Temperature dependence of gas heat capacity: At higher temperatures, how does the molal heat capacity at constant pressure (Cp) of most gases change?

Introduction / Context:
Heat capacity trends with temperature are essential for designing heaters, coolers, and reactors. The molar heat capacity at constant pressure (Cp) of gases determines how much energy is required to raise the temperature of a flowing gas stream and strongly impacts energy balances.

Given Data / Assumptions:

• Most real gases, especially polyatomic, experience excitation of additional degrees of freedom with increasing temperature.
• Ideal-gas approximations with temperature-dependent Cp are commonly used.

Concept / Approach:
As temperature rises, rotational modes are fully excited and vibrational modes become increasingly populated, adding to the energy storage capacity. Consequently, Cp generally increases with temperature for most gases. The variation is not strictly linear over broad ranges, and correlations (e.g., polynomial Cp(T)) are used to compute enthalpy changes accurately.

Step-by-Step Solution:
Recognize that added degrees of freedom contribute to heat capacity.As T increases, vibrational contributions grow, raising Cp beyond its low-T limit.Therefore, the qualitative trend is that Cp increases.Choose “Increases”.

Verification / Alternative check:
Handbook data (e.g., for CO2, N2, H2O vapor) show Cp(T) curves that rise with temperature over typical process ranges, confirming the general trend.

Why Other Options Are Wrong:
Linear variation is not universally accurate; detailed fits are often polynomial.Decrease or no variation contradicts well-documented behavior, except in narrow temperature windows where Cp can be nearly flat.

Common Pitfalls:
Using constant-Cp approximations too far from reference temperatures; confusing Cp with Cv; ignoring vibrational effects at high T.

Final Answer:
Increases