Re: Air pressure and specific heat formula

Date: Thu Jul 19 17:59:26 2001
Posted By: Jason Goodman, Postdoctoral Fellow, Department of Geosciences, University of Chicago
Area of science: Engineering
ID: 994453657.Eg

Message:

Air is very, very close to being an ideal gas. For an ideal gas, the enthalpy is related to temperature by:

  h = Cp T

where Cp is the specific heat at constant pressure. The specific heat is related to the universal gas constant R=8.314 J/(mol K) by the molecular weight and the topology of the molecules. It is independent of temperature and pressure.

For diatomic molecules (which make up 99% of dry air)

  Cp = (7/2) R/ma

where ma is the molecular weight of the gas (For air, ma = 28.966 g/mol). This means that for dry air,

  Cp = 1004.6 J/(kg K)

As I said before, this value is independent of temperature and pressure. My source says that "Corrections for small departures from ideal gas behavior are given in the Smithsonian Meteorological Tables".

Bonus answer, for a question you didn't ask: what is the specific heat for moist air? The specific heat for pure water vapor, which is a polyatomic molecule, is given by

  Cpv = 4 R/mw

where mw is the molecular weight of water (mv = 18.016 g/mol).

Let "q" be the "specific humidity" (mass of water vapor per unit mass of moist air). Then the specific heat is a linear combination of Cp and Cpv:

  Cp = (7/2) (1-q) R/ma + 4 q R/mw

My source for this answer is Atmosphere-Ocean Dynamics, by Adrian Gill, page 40-41.

Notation alert! Most meteorologists use the symbol "R*" for the universal gas constant (R* = 8.314 J/(mol K)), and define R = R*/ma = 287 J/(kg K). I have not done this here, since this answer is for a general audience.

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