the vander wall equation (p+a/v^2 )(v-b)=rt where p is pressure v is volume.

Answer 1

(P + a/V2) (V - b) = RT P is pressure, V is volume and T is temperature. [P] = [F/A]  = [MLT −2/L2] = [ML−1T −2] [V] = [L3] We cannot add or subtract quantities of different dimensions. Therefore [P] = [a/V2] ⇒ [a] = [PV2] = [ML−1T −2 L6] = [M L5T −2] ∴ [a] = [M L5 T −2] Similarly, [b] = [V] =  [L3]