Question

The Van Der Waal’s equation of state for some gases can be expressed as: $(P+\frac{a}{V^2})(V-b)=RT$ Where $P$ is the pressure, $V$ is the molar volume and $T$ is the absolute temperature of the given sample of gas and $a,b$ and $R$ are constants.

Which of the following does not have the same dimension formula as that of $RT$ ?

• A. $PV$
• B. $Pb$
• C. $\frac{a}{V^2}$
• D. $\frac{ab}{V^2}$

Answer 1

The correct option is C $\frac{a}{V^2}$

We can say that:
$\left[PV\right]=\left[RT\right]$
$\Rightarrow$ option (a) is wrong.

As $b$ also has the same dimensions as $V$,
$\left[Pb\right]=\left[RT\right]$
$\Rightarrow$ option (b) is wrong.
For detailed solution please watch the next video.

As $\frac{a}{V^2}$ has same dimensions as that of $P$,
$\left[\frac{ab}{V^2}\right]=\left[RT\right]$
$\Rightarrow$ option (c) is correct.
$\Rightarrow$ option (d) is wrong.