What is the dimensional formula of in the equation where letters have their usual meaning.

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Solution

Q.
What is the dimensional formula of $a b^{- 1}$ in the equation $(P + \frac{a}{V^{2}}) (V - b) = R T,$ where letters have their usual meaning. [2024]

1 $[M^{6} L^{7} T^{4}]$

2 $[M L^{2} T^{- 2}]$

3 $[M^{- 1} L^{5} T^{3}]$

4 $[M^{0} L^{3} T^{- 2}]$

Ans.
(2)

   $[V] = [b]$ It means the dimension of $b = [L^{3}]$

   $[P] = [\frac{a}{V^{2}}] \Rightarrow [a] = [P V^{2}] = [M L^{- 1} T^{- 2}] [L^{6}]$

Dimension of $a = [M L^{5} T^{- 2}]$

   $∴ a b^{- 1} = \frac{[M L^{5} T^{- 2}]}{[L^{3}]} = [M L^{2} T^{- 2}]$

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