Question

The air inside a room is at a temperature of 35C and has a mixing ratio of 7.6 g/kg. Answer the following in (S.I. UNITIS):

Answer 1

Answer:

a. 20.57

b. 73.714°F

c. 15.92hr

d. 7.6g/kg

Explanation:

Mixing ratio = 7.6g/kg

Saturation mixing ratio = 36.94g/kg

Relative Humidity = (mixing ratio/saturation mixing ratio) * 100

Relative Humidity = 7.6/36.94 * 100

= 0.2057 * 100

= 20.57

Dew point

Using the dew point formula

Dp = T - (100 - Relative Humidity)/5

Since the air inside a room is at a temperature of 35°C

Convert Celsius to Fahrenheit

If x equal 35°C

T = 9/5x + 32

T = 9/5*32 + 32

T = 57.6 + 32

T = 89.6F

Dp = 89.6F - (100 - 20.57)/5

Dp = 89.6F - 15.886

Dp = 73.714°F

If the room temperature decreases by 10°F per hour, how many hours will it take for the air to reach saturation?

Time = (inside temperature - ∆t)/5

=(89.6 - 10)/5

=79.6/5

=15.92 hours

15.92hr

At the point of saturation, the Relative Humidity of the system is 100%, initial temperature is 100F, for 100% Relative Humidity, saturation mixing ratio is equal to the actual mixing ratio of 7.6g/kg

Answer 2

Answer:

a. Relative Humidity = 20.57%

b. Dew point = 79.114° F

c. Time required for the air to reach Saturation point = 17 hours.

d. 7.6g/kg of water vapour

Explanation:

a. Relative Humidity

The formula for Relative Humidity is

(Mixing ratio ÷ Saturation mixing ratio) × 100

In the question

Mixing ratio = 7.6g/kg

Temperature = 35°C

Saturation mixing ratio at 35°C is given in Saturation mixing ratio Table = 36.94

Relative Humidity = (7.6g/kg ÷ 36.94) × 100

Relative Humidity = 20.57%

b. Dew point

Formula for Dew point =

T °F - (100 - Relative Humidity) ÷ 5

Temperature = 35°C

Conversion to Fahrenheit =

T°F = T°C × 1.8 + 32

35°C × 1.8 + 32

95°F

Dew point = 95°F - ( 100 - 20.57)÷5

95°F - 15.886

Dew point = 79.114° F

c. At Saturation Point, the Relative Humidity is always equal too 100%

In the question above, Room temperature decreases by 10°F per hour.

Time required for the air to reach Saturation point =

Time(hours) = (Temperature of the air in the room - Decrease in temperature) ÷ 5

Time(hours) = (95°F - 10°F) ÷ 5

= 85°F ÷ 5

= 17 hours

Therefore, the time required for the air to reach Saturation point = 17 hours.

d. It would take 7.6g/kg of water vapour will have to condense out of air to maintain the relative humidity at 100% .