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

One way of writing the equation of state for real gases is : PV=RT[1+(

1.	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» SOLUTION :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)`