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The equation of state of some gases can be expressed as Vander wal equation that is $(P + a / V_{2}) (V - b) = R T$ ; where p is the pressure, V is the volume, T is the absolute temperature and a,b, R are constants. The dimensions of ‘a’ are:

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

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

$[M^{2} L^{5} T^{- 1}]$

$[M^{1} L^{5} T^{- 2}]$

answer is D.

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Detailed Solution

$\frac{a}{V^{2}} =$ corrected term of pressure, therefore dimensions of this is equal to dimensions of pressure $[M L^{- 1} T^{- 2}]$

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

$Therefore dimensions of a = [M^{1} L^{5} T^{- 2}]$

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