Question

The equation of state of a real gas is given by $\left( P + \frac{a}{V^2} \right)(V - b) = RT,$ where $P, V$ and $T$ are pressure, volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\frac{a}{b^2}$ is similar to that of :

• A. PV
• B. R
• C. RT
• D. P

Answer 1

Answer: (D)

P

Answer 2

In the given equation of state for a real gas:

$\left( P + \frac{a}{V^2} \right) (V - b) = RT,$

the term $\frac{a}{V^2}$ must have the same dimensions as pressure $P$ since it is being added to $P$.

The dimensional formula of pressure $P$ is:

$[P] = [F][A^{-1}] = [M][L^{-1}][T^{-2}],$

where $F$ is force and $A$ is area. Therefore, the dimensions of $\frac{a}{V^2}$ must also be the same as $P$.

Since $\frac{a}{V^2}$ has the same dimensions as pressure

The correct option is (D) : P