Question

if P,V and Tare pressure ,volume and temperature respectively of gas, then from the relation (p+a^2/v^2)(v-b)=RT find the dimension of a and b.

Answer 1

$\bold{(P + a/V^2) (V - b) = RT</p><p>P is pressure, V is volume and T is temperature.</p><p>[P] = [F/A] = [MLT^−2/L^2] = [ML^−1T^−2]</p><p>[V] = [L^3]</p><p></p><p>We cannot add or subtract quantities of different dimensions. Therefore</p><p>[P] = [a/V^2] ⇒ [a] = [PV^2] = [ML^−1T^−2 L6] = [M L^5 T^−2]</p><p>∴ [a] = [M L^5 T^−2]</p><p></p><p>Similarly,</p><p>[b] = [V] = [L^3]$