Question

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

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

Answer 1

Answer: (A)

In the equation p, V and T are pressure, volume and temperature respectively.
$ \left( p+\frac{a}{{{V}^{2}}} \right)(V-b)=RT $
Dimensions of $ \frac{a}{{{V}^{2}}} $ will be same as that of pressure.
$ \therefore $ Dimensions of $ \frac{a}{{{V}^{2}}}= $ dimensions of p
$ \Rightarrow $ Dimensions of $ a= $ dimensions of $ p\,\,\times $ dimensions of $ {{V}^{2}} $ $ =[M{{L}^{-1}}{{T}^{-2}}][{{L}^{6}}] $ $ =[M{{L}^{5}}{{T}^{-2}}] $