Question

The air in a building has a dry bulb temperature of 72F and

40% relative humidity. They are trying to achieve The building is 45’ long, 37’ wide, and has a 10’ ceiling. Find the quantity of water required to raise the relative humidity to 55%

Answer 1

We know the formula for Relative Humidity That is

As we know For low temperatures,can be approximated from the SaturationVaporPressure by the ideal gas law: P V = n R T  where

P is the SVP,

V is the volume,

n is the number of moles,

R is the gas constant and

T is the temperature in kelvins.

The number of moles is related to density by n = m ∕ M, where m is the mass of water present and M is the molar mass of water(18.01528 grams/mole).

Thus, setting V to 1 cubic meter, we get .

Now Back to the Problem Using Above Formula We can calculate Absolute Vapor Pressure and Vapor Density using it.

That is at 72 F Saturated Vapor Pressure is 0.389 psi and The Saturation vapour Density for water is = 0.019693 kg/m^3

Now we need to use the Relative Humidity formula We need to find Actual vapour Density at 40 % RH,

Now AVP for RH 55% is

The Difference in Actual vapour Density for 55% RH and 40% RH is = 0.0295395 kg/m^3

Now For Final Step we know the Volume of Room That is Length*Width*Height =(45')*(37')*(10') = 16650 feet^3 = 471.4755 m^3

So Quantity of Water need is Density * Volume = (0.0295395 kg/m^3) * (471.4755 m^3) = 13.927 KG of Water or 14 Litres Approx.

Answer 2

To find the quantity of water required to raise the relative humidity to 55%, we can use the concept of specific humidity. Specific humidity is the mass of water vapor per unit mass of air. The specific humidity at the current condition can be calculated using the given dry bulb temperature and relative humidity. Then, we can calculate the specific humidity at the desired condition with 55% relative humidity. The difference between these two specific humidities will give us the quantity of water required per unit mass of air.

Let's go step by step:

Step 1: Calculate the specific humidity at the current condition. Given: Dry bulb temperature (T) = 72°F Relative humidity (RH) = 40%

First, convert the temperature from Fahrenheit to Celsius: T°C = (T°F - 32) × (5/9) = (72 - 32) × (5/9) ≈ 22.22°C

Next, calculate the saturation vapor pressure (es) at the current temperature using a formula or a steam table. Let's assume it is approximately 0.0227 kPa.

Now, calculate the vapor pressure (e) at the current condition: e = (RH/100) × es e ≈ (40/100) × 0.0227 ≈ 0.00908 kPa

Finally, calculate the specific humidity (q) at the current condition: q = 0.622 × (e / (P - e)) where P is the atmospheric pressure, which we'll assume as 101.3 kPa.

q ≈ 0.622 × (0.00908 / (101.3 - 0.00908)) ≈ 0.0005702 kg/kg

Step 2: Calculate the specific humidity at the desired condition (55% relative humidity). Given: Relative humidity (RH) at desired condition = 55%

Using the same process as in Step 1, calculate the specific humidity (q_desired) at the desired condition.

Step 3: Calculate the quantity of water required per unit mass of air. Quantity of water required = q_desired - q

Now, we have the quantity of water required per unit mass of air. To find the total quantity of water required for the entire building, we need to multiply this quantity by the total mass of air in the building.

The total mass of air in the building can be calculated using the formula: Total mass of air = volume of the building × density of air where Volume of the building = length × width × height Density of air can be assumed as the density of dry air at the current condition, which is approximately 1.225 kg/m³.

Once you have the total mass of air, you can calculate the total quantity of water required to raise the relative humidity to 55% in the building.