Heat Capacity Ratio Table

k = Cp/Cv for Common Fluids


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Information and Definitions

Heat Capacity Ratio (γ = Cp/Cv)

The heat capacity ratio, also called the adiabatic index, is the ratio of constant-pressure to constant-volume specific heats: γ = Cp/Cv. It describes how a gas responds during adiabatic compression/expansion and appears in compressible flow relations.

Typical Values and Temperature Dependence

Monatomic gases (He, Ne) have γ ≈ 1.66; diatomic gases (Air, N₂, O₂) have γ ≈ 1.4 near ambient; polyatomic gases have lower γ (≈1.2–1.35). γ decreases with temperature as additional molecular degrees of freedom become active.

Key Uses in Engineering

  • Sonic speed: a = √(γ·R·T) for ideal gases.
  • Isentropic relations: p, T, and ρ changes across nozzles/compressors use γ.
  • Critical (choked) flow: mass flow through orifices depends on γ.
  • Energy balance: γ affects compression work and expansion performance.

Units and Assumptions

γ is dimensionless. Values are often reported under ideal-gas assumptions; real-gas effects can alter Cp and Cv at high pressures/temperatures.

Data Notes

This table lists γ for common fluids; values may be temperature-specific. For precision, use temperature-dependent Cp(T), Cv(T) to compute γ(T).

Heat Capacity Ratio References

1 Moran, M. J., Shapiro, H. N., et al. (2014) Fundamentals of Engineering Thermodynamics.

2 Çengel, Y. A., Boles, M. A. (2015) Thermodynamics: An Engineering Approach.

3 NIST Chemistry WebBook — Thermophysical properties and specific heats.

4 NASA Glenn Coefficients for Thermodynamic Properties of Selected Substances.

5 White, F. M. (2006) Fluid Mechanics — Compressible flow sections.

6 Fox, R. W., McDonald, A. T., Pritchard, P. J. (2011) Introduction to Fluid Mechanics.

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7 Pressure Temperature Compensation Formula - Understand how temperature affects pressure and flow measurements.

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Frequently Asked Questions

Q1 What does γ = Cp/Cv represent?

A1 γ is the ratio of specific heat at constant pressure to that at constant volume. It governs how gases change temperature and pressure in adiabatic processes and is central to compressible flow calculations.

Q2 Why does γ change with temperature?

A2 As temperature rises, more molecular vibrational/rotational modes become active, increasing Cp more than Cv, which tends to lower γ. Polyatomic gases show stronger temperature dependence than monatomic gases.

Q3 How do I use γ to estimate speed of sound?

A3 For ideal gases, speed of sound is a = √(γ·R·T). Use γ appropriate to the gas and temperature; R is the specific gas constant and T is absolute temperature.

Q4 Which calculations depend on γ in orifice/nozzle flow?

A4 Critical pressure ratio, choked flow conditions, and isentropic expansion/compression relations use γ. Mass flow and discharge coefficients are often derived with γ-dependent formulas.

Q5 Is γ the same as k?

A5 Yes. Many references use k for the heat capacity ratio; γ and k are interchangeable in most equations.