1-3
where
e
w
(T)
= the saturation vapor pressure of air with respect to
water (at temperature
T
), and is the partial pressure
exerted by the water vapor constituent,
and
P
= the absolute (or total) pressure of the gas.
The mole fraction of water vapor which would exist in a saturated gas sample at the chamber
pressure,
P
c
, and chamber temperature,
T
c
, would be the quantity,
X
w
,
which is needed to
calculate the relative humidity relationship previously discussed. Here, the mole fraction,
under saturated conditions, may be expressed by
X
w
=
e
w
(T
c
)
P
c
where
e
w
(T
c
)
= the saturation vapor pressure of air with respect to
water at the chamber temperature,
T
c
, and
P
c
= the measured absolute pressure in the chamber
expressed in the same units as
e
w
(T
c
)
.
The other quantity,
X
v
, required for the calculation of relative humidity, is that mole fraction
of water vapor which actually exists in the air sample within the chamber at pressure
P
c
, and
temperature
T
c
. If the chamber pressure,
P
c
, were used in the calculation of the mole fraction
X
v
, the expression would be
X
v
=
P
v
P
c
which would require direct measurement of the water vapor content. However, this
requirement is eliminated by using the relationship
e
w
(T
s
)
P
s
=
P
v
P
c
where
e
w
(T
s
)
= the saturation vapor pressure of air with respect to
water at the temperature of saturation,
T
s
,
(the
saturation temperature), and
P
s
= the measured absolute (or total) pressure at which the
sample is saturated (the saturation pressure).
The basis for this relationship lies in the fact that the number of molecules of the constituents
within a sample of gas remain constant regardless of the pressure or temperature, provided
that the temperature or pressure applied does not cause a change in phase (i.e., gas to liquid).
Since the saturation vapor pressure,
e
w
(T)
, is a well known function of the temperature alone,
the total pressure at saturation, P
s
, may be adjusted to any reasonable value to achieve the
desired mole fraction of water vapor. Relying on this relationship, the mole fraction of water
vapor entering the chamber (and at chamber temperature) may be written as that mole
fraction of water vapor existing in the saturator at the saturation pressure and temperature.
Thus,
X
v
=
e
w
(T
s
)
P
s
