### Units And Dimensions Question 3

#### Question 3 - 2024 (27 Jan Shift 2)

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 :

(1) PV

(2) $P$

(3) RT

(4) $R$

## Show Answer

#### Answer: (2)

#### Solution:

$[P]=\left[\frac{a}{V^{2}}\right] \Rightarrow[a]=\left[PV^{2}\right]$

And $[V]=[b]$

$\frac{[a]}{\left[b^{2}\right]}=\frac{\left[PV^{2}\right]}{\left[V^{2}\right]}=[P]$