One way of writing the equation of state for real gases is
`PV=RT[1+(B)/(V)+….]`
where `B` is a constant. Derive an approximate expression for `B` in terms of the van der Waals constants `a` and `b`.

Explanation

According to van der Waals' equation
`[P+(a)/(V^(2))][V -b] =RT`
or ` P =(RT)/((V -b)) - (a)/(V)`
or `PV =RT [(V)/(V-b)-(a)/(VRT)]`
or `PV = RT[(1-(b)/(V))^(-1) - (a)/(VRT)]`
`:' [1 -(b)/(V)]^(-1) = 1 +(b)/(V) + ((b)/(V))^(2)+…`
`PV =RT[1+(b)/(V) + ...(a)/(VRT)]`
`PV =RT [1+(b -(a)/(RT)).(1)/(V)+...]`
`B =b - (a)/(RT)` .