1-6
1.2.6 Enhancement Factor Ratio
The term
ƒ
w
(P
s
,T
s
)
ƒ
w
(P
c
,T
c
)
, in equation 3 of section 1.2.3, referred to as the "enhancement factor
ratio", corrects for the non-ideal behavior of air when it is used as the carrier gas. Note that
the individual enhancement factors, ƒ
w
, are functions of two independent variables; pressure,
P
, and temperature,
T
. Since temperature differences within the system are relatively quite
small, and pressure differences relatively large, it is typically the pressure terms,
P
c
and
P
s
,
which dominate the formulas and bring about the greatest change in the enhancement factor
ratio. As applied to the two pressure humidity generator, this enhancement factor ratio may
be loosely viewed then as a pressure correction. At a relative humidity of 100%, the
pressures P
c
and P
s
would be equal, causing the enhancement factor ratio to equal 1.0
(ignoring temperature differences), thereby not affecting the relative humidity calculation.
Conversely, at low relative humidities (i.e., 5%), where the pressures
P
c
and
P
s
differ greatly
(i.e.,
P
s
≈20 •
Pc
), the enhancement factor ratio may exceed 1.06, affecting relative humidity
calculations by 0.3% or more. A formula for calculation of the enhancement factor ƒ
w
(P,T)
at any given pressure and temperature is given by Greenspan as
ƒ
w
(P,T)
=
exp
( )
( )
−
+
−
1
1
T
e
P
P
T
e
w
w
β
α
where
P
= the absolute pressure in Pascals, and
e
w
(T
) = the saturation vapor pressure (in Pascals) at
temperature,
T
.
The two remaining variables,
α
and
β
, as derived by Greenspan are given as
α
=
∑
i=0
3
A
i
T
i
and
β
=
exp
∑
i=0
3
B
i
T
i
where
A
0
= 3.53624 x 10
-4
A
1
= 2.93228 x 10
-5
A
2
= 2.61474 x 10
-7
A
3
= 8.57538 x 10
-9
B
0
= -1.07588 x 10
1
B
1
= 6.32529 x 10
-2
B
2
= -2.53591 x 10
-4
B
3
= 6.33784 x 10
-7
, and
T
= temperature of the gas in °C.
This formula for the enhancement factor is valid for pressures up to approximately 300 PSIA
and over the temperature range of 0 to 100 °C. Therefore it is also valid over the operating
range of the humidity generator. Note that to obtain the enhancement factor ratio, the
formula must be calculated once at the saturation pressure and temperature,
P
s
and
T
s
, and
then again at the chamber pressure and temperature,
P
c
and
T
c
.
Содержание 2500 series
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