Question

Temperature (T) = 180C

Relative Humidity (RH) = 42% = 0.42

1. CALCULATION OF SATURATION VAPOR PRESSURE AND VAPOR PRESSURE

CALCULATION USING FORMULA

Saturation Vapor Pressure =

es = 6.11 x 107.5T/(237.3+T)

= 6.11 x 107.5*18/(237.3+18)

=20.64 mb                      (mb = millibar)

RH = e / es                           (e = vapor pressure)

e = es x RH = 20.64 x 0.42 = 8.67 mb

CALCULATION FROM TABLE OF SATURATION VAPOR PRESSURE

From table,

At T=17.80C, es=20.3 mb

At T=18.30C, es=21.1 mb

Interpolating above values to obtain es at T = 180C

es = 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

1. CALCULATION OF ELEVATION AT WHICH CONDENSATION WILL BEGIN

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 (es)

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, es = e = 8.67 mb

es = 6.11 x 107.5T/(237.3+T)

8.67= 6.11 x 107.5T/(237.3+T)

Or,

107.5T/(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 = 4.9090C

Also from Saturation Vapor Pressure Table, the saturation vapor pressure is 8.7 mb at 50C and our required es is 8.67 mb. Thus 4.9090C found from formula tallies with table value.

Hence, condensation will occur at 4.9090C.

Present Temperature = 180C

Air Mass cools at a rate of -100C / km, that is

100C cooling is achieved by a rise in 1 km

10C cooling is achieved by a rise in 1/10 km

(18-4.909)0C 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.

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