Question

The equation of state of some gases can be expressed as$\left(p+\frac{a}{V^{2}}\right)=\frac{R\theta}{V},$ where $P$ is the pressure, $V$ the volume $\theta$ the absolute temperature and a and b are constants. The dimensional formula of a is

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

Answer 1

Answer: (A)

By the principle of dimensional homogeneity
$\left[p\right]=\left[\frac{a}{V^{2}}\right]\Rightarrow \left[a\right]=\left[p\right]\times\left[V^{2}\right]=\left[ML^{-1}T^{-2}\right]\left[L^{6}\right]$
$=\left[ML^{5}T^{-2}\right] $