Physics

In the gas equation, $(P +\dfrac{a}{V^2}) (V - b) = RT$ , where P is pressure, V is volume, R is gas constant and T is temperature. Calculate the dimensional formula of a and b.

SOLUTION
Given equation is,
$(P + \dfrac{a}{V^2}) (V - b)= RT$
Applying principle of homogeneity,
Dimensional formula of$\dfrac{a}{V^2}$ = Dimensional formula of P $\therefore$ Dimensional formula of a = Dimensional formula of $P.V^2$
$= [M^1L^{-1}T^{-2} . L^6]$
$=[M^1L^5T^{-2}]$
Similarly dimensional formula Dimensional formula of V =
$=[M^0L^3T^0]$

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