Answer :
Given, the following data: Atmospheric air is at 100.8 kPa, 30°C dry bulb and 21°C wet bulb.Dimensions of room = 5.0 m x 4.0 m x 3.3 m high.The formula to find out the total mass of moist air in the room is as follows:
Total mass of moist air = Density of moist air × Volume of room × Specific heat of moist air × ΔT
Step 1: To calculate the density of moist air, use the formula,
ρ = p/(R_m*T)
where p is the pressure,T is the temperature,R_m is the specific gas constant of moist air.R_m for moist air is 0.287 kJ/kg·Kρ
= 100.8/(0.287*303)
= 1.162 kg/m³
Step 2: To calculate the volume of the room:Volume of the room = Length × Breadth × Height
= 5.0 m × 4.0 m × 3.3 m
= 66 m³
Step 3: To calculate the specific heat of moist air, use the formula,
Cpa = 1.006 + (1.86 × Humidity Ratio)Cpa
= 1.006 + (1.86 × 0.017)
= 1.04002 kJ/kgK
Step 4: Calculate ΔTΔT = (dry bulb temperature) - (wet bulb temperature)
= 30 - 21
= 9°C
Step 5: Putting the values in the formula,
Total mass of moist air = Density of moist air × Volume of room × Specific heat of moist air × ΔT
Total mass of moist air = 1.162 kg/m³ × 66 m³ × 1.04002 kJ/kgK × 9 KTotal mass of moist air
= 664.2 kg/s
Therefore, the total mass of moist air in the room is 664.2 kg/s.
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