Modern Engineering Thermodynamics

418 CHAPTER 12: Mixtures of Gases and Vapors
CRITICAL THINKING
On page 77 of the July/August 1993 issue of Family Handyman magazine, a helpful hint is given on how to determine the
amount of propane remaining a cook stove tank. According to this magazine you just “Pour a cup of hot water over the
outside of the tank. A condensation line will appear on the tank surface at the level of the remaining propane.”
Since the formation of a “condensation line” requires reducing the liquid-vapor interface inside the tank to a temperature
below the dew point temperature, can you explain how this test works? Are there any conditions under which this test
would not work? (Hint: Look at the thermodynamics of the propane’s evaporation and condensation processes that result
from the heating by the hot water and the subsequent cooling by the local atmosphere.)
this mixture are treated as ideal gases (even though we say water vapor and not water gas). This particular mixture
of ideal gases is important because of its meteorological and environmental comfort implications.
To begin this discussion, we define two new composition measures for the amount of water vapor present in the
mixture. Both measures are a type of humidity, as is shown. 5
1. The relative humidity ϕ is the ratio of the actual partial pressure of the water vapor present in the mixture to
the saturation pressure of the water vapor at the temperature of the mixture, or
Relative humidity = ϕ = p w
p sat
(12.24)
The value of p sat can be found in Table C.1 in Thermodynamic Tables to accompany Modern Engineering Thermodynamics
at the temperature of the mixture. Since 0 ≤ ϕ ≤ 1, the relative humidity is normally reported as a
percentage. This is the common meteorological humidity measure.
2. The humidity ratio ω is the ratio of the mass of water vapor present in the mixture divided by the mass of dry
air present in the mixture, or
Humidity ratio ω = m w
m a
(12.25)
where m m = m a + m w , and p m = p a + p w = atmospheric pressure. Assuming ideal gas behavior for both the
air and water vapor, we can write m w = p w V m / ðR w T m Þ and m a = p a V m / ðR a T m Þ, then
ω = p wR a
p a R w
= p wM w
p a M a
= 18:016p w
= 0:622 p
w
= 0:622
28:97p a p a
p w
p m − p w
(12.26a)
Dew point
temperature
isotherm
From Eq. (12.24), we find that p w = ϕp sat , and substituting this into Eq. (12.26a)
provides a formula that relates the two humidity measures:
ω = 0:622ϕ p
sat
ϕp sat
= 0:622
p a p m − p w
(12.26b)
T
p w
Atmospheric
temperature
isotherm
A colorful term from the meteorological profession is the dew point temperature
T DP , which is the temperature at which liquid water (dew) condenses
out of the atmosphere at constant atmospheric pressure (and consequently at
constant water vapor partial pressure):
ω
FIGURE 12.1
The partial pressure and dew point temperature of
a mixture of water vapor and dry air.
T DP = T sat ðevaluated at p w Þ (12.27)
If the partial pressure of the water vapor (p w ) is known, then the dew point
temperature can be found in Table C.2. Figure 12.1 illustrates these concepts
on a pressure-specific volume schematic.
5 Since neither of these two humidity measures corresponds to any of the four composition measures previously discussed, this brings
the number of composition measures used in this chapter to six.