Question

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`.

Answer 1

According to the van der Waals equation,
`(P+(a))/(v^(2))(V-b)=RT`
or `P=(RT)/(V-b)-(a)/(V^(2))`
or `Pv=(RTV)/(V-b)-(a)/(V)`
or `Pv=RT(1-(b)/(V))^(-1)-(a)/(V)=RT(1+(b)/(V))-(a)/(V)`
Neglecting higher powers of `b//V`
or `PV=RT(1+(b)/(V)-(a)/(VRT))=RT[1+(1)/(V)(b-(a)/(RT))]`
Comparing with the given form of the equation, we get
`B=b-(a)/(RT)`