The equation of state of a real gas is expressed as left(P + dfrac a V^2 right)(V - b) = RT, where P is pressure, V is volume, T is absolute temperature, and a, b, R are constants. What are the dimensions of the constant a?

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NEET Physics QUESTION #7217

Question 1

The equation of state of a real gas is expressed as $\left(P + \dfrac{a}{V^2}\right)(V - b) = RT$, where $P$ is pressure, $V$ is volume, $T$ is absolute temperature, and $a$, $b$, $R$ are constants. What are the dimensions of the constant $a$?

$[ML^5T^{-2}]$✔️
$[ML^{-1}T^{-2}]$
$[L^3]$
$[L^6]$

Correct Answer Explanation

Since quantities added or subtracted must have the same dimensions, $\dfrac{a}{V^2}$ must have the same dimensions as pressure $P$.

$[P] = [ML^{-1}T^{-2}]$ and $[V^2] = [L^6]$

Therefore: $[a] = [P][V^2] = [ML^{-1}T^{-2}][L^6] = [ML^5T^{-2}]$

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