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 constant a and b

Answer 1

According to van der Waals equation,
`(P+(a)/(V_(2)))(V-b)=RT " "rArr " " P=(RT)/(V-b)-(a)/(v_(2)) rArr " " 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)
`rArr " " PV=RT (1+(b)/(V)-(a)/(VRT))=RT[1+(1)/(V)(b-(a)/(RT))]`
Comparing with the given form of teh equation, `B=b-(a)/(RT)`