Condition of Partial Saturation
45
Either Eq. (3.16) or Fig. 3.2 can be used to find vapor pressure from wet
and dry bulb temperatures, later we give examples of both. Finding wet
bulb temperature from vapor pressure and air temperature using Fig. 3.2
is also easily done. Finding T, from the psychrometer equation, however,
is somewhat more challenging, since Tw appears in the linear term and
implicitly in e,(Tw). There is no explicit solution to this equation, but
a solution can be found by standard mathematical methods for solving
nonlinear equations.
Example 3.3. When air temperature is 23" C and vapor pressure is
1.1 kPa, use Fig. 3.2 to find relative humidity, dew point temperature,
and wet bulb temperature.
Solution. Enter Fig. 3.2 at T = 23" C and ea = 1 . 1 kPa. This point
is just below the line for h, = 0.4, so the humidity is estimated to be
0.39. The dew point temperature is the intersection of the h, = 1 line and
e, = 1.1 kPa. The dew point temperature is therefore around 8" C. To find
the wet bulb temperature, place a straight edge on Fig. 3.2 with the edge
parallel to the wet bulb lines and passing through the point T = 23" C,
ea = 1.1 H a . Read the temperature on the scale along the h, = 1 line,
it is approximately 14.5" C. Note that the wet bulb temperature always
lies between the air temperature and the dew point temperature unless the
humidity is 1 ; then they are all equal.
Example 3.4. Find the vapor pressure and vapor mole fraction at the
surface of melting snow at 1300 m elevation.
Solution. The temperature of melting ice and snow is 0" C. Since the
surface is pure water, the vapor pressure at the surface is the saturation
vapor pressure for that surface temperature. From Table A.3 the saturation
vaporpressure at 0" C is 0.6 1 1 kPa. Using Eq. (3.7), the pressure at 1300 m
elevation is 101.3 exp(- 1300/8200) = 86 kPa. The vapor mole fraction
is C, = 0.61 1 kPa/86 kPa = 0.007 mol/mol or 7 mmol/mol.
Example 3.5. A psychrometer gives an air temperature of 30" C and
a wet bulb temperature of 19" C. Use the psychrometer equation and
other formulae to find the vapor pressure, relative humidity, dew point
temperature, and vapor deficit of the air. Assume the measurement is
made at sea level.
Solution. To use the psychrometer equation the saturation vapor pressure
at wet bulb temperature needs to be known. Table A.3 gives e,(Tw) =
2.20 kPa. The saturation vapor pressure at air temperature is also needed
to find the humidity. Again, from Table A.3 it is e, (T,) = 4.24 kPa. Using
the psychrometer equation (Eq. (3.16)) gives
45
Either Eq. (3.16) or Fig. 3.2 can be used to find vapor pressure from wet
and dry bulb temperatures, later we give examples of both. Finding wet
bulb temperature from vapor pressure and air temperature using Fig. 3.2
is also easily done. Finding T, from the psychrometer equation, however,
is somewhat more challenging, since Tw appears in the linear term and
implicitly in e,(Tw). There is no explicit solution to this equation, but
a solution can be found by standard mathematical methods for solving
nonlinear equations.
Example 3.3. When air temperature is 23" C and vapor pressure is
1.1 kPa, use Fig. 3.2 to find relative humidity, dew point temperature,
and wet bulb temperature.
Solution. Enter Fig. 3.2 at T = 23" C and ea = 1 . 1 kPa. This point
is just below the line for h, = 0.4, so the humidity is estimated to be
0.39. The dew point temperature is the intersection of the h, = 1 line and
e, = 1.1 kPa. The dew point temperature is therefore around 8" C. To find
the wet bulb temperature, place a straight edge on Fig. 3.2 with the edge
parallel to the wet bulb lines and passing through the point T = 23" C,
ea = 1.1 H a . Read the temperature on the scale along the h, = 1 line,
it is approximately 14.5" C. Note that the wet bulb temperature always
lies between the air temperature and the dew point temperature unless the
humidity is 1 ; then they are all equal.
Example 3.4. Find the vapor pressure and vapor mole fraction at the
surface of melting snow at 1300 m elevation.
Solution. The temperature of melting ice and snow is 0" C. Since the
surface is pure water, the vapor pressure at the surface is the saturation
vapor pressure for that surface temperature. From Table A.3 the saturation
vaporpressure at 0" C is 0.6 1 1 kPa. Using Eq. (3.7), the pressure at 1300 m
elevation is 101.3 exp(- 1300/8200) = 86 kPa. The vapor mole fraction
is C, = 0.61 1 kPa/86 kPa = 0.007 mol/mol or 7 mmol/mol.
Example 3.5. A psychrometer gives an air temperature of 30" C and
a wet bulb temperature of 19" C. Use the psychrometer equation and
other formulae to find the vapor pressure, relative humidity, dew point
temperature, and vapor deficit of the air. Assume the measurement is
made at sea level.
Solution. To use the psychrometer equation the saturation vapor pressure
at wet bulb temperature needs to be known. Table A.3 gives e,(Tw) =
2.20 kPa. The saturation vapor pressure at air temperature is also needed
to find the humidity. Again, from Table A.3 it is e, (T,) = 4.24 kPa. Using
the psychrometer equation (Eq. (3.16)) gives