P + a V 2 V - b = R T represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a , b , R are the constants. The physical quantity, which has dimensional formula as that of b 2 a , will be :

Step-by-step solution

According to the principle of dimensional homogeneity, the dimensions of each terms of a dimensional equation on both sides are the same. So, dimension of b and V will be same, b = V And dimension of a V 2 and P will be same, a V 2 = P From above two relations, we have a b 2 = P ∴ b 2 a = 1 P = M L - 1 T - 2 - 1 Thus, M - 1 L 1 T 2 is the dimension of compressibility.