Handbook of air conditioning and refrigeration / Shan K

2.4 HUMIDITY
Humidity Ratio
Relative Humidity
Amplifier(s). The measured electric signal from the temperature sensor is amplified at the solid
state amplifier to produce an output for indication. The number of amplifiers is matched with the
number of the sensors used in the temperature indication system.
Indicator. An analog-type indicator, one based on directly measurable quantities, is usually a
moving coil instrument. For a digital-type indicator, the signal from the amplifier is compared with
an internal reference voltage and converted for indication through an analog-digital transducer.
The humidity ratio of moist air w is the ratio of the mass of water vapor m w to the mass of dry air m a
contained in the mixture of the moist air, in lb/lb (kg/kg). The humidity ratio can be calculated as
w � (2.14)
Since dry air and water vapor can occupy the same volume at the same temperature, we can apply the
ideal gas equation and Dalton’s law for dry air and water vapor. Equation (2.14) can be rewritten as
m w
m a
w � m w
m a
� p wVR aT R
P aVR wT R
� (2.15)
where Ra, Rw � gas constant for dry air and water vapor, respectively, ft�lbf/lbm�°R(J/kg�K). Equation
(2.15) is expressed in the form of the ratio of pressures; therefore, pw and pat must have the
same units, either psia or psf (Pa).
For moist air at saturation, Eq. (2.15) becomes
53.352
� 0.62198
85.778 pat � pw pat � pw where p ws � pressure of water vapor of moist air at saturation, psia or psf (Pa).
(2.16)
The relative humidity � of moist air, or RH, is defined as the ratio of the mole fraction of water vapor
x w in a moist air sample to the mole fraction of the water vapor in a saturated moist air sample
x ws at the same temperature and pressure. This relationship can be expressed as
And, by definition, the following expressions may be written:
p w
w s � 0.62198
� � x w
x w �
x ws �
� R a
R w
p ws
p at � p ws
�T,p x ws
n w
n a � n w
n ws
n a � n ws
p w
p at � p w
p w
PSYCHROMETRICS 2.7
(2.17)
(2.18)
(2.19)