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

Answer 1

Answer: (A)

By the principle of dimensional homogeneity

$\left[p\right]=\left[\frac{a}{V^2}\right]\Rightarrow \left[a\right]=\left[p\right]\times \left[V^2\right]=\left[M{L}^{-1}{T}^{-2}\right]\left[L^6\right]$

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