Exercise 20: humidity name cise 20 problems-part iii (english units) the following chart (round off relative humidity to the nearest percent) misdng ratio air teapaturate ge relative humidity (%) ng ratioair temperature saturation mixing ratio (g/kg (g/kg) 2.8 2.8 c°f) 30°f 90°f 13.2 11.1 36.5 22.3 the air inside a room is at a temperature of 65°f and has a mixing ratio of 5.2 g/kg. (a) (b) (c) 2· what is the relative humidity? what is the dew point? if the mixing ratio remains the same, but the temperature of the room increases to 80°f, what is the new relative humidity? 3. the air inside a room is at a temperature of 70°f and has a mixing ratio of 7.6 g/kg. 20.8% (a) what is the relative humidity? (b) what is the dew point? (c) if the room temperature decreases by 10°f per hour, how many (d) after reaching saturation, if the temperature of the room hours will it take for the air to reach saturation? hours continues to decrease for one more hour, 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%?

The dew point is the temperature at which air is saturated with water vapor, which is the gaseous state of water.

When air has reached the dew-point temperature at a particular pressure, the water vapor in the air is in equilibrium with liquid water, meaning water vapor is condensing at the same rate at which liquid water is evaporating.

Below the dew point, liquid water will begin to condense on solid surfaces (such as blades of grass) or around solid particles in the atmosphere (such as dust or salt), forming clouds or fog.

Dew point is closely linked to relative humidity, which is the ratio of the pressure of water vapor in a parcel of air relative to the saturation pressure of water vapor in that same parcel of air at a specific temperature. Relative humidity (RH) is expressed as a percentage.

The relative humidity is 100 percent when the dew point and the temperature are the same. If the temperature drops any further, condensation will result, and liquid water will begin to form.

Compared to relative humidity, dew point is frequently cited as a more accurate way of measuring the humidity and comfort of the air, since it is an absolute measurement (unlike relative humidity).

Most people are comfortable with a dew-point temperature of 60 degrees Fahrenheit (16 degrees Celsius) or lower. At a higher dew point of, for example, 70 F (21 C), most people feel hot or "sticky" because the amount of water vapor in the air slows the evaporation of perspiration and keeps the body from cooling.

rain is most likley to follow

Explanation:

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% .

(a). The relative humidity is 20.57%

(b). The dew point is 79.114°F

(c). It take for the air to reach saturation is 17 hours.

(d). The water is 7.6g/kg.

Explanation:

Given that,

Temperature = 35°

Mixing ratio = 7.6 g/kg

(a). We need to calculate the relative humidity

Using formula of relative humidity

[tex]relative humidity=\dfrac{mixing\ ratio}{36}\times100[/tex]

[tex]relative humidity=\dfrac{7.6}{36.94}\times100[/tex]

[tex]relative humidity=20.57\%[/tex]

(b). We need to calculate the dew point

Using formula of dew point

[tex]dew\ point=T^{\circ}F-\dfrac{(100-relative\ humidity)}{5}[/tex]

Put the value into the formula

[tex]dew\ point=95-\dfrac{100-20.57}{5}[/tex]

[tex]dew\ point=79.114^{\circ}F[/tex]

(c). If the room temperature decreases by 5°C per hour

We need to calculate the time

Using formula of time

[tex]t=\dfrac{T_{a}-increase\ temperature}{5}[/tex]

Put the value into the formula

[tex]t=\dfrac{95-10}{5}[/tex]

[tex]t=17\ hours[/tex]

(d). If the temperature of the room continues to decrease for one more hour,

We need to calculate the how many grams of water vapor

Using given data

The water of 7.6g/kg vapour will have to condense out of air for the maintain relative humidity at 100%

Hence, (a). The relative humidity is 20.57%

(b). The dew point is 79.114°F

(c). It take for the air to reach saturation is 17 hours.

(d). The water is 7.6g/kg.

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