Complete the following chart (round off relative humidity to the nearest percent

Question

Complete the following chart (round off relative humidity to the nearest percent). The air inside a room is at a temperature of 18.3 degree C and has a mixing ratio of 5.2 g/kg. What is the relative humidity? _____ % What is the dew point? _____ degree C If the mixing ratio remains the same, but the temperature of the room increases to 26.7 degree C, what is the new relative humidity? _____ % The air inside a room is at a temperature of 35 degree C and has a mixing ratio of 7.6 g/Kg. What is the relative humidity? _____ % What is the dew point? _____ degree C If the room temperature decreases by 5 degree C per hour, how many hours will it take for the air to reach saturation? _____ hours After reaching saturation, if the temperature of the room continues to decrease for one more hour, approximately how many grams of water vapor (per kg of air) will have had to condense out of the air to maintain a relative humidity of 100%? _____ g/kg

Explanation / Answer

1.

a. Saturation Mixing Ratio =3.53gm/kg

relative Humidity, RH = actual mixing ratio/saturation mixing ratio = 2.8/3.53 =0.79=79%

b. Saturation Mixing Ratio =31.33gm/kg

  relative Humidity, RH = actual mixing ratio/saturation mixing ratio = 2.8/31.33 =0.089=8.9%

c. Air temperature, T = 18.14oC

Relative Humidity, RH = actual mixing ratio/saturation mixing ratio = 11.1/13.2 = 0.84=84%

d. Air temperature, T = 35oC

  Relative Humidity, RH = actual mixing ratio/saturation mixing ratio = 22.3/36.5 = 0.61=61%

2.

Air temperature =18.3oC

mixing ratio = 5.2gm/kg

From table, saturation mixing ratio= 13.34

a)

Relative Humidity, RH = Mixing Ratio/Saturation Mixing Ratio = 5.2/13.34=.389 =39%

b)

Dew point, Td = T - ((100 - RH)/5.)

= 18.3-((100-39)/5) =6oC

c)

If temperature becomes, T=26.7oC, the saturation mixing ratio = 22.52gm/kg

Relative humidity, RH =Actual mixing Ratio/Saturation mixing Ratio = 5.2/22.52=0.23 =23%

3)

Temperature= 35oC

Mixing ratio=7.6gm/kg

From table saturation mixing ratio= 36.94g/kg

a)

Relative Humidity, RH = Mixing Ratio/Saturation Mixing Ratio = 7.6/36.94=0.205=20.5%

b) Dew point, Td =T - ((100 - RH)/5.) = 35-((100-20.5)/5) =19.1oC

c)

At the saturation point, relative humidity =100%

Temperature =35oC

Actual mixing ratio=7.6gm/kg

So for 100% relative humidity, saturation mixing ratio =actual mixing ratio= 7.6gm/kg

Saturation mixing ratio = 7.6gm/kg at temperature of 10oC

Initial room temperature is 35oC and it reduced by 5oC/hour and it will take 35-10/5 =5 hours to reach saturation.

d)

After saturation, if it will again decrease for 1 hour, then the temperature become 5oC and the saturation mixing ratio become 5.4gm/kg.

But the actual mixing ratio is 7.6gm/kg. So inorder to maintain a relative humidity of 100% it will have to reduce the actual mixing ratio to 5.4gm/kg. So around 7.6-5.4 =2.2gm of water vapor/kg of air will have to condense.

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