Question

On a relatively cool summer morning in Denver, Colorado, the temperature was 13 °Celsius and the air was partially saturated with RH = 50%. That afternoon, the temperature rose to 32 °Celsius. If the same air mass remained in place all day (meaning the moisture content did not change throughout the day).

a. Would the relative humidity increase or decrease in the afternoon?

b. What was the relative humidity during that afternoon (rounded to the nearest whole percent)?

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Answer 1

1. Relative humidity(RH) is the amount of water vapour present in the atmosphere compared to the maximum amount of water vapour atmosphere can hold. This maximum amount of water vapour atmosphere can hold vary with temperature, given by the Clausius-Clapeyron equation. As temperature rises, water holding capacity also increases which will result in a reduction of RH, provided water vapour content in the atmosphere is not varying. So RH would decrease in the afternoon.

2.

from Clausius-Clapeyron equation, e_s at a temperature, T

e_s at 13^oC,

e_s=6.1094exp((17.625*13)/(13+243.04))

=14.87 hPa

from RH, e at 13^oC

e= (RH*e_s)/100

=(50*14.87)/100

=7.43 hPa

e_s at 32^oC,

e_s=6.1094exp((17.625*32)/(32+243.04))

=47.45 hPa

e remains the same as moisture content is not changing,

therefore RH at 32^oC,

RH=(7.43/47.45)*100

= 15.6%