Modern Engineering Thermodynamics

12.4 Psychrometrics 419
EXAMPLE 12.6
On a particular day, the weather forecast states that the relative humidity is 56.8% when the atmospheric temperature and
pressure are 25.0°C and 0.101 MPa, respectively. Determine:
a. The partial pressure of the water vapor in the atmosphere.
b. The humidity ratio of the atmosphere.
c. The dew point temperature of the atmosphere.
Solution
a. From Table C.1b, we find that
p sat ð25:0°CÞ = 0:003169 MPa
and, from Eq. (12.24), we can calculate the partial pressure of the water vapor present in the mixture as
p w = ϕp sat = 0:568ð0:003169 MPaÞ = 0:00180 MPa = 1:80 kPa
b. From Dalton’s law for partial pressure, we can find the partial pressure of the dry air in the mixture as
p a = p m − p w = 101 − 1:8 = 99:2 kPa
then, Eq. (12.26a) gives the humidity ratio ω as
ω = 0:622ðp w /p a Þ = 0:622ð1:80/99:2Þ = 0:0113 kg H 2 O per kg of dry air
Note that, since the value of ω is not constrained to lie between 0 and 1, it is not reported as a percentage.
c. Using Eq. (12.27) and Table C.2b, we find the dew point temperature to be
T DP = T sat ð0:00180 MPaÞ = 15:8°C
Exercises
12. If the relative humidity in Example 12.6 is 45.0% rather than 56.8% and all the remaining variables are the same,
determine the new dew point temperature. Answer: T DP = 12.1°C.
13. Suppose the atmospheric temperature in Example 12.6 is 20.0°C rather than 25.0°C and all other variables remain the
same. Determine the humidity ratio of this mixture. Answer: ω = 0.00830 kg H 2 O per kg of dry air.
14. Rework Example 12.6 for a relative humidity of 35.0%, an atmospheric temperature of 20.0°C, and an atmospheric
pressure of 0.101 MPa. Answer: (a) p w = 0.820 kPa, (b) ω = 5.00 × 10 −3 kg H 2 O per kg of dry air, (c) T DP = 4.00°C.
The steady state, steady flow, isothermal boundary energy and entropy rate balances for a mixture of dry air and
water vapor with negligible flow stream kinetic and potential energies can be written either on an unmixed
component basis as
_Q − _W + _m a ðh 1 − h 2 Þ a
+ _m w ðh 1 − h 2 Þ w
= 0 (12.28)
and
_Q /T b + _m a ðs 1 − s 2 Þ a + _m w ðs 1 − s 2 Þ w + _S p = 0 (12.29)
or on a premixed mixture basis as
_Q − _W + _m m ðh 1 − h 2 Þ m = 0
and
_Q /T b + _m m ðs 1 − s 2 Þ m
+ _S p = 0
where the mixture enthalpy and entropy changes are given by
ðh 1 − h 2 Þ m
= w a ðh 1 − h 2 Þ a
+ w w ðh 1 − h 2 Þ w
and
ðs 1 − s 2 Þ m
= w a ðs 1 − s 2 Þ a
+ w w ðs 1 − s 2 Þ w