Heat capacity of gases at pressure and critical behavior: Pick the incorrect statement regarding Cp of gases at elevated pressures and near the critical point.

Introduction / Context:
Real-gas heat capacities deviate from ideal behavior as pressure increases, and they exhibit singular behavior near the critical point. Knowing which qualitative statements hold is important for process design and property estimation in compressors, heaters, and reactors.

Given Data / Assumptions:

• Pure gases away from strong associating effects.
• Comparison across moderate pressures and near the critical region.
• Qualitative trends are sought, not exact numbers.

Concept / Approach:
At modest pressures and temperatures above the critical, Cp changes with pressure are usually small; many engineering calculations neglect them. Near the critical point, thermodynamic response functions such as Cp can become very large and, in the limit, diverge. A blanket claim that Cp increases substantially for all gases with pressure is incorrect and overgeneralized.

Step-by-Step Solution:
Assess (a): Reasonable engineering approximation—often negligible at moderate pressures above Tc.Assess (b): Overstated and not universally true; some gases show small changes or non-monotonic trends.Assess (c): Correct; Cp diverges at the critical point for pure fluids.Therefore, the single incorrect statement is (b).

Verification / Alternative check:
Equations of state and corresponding-states charts show Cp anomalies near criticality and mild pressure dependence away from it, validating (a) and (c) while refuting (b).

Why Other Options Are Wrong:
(a) and (c) are acceptable generalizations; (d) cannot be true because at least one statement ((c)) is correct.

Common Pitfalls:

• Assuming ideal-gas Cp everywhere; ignoring critical-region anomalies.
• Overgeneralizing pressure effects without considering temperature relative to Tc.

Final Answer:
For all gases, Cp increases substantially with pressure above atmospheric pressure.