Water Vapor and Other Gases
Now, using Eq. (3.1 I), h, = 1.46 kPa14.24 Wa = 0.345. The vapor
deficit (Eq. (3.12)) is D = 4.24 kPa - 1.46 kPa = 2.78 kPa. The dew
point temperature can be obtained from Table A.3 or from Eq. (3.14).
In Table A.3, follow down the vapor pressure column until you find the
vapor pressure just smaller than 1.46 H a . This is at 12" C. The dew
point temperature therefore lies between 12" C and 13" C. The difference
between the value at 12" C and 1.46 kPa is 58 Pa; the difference between
the value at 12 and 13" C is 95 Pa. Our value of 1 A6 kPa is therefore 58/95
or 0.6 of the way between 12 and 13" C. The dew point temperature is
therefore Td = 12.6' C. Using Eq. (3.14):
Example 3.6. The vapor pressure of air at a ski resort is 0.4 kPa. A
machine to make artificial snow emits water droplets which quickly cool
to the wet bulb temperature. At what air temperature will the droplets just
reach freezing temperature at an altitude of 2400 m?
Solution. Ice melts at 0' C, but often cools a few degrees below this temperature before freezing (super cools). For this problem we will assume a
freezing temperature of -2" C. Rearranging the psychrometer equation
(Eq. (3.16)) to find air temperature gives
es(Tw) - ea
Ta = Tw +
YPa
0.53kPa - 0.4kPa
= 0.6"C.
= -2 + 6.67 x ~o-~c-' x 0.75 x lOlkPa
Therefore, expect the droplets to start freezing at an air temperature
slightly above zero.
Example 3.7. A humidity sensor at air temperature reads 0.23 when
the air temperature is 16" C. What is the vapor pressure, dew point
temperature, and wet bulb temperature?
Solution. Entering Fig. 3.2 at the T = 16" C line and h, = 0.23 gives
a vapor pressure of about 0.4 kPa. The wet bulb temperature is obtained
by moving along a line through the vapor pressure, temperature point,
parallel to the psychrometer lines. It is approximately 7.5" C. The dew
point temperature cannot be obtained from Fig. 3.2 because it does not
go low enough. Table A.3 also fails to go low enough for this problem.
Before turning to the formula to obtain this value, try calculating a more
precise value for the vapor pressure. From Table A.3, the saturation vapor
pressure at 16" C (air temperature) is 1.82 H a . Rearranging Eq. (3.1 1) to
compute vapor pressure gives:
Now, using Eq. (3.1 I), h, = 1.46 kPa14.24 Wa = 0.345. The vapor
deficit (Eq. (3.12)) is D = 4.24 kPa - 1.46 kPa = 2.78 kPa. The dew
point temperature can be obtained from Table A.3 or from Eq. (3.14).
In Table A.3, follow down the vapor pressure column until you find the
vapor pressure just smaller than 1.46 H a . This is at 12" C. The dew
point temperature therefore lies between 12" C and 13" C. The difference
between the value at 12" C and 1.46 kPa is 58 Pa; the difference between
the value at 12 and 13" C is 95 Pa. Our value of 1 A6 kPa is therefore 58/95
or 0.6 of the way between 12 and 13" C. The dew point temperature is
therefore Td = 12.6' C. Using Eq. (3.14):
Example 3.6. The vapor pressure of air at a ski resort is 0.4 kPa. A
machine to make artificial snow emits water droplets which quickly cool
to the wet bulb temperature. At what air temperature will the droplets just
reach freezing temperature at an altitude of 2400 m?
Solution. Ice melts at 0' C, but often cools a few degrees below this temperature before freezing (super cools). For this problem we will assume a
freezing temperature of -2" C. Rearranging the psychrometer equation
(Eq. (3.16)) to find air temperature gives
es(Tw) - ea
Ta = Tw +
YPa
0.53kPa - 0.4kPa
= 0.6"C.
= -2 + 6.67 x ~o-~c-' x 0.75 x lOlkPa
Therefore, expect the droplets to start freezing at an air temperature
slightly above zero.
Example 3.7. A humidity sensor at air temperature reads 0.23 when
the air temperature is 16" C. What is the vapor pressure, dew point
temperature, and wet bulb temperature?
Solution. Entering Fig. 3.2 at the T = 16" C line and h, = 0.23 gives
a vapor pressure of about 0.4 kPa. The wet bulb temperature is obtained
by moving along a line through the vapor pressure, temperature point,
parallel to the psychrometer lines. It is approximately 7.5" C. The dew
point temperature cannot be obtained from Fig. 3.2 because it does not
go low enough. Table A.3 also fails to go low enough for this problem.
Before turning to the formula to obtain this value, try calculating a more
precise value for the vapor pressure. From Table A.3, the saturation vapor
pressure at 16" C (air temperature) is 1.82 H a . Rearranging Eq. (3.1 1) to
compute vapor pressure gives: