The given graph represents the variation of Z (compressibility factor = nRTPV) versus P, for three real gases A, B and C. Identify the only incorrect statement.
(A)For the gas A,a=0 and its dependence on P is linear at all pressure.
(B)For the gas B,b=0 and its dependence on P is linear at all pressure.✓ Correct
(C)For the gas C, which is 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 real gases.
Answer: (B)
Solution
From the van der Waals equation, the compressibility factor Z can be analyzed:
Gas A (Z increases linearly from Z=1): This represents a gas where attractive forces are negligible (a=0), so only repulsive forces (b≠0) matter. Statement (A) is correct.
Gas B (Z decreases then increases): This would represent a gas where b=0 but a≠0. However, the statement says b=0 AND linear dependence at all pressures, which is incorrect because the graph shows non-linear behavior for gas B. Statement (B) is incorrect.
Gas C shows typical real gas behavior with both a and b non-zero. Statement (C) is correct.
At high pressure, repulsive forces dominate for all real gases, making Z>1 with positive slope. Statement (D) is correct.
Therefore, statement (B) is the only incorrect one.
JEE Advanced · 2006 · 09 Apr 2006 · One or more correct options
