Question

find dimension of a and b in equation (p+a/
${v}^{2}$) (v-b)= RT p= pressure v=volume​

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

${\bigstar}\tt\:{\huge(}P+\dfrac{a}{V^2}{\huge)}(V-b)=RT$

• P denotes pressure
• v denotes volume

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find dimension of a and b.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

⛥ Only like quantities having the same dimensions can be added to or substracted from each other.

❍ Dimension of a :

$:\implies\sf\:[P]=\dfrac{[a]}{[V]^2}$

$:\implies\sf\:[a]=[P][V]^2$

$:\implies\sf\:[a]=[M^1L^{-1}T^{-2}][L^3]^2$

$:\implies\underline{\boxed{\bf{\red{[a]=[M^1L^5T^{-2}]}}}}$

❍ Dimension of b :

$:\implies\sf\:[b]=[V]$

$:\implies\underline{\boxed{\bf{\blue{[b]=[L^3]}}}}$