The given graph represents the variations of compressibility factor `Z=PV//nRT` vs `P` for three real gases `A`, `B`, and `C`.

Identify the incorrect statements.

Options

A. For the gas A , a= 0 and its dependence on P is linear at all pressure
B. For the gas B m b = 0 and its dependence on P is linear at all pressure
C. For the gas C , which iis typical real gas for which neither a nor b=0 .By knowing the minima and the point of intersection with Z = 1 , a and b can be calculated
D. At high pressure , the slope is positive for all gases

Answer

B

Explanation

Compressibility factor Z = PV/n R T
van der Waal.s equation `(p + (n^(2)a)/(V^(2)))(V-nb)` = nRT
(a) For gas A if a = 0 then :
`P(V-nb) = nRT`
`Pv - Pnb = nRT`
`(PV)/(nRT) -(Pnb)/(nRT) =(nRT)/(nRT)`
`Z - P (b/(RT))=1 rArr Z = 1 + P (b/(RT))`
The value of Z will depend on the value of P and as the value of P increases , the value of Z will increase linearly .
(b) For gas B if b = 0 then :
`(P +(n^(2)a)/(V^(2)))(V)=nRT`
`PV +(n^(2)a)/V = nRT`
`(PV)/(nRT)+(na)/(VRT) =(nRT)/(nRT)`
`Z = 1-(na)/(VRT)` So the value of Z is independent of P . But in the graph it is shown that the value of Z is dependent on linearly .So our hypothesis that b = 0 is wrong .
(c ) The value of .a. and .b. can be calculated by knowing two conditions (i) the value of minim for gas C and the intersection point at Z =1 .
(d) It is known that for all real gases `Z gt 1 ` .