Question

The equation of the state of a gas is expressed as (P+a/V) (V-b) = nRT, where
P=pressure, V=volume, T=temp and na,b,R are constants. The dimensions of 'a' will
be...?​

Answer 1

Given :

➳ The equation of the state of a gas has been been provided.

$\bigstar\:\boxed{\bf{(P+\frac{a}{V})(V-b)=nRT}}$

• P = pressure
• V = volume
• T = temperature
• n, a, b and R are constants

To Find :

➺ Dimensions of a.

SoluTion :

✴ Dimension formula :

$:\implies\bf\:Pressure(P)=[M^1L^{-1}T^{-2}]$

$:\implies\bf\:Volume(V)=[L^3]$

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

$\leadsto\sf\:[P]=\dfrac{[a]}{[V]}$

$\leadsto\sf\:[a]=[P][V]$

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

$\leadsto\underline{\boxed{\bf{\purple{[a]=[M^1L^2T^{-2}]}}}}$