An exponential expression for gas heat capacity, enthalpy, and entropy

• Gas CP varies as a function of temperature following an Arrhenius type dependency.
• An exponential 3-parameter model approximates CP, ΔH and ΔS up to 6000 K.
• Fitted parameters relate to degrees of freedom and number of atoms in the molecule.
• Maximum deviation from the experimental data are within about 1% at all temperatures.

Gas heat capacity, CP, is a fundamental extensive thermodynamic property depending on molecular transitional, vibrational and rotational energy. Empirical four-parameter polynomials approximate the sigmoidal CP trends for temperatures up to 1500 K and adding parameters extends the range. However, the fitted parameters have no physical significance and diverge beyond their range at high temperature. Here we propose an exponential expression for CP whose fitted parameters relate to the shape of the CP versus T curve and to molecular properties: CP = CP0 + CP∞[1 + ln(T)(1 + Ti/T)] exp(−Ti/T). It accounts for more than 99% of the variance with a deviation of ∼1% from 298 K to 6000 K for linear C1–C7 hydrocarbons and N2, H2O, O2, C2H4, H2, CO, and CO2. We also provide an integrated form for enthalpy and an approximation to calculate entropy variations. This model replaces empirical polynomials with an expression whose constants are meaningful.

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