Temperature (T) = 18^{0}C
Relative Humidity (RH) = 42% = 0.42
CALCULATION USING FORMULA
Saturation Vapor Pressure =
e_{s} = 6.11 x 10^{7.5T/(237.3+T)}
^{ } = 6.11 x 10^{7.5*18/(237.3+18)}
=20.64 mb (mb = millibar)
RH = e / e_{s} (e = vapor pressure)
e = e_{s} x RH = 20.64 x 0.42 = 8.67 mb
CALCULATION FROM TABLE OF SATURATION VAPOR PRESSURE
From table,
At T=17.8^{0}C, e_{s}=20.3 mb
At T=18.3^{0}C, e_{s}=21.1 mb
Interpolating above values to obtain e_{s} at T = 18^{0}C
e_{s} = 20.3 + { (21.1-20.3)/(18.3-17.8)}x(17-17.8)
= 20.62 mb
e = 20.62 x 0.42 = 8.66 mb
Hence, both values from formula and table are approximately equal as can be seen above.
Saturation Vapor Pressure = 20.64 mb
Vapor Pressure = 8.67 mb
Condensation begins when the atmosphere can no longer hold any more water vapor. That is when Relative Humidity is 1 (100%).
Thus RH =1 is achieved, when vapor pressure (e) equals to saturation vapor pressure (e_{s})
As the air mass rises, its temperature decreases. We need to find the temperature at which saturation vapor pressure is equal to the vapor pressure
That is, the temperature at which, e_{s} = e = 8.67 mb
e_{s} = 6.11 x 10^{7.5T/(237.3+T)}
8.67= 6.11 x 10^{7.5T/(237.3+T)}
Or,
10^{7.5T/(237.3+T)} = 8.67 / 6.11 = 1.419
Taking Log Base 10 on both sides,
7.5T/(237.3+T) = log 1.419 = 0.152
7.5T = 36.07 +0.152T
7.348T = 36.07
T = 36.07/7.348 = 4.909^{0}C
Also from Saturation Vapor Pressure Table, the saturation vapor pressure is 8.7 mb at 5^{0}C and our required e_{s} is 8.67 mb. Thus 4.909^{0}C found from formula tallies with table value.
Hence, condensation will occur at 4.909^{0}C.
Present Temperature = 18^{0}C
Air Mass cools at a rate of -10^{0}C / km, that is
10^{0}C cooling is achieved by a rise in 1 km
1^{0}C cooling is achieved by a rise in 1/10 km
(18-4.909)^{0}C cooling is achieved by a rise in (1/10)*(18-4.909) km
=1.3091 km
Hence, at an elevation of 1.3091 km above present position, the air mass will start to condense.
An air mass has a temperature of 18°C and a relative humidity of 42%. a) Determine the vapor pres...