Question

An apartment has the dimensions 18m by 9m by 6m. The temperature is 25 degree C, and the relative humidity is 54 percent. What is the total mass (in kg) of water vapor in the air in the apartment?

Answer 1

381.33 kg

Step-by-step explanation:

relative humidity is 54%, it means that when saturation vapor pressure is 100 pascals, partial vapor pressure is 54 pascals [taking Pascals as no unit is mentioned]

Now, using PV = nRT

⇒
`PV = (w)/(M)RT`

⇒
`w = (PVM)/(RT)`

here input P = 54 Pascals, V = (18*9*6)X10^3 L, T = (25+273)°K

R = 8.314 Jmol^-1K^-1, M = mass of water in kg = 18X10^-3 kg

Answer 2

Total mass: m = 12 kg

Step-by-step explanation:

Given:

a = 18 m

b = 9 m

c = 6 m

t = 25°C

φ = 54%

__________

m - ?

The volume of the apartment:

V = a·b·c = 18·9·6 = 972 m³

From the table of saturated water vapor we obtain the density:

ρ₀ = 23.0 g/m³

Air humidity formula:

φ = ρ·100% / ρ₀

Water vapor density:

ρ = φ·ρ₀ / 100% = 54% · 23.0 / 100% ≈ 12.42 g/m³

Total mass:

m = ρ·V = 12.42·972 ≈ 12 070 g or m ≈ 12 kg