The equation of state for a real gas at high temperature is given by P = (nRT/V - b) - a/T1/2V(V + b) where n, P, V & T are the number of moles, pressure, volume & temperature respectively & R is the universal gas constant. Find the dimensions of constant a in the above equation.

Dear Student,
Equation given by you can be simplified as


Vander Waal's equation for gas is given byP+naV2V-nb=nRTP is pressure, V is volume and T is temperature. [P] = [FA]  = [MLT 2L2] = [ML1T 2] [V] = [L3]Now, From the principle of homogeneity of dimensions,we haveP=aV2a=PV2=ML-1T-2L32=ML5T-2


Regards,

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