This paper demonstrates the use of equations of state (EOS) for determining the constant-pressure and constantvolume heat capacities (𝐶௉, 𝐶௏) as a classroom experience. Typical undergraduate thermodynamics courses often emphasize ideal-gas behavior and phase equilibria more than caloric properties. Non-ideal gas EOS, namely the van der Waals (vdW) and Redlich-Kwong (RK) are employed in the study and serve as density-dependent departure functions. An ideal-gas polynomial correlation was used to provide the temperature dependence of the heat capacity. The thermodynamical relation involving the relationship between P, V and T were used to compute heat capacity of carbon dioxide at 400 K. The Wagner/NIST EOS (via CoolProp) serve as highly accurate and standard benchmarks. RK predicts both 𝐶௉ and 𝐶௏ within 2-22% up to 160 bar, whereas vdW deteriorates to 2- 26% error and consistent with its analytic structure-predicts no volume dependence of 𝐶௏. The case study illustrates how cubic EOS behavior can be used to predict caloric properties and provides a learning experience for undergraduate thermodynamics students.

Shashi B. Lalvani, "Estimating Real-Gas Heat Capacities Using Cubic Equations of State: An Undergraduate Chemical Engineering Thermodynamics Case Study with CO2" International Journal of Scientific Research and Engineering Development, V9(5): Page(1341-1347) September - October 2026. ISSN: 2581-7175. www.ijsred.com. Published by Scientific and Academic Research Publishing.