The given graph represents the variation of Z (compressibility factor`=(PV)/(nRT)`) versus P, for three real gases A,B and C. Identify incorrect statement.

Options

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

Answer

C

Explanation

van der Waals equation is
`(P+(a)/(V^(2)))(V-b)=RT`
When `a=0,P(v-b)=RT or Pv=RT+Pb`
or `(PV)/(RT), i.e., Z=1+(Pb)/(RT)`. Thus, `Zgt1` and increases with increase of pressure. Hence (a) is correct.
When b=0, `(P+(a)/(V^(2)))V=RT" or "PV+(a)/(V)=RT`
or `(PV)/(RT), i.e., Z=1-(a)/(RTV)` Thus, `Z lt 1` and decreases with increase of pressure. Hence (b) is correct.
Statement(d) is also correct. Hence, the only wrong statement is (c ).