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Chapter 4 – Theoretical Basis of @Air Functions
Page 23
Bww , Cwww = virial coefficients of water vapor
Baw , Caaw , Caww = virial coefficients of the mixture
ASHRAE uses polynomial equations for estimating the virial coefficients of air and water vapor
as presented by Hyland and Wexler [8]. These equations are derived from the data presented
by the NBS [1] .
While these equations produce reasonable results, they are limited in
temperature range from about -100 °C to 200 °C and are clearly inadequate for this
application, which supports temperatures up to 2000 °K.
Instead of using polynomial equations, Techware has developed a gas property database from
the NBS [1] data. The database includes virial coefficients as well as ideal gas properties for
enthalpy, entropy and specific heat that span the range of temperatures from 180 °K to
2000 °K. Coefficients are extracted from the database at any desired temperature using nonlinear interpolation.
The molar enthalpy of moist air, hm can be described by the equation
(
)
(
)
hm = x a hao + ha' + x w hwo + hw' +
dB ⎞ 1 ⎛
1 dCm ⎞ 1 ⎤
⎡⎛
RT ⎢⎜ Bm − T m ⎟ + ⎜ Cm − T
⎟
dT ⎠ v ⎝
2 dT ⎠ v 2 ⎥⎦
⎣⎝
where,
hao = ideal gas molar enthalpy for air
hwo = ideal gas molar enthalpy for water
ha' = constant to adjust reference state for air
hw' = constant to adjust reference state for water
The molar entropy of moist air, sm can be described by the equation
⎛ Pv ⎞
sm = x a sao + sa' + x w swo + s w' − R ln P + x a R ln⎜
⎟+
⎝ x a RT ⎠
(
)
(
)
⎛ Pv ⎞
dBm ⎞ 1 1 ⎛
dCm ⎞ 1 ⎤
⎡⎛
x w R ln⎜
⎟ − R ⎢⎜ Bm − T
⎟ + ⎜ Cm − T
⎟
dT ⎠ v 2 ⎝
dT ⎠ v 2 ⎥⎦
⎝ x w RT ⎠
⎣⎝
where,
sao = ideal gas molar entropy for air
swo = ideal gas molar entropy for water
sa' = constant to adjust reference state for air
sw' = constant to adjust reference state for water
@Air for Windows Version 4.0 - User's Manual