The Vander Waal’s equation of state for real gases is given as which of the following terms has dimensions different from that of energy

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$\frac{a b}{V^{2}}$

$b P$

$\frac{a}{V^{2}}$

$P V$

answer is B.

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Detailed Solution

$P V =$ [energy]

Vander Waal’s equation is $(P + \frac{a}{V^{2}}) (V - b) = n R T$

The dimensions of $\frac{a}{V^{2}}$ should be that of and is that of volume

Work done (or energy) should have the dimensions of $P V$

$∴ [\frac{a}{V^{2}} \times b] =$ [Energy]

$[b P] =$ [Energy]

$[\frac{a}{V^{2}}] = [P]$ is having dimensions different from energy

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