Question

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

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

Dimensional formula of Pressure is $\left[M^1{L}^{-1}{T}^{-2}\right]$

Dimensional formula of Volume is $\left[M^0{L}^3{T}^0\right]$

From the given equation:

$P+\frac{a}{V^2}=\frac{R\theta }{V}$

Dimensional formula of $\frac{a}{V^2}$ is same as pressure.

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

Therefore dimensional formula of a is $\left[M^1{L}^5{T}^{-2}\right]$