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Dimensional Analysis

The Vander wa...

Question

The Vander waal's equation for ideal gas is given by $(p + \frac{a}{V^{2}}) (V - b) = R T$ where $P$ is pressure, $V$ is volume $a$ and $b$ are constants, $R$ is universal gas constant and $T$ is absolute temperature. Then the dimensions of $\frac{a}{b}$ are same as that of:

A

Force

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B

Momentum

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C

Energy

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D

Power

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Solution

The correct option is D Energy
$\frac{a}{v^{2}} = P = M^{1} L^{- 1} T^{- 2} \Rightarrow a = M^{1} L^{5} T^{- 2}$
$B S h o u l d h a v e d i m e n s i o n o f V \to V o l u m e$
$S o, \frac{a}{b} = \frac{(M^{1} L^{5} T^{- 2})}{L^{3}} = M^{1} L^{2} T^{- 2}$
$F o r c e = M^{1} L^{1} T^{- 2}$
$M o m e n t u m = M^{1} L^{1} T^{- 1}$
$E n e r g y = M^{1} L^{2} T^{- 2}$
$P o w e r = M^{1} L^{2} T^{- 3}$
$\Rightarrow$ Option C is correct.

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