Thermodynamics and Water Vapour - Transport in the Atmosphere-Vegetation-Soil Continuum - page 348

Appendix B

Thermodynamics and Water Vapour

This appendix summarizes some basic atmospheric thermodynamics and moisture
variables. An overview of some physical constants is given in Table B.3 .

B.1 Some Basic Thermodynamics
Air is a mixture of gases. The fractions of most constituents are rather constant, except
for water vapour, which is highly variable (see Table B.1 ).
The equation of state for a perfect gas reads:

*

R
M T

p = ρ = ρ T (B.1)

where p is pressure, ρ is the density, T is the temperature, R* is the universal gas
constant 8314 J kmol -1 K -1 , M is the molar mass of the gas and R is the speciic gas
constant. Because air is a mixture of gases, irst the molar mass of this mixture needs
to be determined. If the composition is given in terms of volume fractions ( f v, i ) and
given the fact that in a gas a mole of any gas occupies the same volume, the molar
mass of the mixture can be determined simply as:

= ∑ v, Mf M (B.2)

i i

i

With the data from Table B.1 , this yields for dry air (air without water vapour):
M d

1
. .
Based on Dalton's law, which states that the total pressure is the sum of the partial
pressures of the constituents, it can be derived that the molar mass of a mixture with
constituents with molar masses M i and mass fractions f m, i is:

−

= 28 976 kg mol

− 1

f
M

= 


 

∑

m, i

M

(B.3)

 

i

i

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