Question

Determine the density, specific gravity, and mass of the air in a room whose dimensions are 4m × 5m × 6m at 100 kPa and 25° C.

(a) 1.16 kg/m^3, 0.00116, 140 kg

(b) 1.17 kg/m^3, 0.00117, 140 kg

(c) 1.15 kg/m^3, 0.00115, 140 kg

(d) 1.14 kg/m^3, 0.00114, 140 kg

This question was addressed to me in semester exam.

My doubt is from Basic Energy Concepts topic in portion Energy Balance of Bioprocess Engineering

Answer 1

Correct choice is (b) 1.17 kg/m^3, 0.00117, 140 kg

To elaborate: At specified conditions, air can be treated as ideal gas.

The gas constant of air is R = 0.287 k Pa-m^3/Kg K

The density of the air is determined from the ideal-gas relation, P = ρ R T to be

ρ = P/RT = (100 kPa)/((0.287 k Pa-m^3/Kg K) (25+273.15)K) = 1.17 kg/ m^3

Then the specific gravity of the air becomes

SG = (ρ)/ρH2O = (1.17 kg/m^3)/(1000 kg/m^3) = 0.00117

Finally, the volume and mass of the air in the room are

V = (4m) (5m) (6m) = 120 m^3

m = ρV = (1.17 kg/m^3) (120 m^3) = 140 kg.