When is the pressure effect on the heat capacity of gases negligible?

Introduction / Context:
Gas heat capacities (Cp and Cv) depend mainly on temperature for ideal gases and only weakly on pressure at sufficiently low pressures. Recognising when pressure corrections can be neglected simplifies calculations and avoids unnecessary complexity.

Given Data / Assumptions:

• Ideal-gas behaviour holds near 1 atm (or lower) for many gases away from condensation regions.
• Critical temperature alone does not determine pressure dependence of Cp.

Concept / Approach:
In the ideal-gas limit, Cp and Cv are independent of pressure. Real-gas deviations increase with pressure and proximity to phase boundaries. Thus, at pressures below about one atmosphere, the pressure effect is generally negligible for many engineering estimates.

Step-by-Step Solution:

Verification / Alternative check:
Standard property tables and correlations (e.g., NASA polynomials) typically provide Cp as a function of T only for ideal-gas use, reflecting negligible pressure effect near 1 atm.

Why Other Options Are Wrong:

• (b): Being below the critical temperature does not inherently ensure negligible pressure effects.
• (c) and (d): Include the incorrect condition or deny the correct one.

Common Pitfalls:
Applying high-pressure corrections unnecessarily in low-pressure design problems, complicating the analysis without benefit.

Final Answer:
at pressures below one atmosphere