Question

The equation of state of some gases can be expressed as $(P+\frac{a}{V^2})(V-b)=RT$, where $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature , and $a$, $b$ and $R$ are constants. The dimensions of '$a$' are

• A. $\left[M{L}^5{T}^{-2}\right]$
• B. $\left[M{L}^{-1}{T}^{-2}\right]$
• C. $\left[L^3\right]$
• D. $\left[L^6\right]$

Answer 1

Answer: (A)

$\left[M{L}^5{T}^{-2}\right]$

Since $P$ is being added to $\frac{a}{V^2}$, thus they must have same dimensions.
Now dimension of Pressure is that of Force per unit area = $M{L}^{-1}{T}^{-2}$
Thus, $M{L}^{-1}{T}^{-2}=\frac{|a|}{L^6}$ or $|a|=M{L}^5{T}^{-2}$