Question

The equation of state of some gases can be expressed as $\left(P+\frac{a}{V^{2}}\right)\left(V-b\right)=RT$, 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. $[ML^5T^{-2}]$
• B. $[M^{-1}L^5 T^2]$
• C. $[ML^{-5}T^{-1}]$
• D. $[ML^5 T^1]$

Answer 1

Answer: (A)

$[ML^5T^{-2}]$

Answer 2

By principle of dimensional homogenity, $\left[\frac{a}{V^{2}}\right]=\left[P\right]$ $\left[a\right]=\left[P\right]\left[V^{2}\right]$ $=\left[ML^{-1}T^{-2}\right]\times\left[L^{6}\right]$ $=\left[ML^{5}T^{-2}\right]$